types of hypothesis in machine learning

• Comprehensive Learning Paths
• 150+ Hours of Videos
• Complete Access to Jupyter notebooks, Datasets, References.

Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference

• September 21, 2023

Explore the intricacies of hypothesis testing, a cornerstone of statistical analysis. Dive into methods, interpretations, and applications for making data-driven decisions.

In this Blog post we will learn:

• What is Hypothesis Testing?
• Steps in Hypothesis Testing 2.1. Set up Hypotheses: Null and Alternative 2.2. Choose a Significance Level (α) 2.3. Calculate a test statistic and P-Value 2.4. Make a Decision
• Example : Testing a new drug.
• Example in python

1. What is Hypothesis Testing?

In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it’s biased. By rolling it a few times and analyzing the outcomes, you’d be engaging in the essence of hypothesis testing.

Think of hypothesis testing as the scientific method of the statistics world. Suppose you hear claims like “This new drug works wonders!” or “Our new website design boosts sales.” How do you know if these statements hold water? Enter hypothesis testing.

2. Steps in Hypothesis Testing

• Set up Hypotheses : Begin with a null hypothesis (H0) and an alternative hypothesis (Ha).
• Choose a Significance Level (α) : Typically 0.05, this is the probability of rejecting the null hypothesis when it’s actually true. Think of it as the chance of accusing an innocent person.
• Calculate Test statistic and P-Value : Gather evidence (data) and calculate a test statistic.
• p-value : This is the probability of observing the data, given that the null hypothesis is true. A small p-value (typically ≤ 0.05) suggests the data is inconsistent with the null hypothesis.
• Decision Rule : If the p-value is less than or equal to α, you reject the null hypothesis in favor of the alternative.

2.1. Set up Hypotheses: Null and Alternative

Before diving into testing, we must formulate hypotheses. The null hypothesis (H0) represents the default assumption, while the alternative hypothesis (H1) challenges it.

For instance, in drug testing, H0 : “The new drug is no better than the existing one,” H1 : “The new drug is superior .”

2.2. Choose a Significance Level (α)

When You collect and analyze data to test H0 and H1 hypotheses. Based on your analysis, you decide whether to reject the null hypothesis in favor of the alternative, or fail to reject / Accept the null hypothesis.

The significance level, often denoted by $α$, represents the probability of rejecting the null hypothesis when it is actually true.

In other words, it’s the risk you’re willing to take of making a Type I error (false positive).

Type I Error (False Positive) :

• Symbolized by the Greek letter alpha (α).
• Occurs when you incorrectly reject a true null hypothesis . In other words, you conclude that there is an effect or difference when, in reality, there isn’t.
• The probability of making a Type I error is denoted by the significance level of a test. Commonly, tests are conducted at the 0.05 significance level , which means there’s a 5% chance of making a Type I error .
• Commonly used significance levels are 0.01, 0.05, and 0.10, but the choice depends on the context of the study and the level of risk one is willing to accept.

Example : If a drug is not effective (truth), but a clinical trial incorrectly concludes that it is effective (based on the sample data), then a Type I error has occurred.

Type II Error (False Negative) :

• Symbolized by the Greek letter beta (β).
• Occurs when you accept a false null hypothesis . This means you conclude there is no effect or difference when, in reality, there is.
• The probability of making a Type II error is denoted by β. The power of a test (1 – β) represents the probability of correctly rejecting a false null hypothesis.

Example : If a drug is effective (truth), but a clinical trial incorrectly concludes that it is not effective (based on the sample data), then a Type II error has occurred.

Balancing the Errors :

In practice, there’s a trade-off between Type I and Type II errors. Reducing the risk of one typically increases the risk of the other. For example, if you want to decrease the probability of a Type I error (by setting a lower significance level), you might increase the probability of a Type II error unless you compensate by collecting more data or making other adjustments.

It’s essential to understand the consequences of both types of errors in any given context. In some situations, a Type I error might be more severe, while in others, a Type II error might be of greater concern. This understanding guides researchers in designing their experiments and choosing appropriate significance levels.

2.3. Calculate a test statistic and P-Value

Test statistic : A test statistic is a single number that helps us understand how far our sample data is from what we’d expect under a null hypothesis (a basic assumption we’re trying to test against). Generally, the larger the test statistic, the more evidence we have against our null hypothesis. It helps us decide whether the differences we observe in our data are due to random chance or if there’s an actual effect.

P-value : The P-value tells us how likely we would get our observed results (or something more extreme) if the null hypothesis were true. It’s a value between 0 and 1. – A smaller P-value (typically below 0.05) means that the observation is rare under the null hypothesis, so we might reject the null hypothesis. – A larger P-value suggests that what we observed could easily happen by random chance, so we might not reject the null hypothesis.

2.4. Make a Decision

Relationship between $α$ and P-Value

When conducting a hypothesis test:

We then calculate the p-value from our sample data and the test statistic.

Finally, we compare the p-value to our chosen $α$:

• If $p−value≤α$: We reject the null hypothesis in favor of the alternative hypothesis. The result is said to be statistically significant.
• If $p−value>α$: We fail to reject the null hypothesis. There isn’t enough statistical evidence to support the alternative hypothesis.

3. Example : Testing a new drug.

Imagine we are investigating whether a new drug is effective at treating headaches faster than drug B.

Setting Up the Experiment : You gather 100 people who suffer from headaches. Half of them (50 people) are given the new drug (let’s call this the ‘Drug Group’), and the other half are given a sugar pill, which doesn’t contain any medication.

• Set up Hypotheses : Before starting, you make a prediction:
• Null Hypothesis (H0): The new drug has no effect. Any difference in healing time between the two groups is just due to random chance.
• Alternative Hypothesis (H1): The new drug does have an effect. The difference in healing time between the two groups is significant and not just by chance.

Calculate Test statistic and P-Value : After the experiment, you analyze the data. The “test statistic” is a number that helps you understand the difference between the two groups in terms of standard units.

For instance, let’s say:

• The average healing time in the Drug Group is 2 hours.
• The average healing time in the Placebo Group is 3 hours.

The test statistic helps you understand how significant this 1-hour difference is. If the groups are large and the spread of healing times in each group is small, then this difference might be significant. But if there’s a huge variation in healing times, the 1-hour difference might not be so special.

Imagine the P-value as answering this question: “If the new drug had NO real effect, what’s the probability that I’d see a difference as extreme (or more extreme) as the one I found, just by random chance?”

For instance:

• P-value of 0.01 means there’s a 1% chance that the observed difference (or a more extreme difference) would occur if the drug had no effect. That’s pretty rare, so we might consider the drug effective.
• P-value of 0.5 means there’s a 50% chance you’d see this difference just by chance. That’s pretty high, so we might not be convinced the drug is doing much.
• If the P-value is less than ($α$) 0.05: the results are “statistically significant,” and they might reject the null hypothesis , believing the new drug has an effect.
• If the P-value is greater than ($α$) 0.05: the results are not statistically significant, and they don’t reject the null hypothesis , remaining unsure if the drug has a genuine effect.

4. Example in python

For simplicity, let’s say we’re using a t-test (common for comparing means). Let’s dive into Python:

Making a Decision : “The results are statistically significant! p-value < 0.05 , The drug seems to have an effect!” If not, we’d say, “Looks like the drug isn’t as miraculous as we thought.”

5. Conclusion

Hypothesis testing is an indispensable tool in data science, allowing us to make data-driven decisions with confidence. By understanding its principles, conducting tests properly, and considering real-world applications, you can harness the power of hypothesis testing to unlock valuable insights from your data.

More Articles

F statistic formula – explained, correlation – connecting the dots, the role of correlation in data analysis, sampling and sampling distributions – a comprehensive guide on sampling and sampling distributions, law of large numbers – a deep dive into the world of statistics, central limit theorem – a deep dive into central limit theorem and its significance in statistics, similar articles, complete introduction to linear regression in r, how to implement common statistical significance tests and find the p value, logistic regression – a complete tutorial with examples in r.

Subscribe to Machine Learning Plus for high value data science content

© Machinelearningplus. All rights reserved.

Machine Learning A-Z™: Hands-On Python & R In Data Science

Free sample videos:.

Machine Learning

Artificial Intelligence

Control System

Supervised Learning

Classification, miscellaneous, related tutorials.

Interview Questions

• Send your Feedback to [email protected]

Help Others, Please Share

Learn Latest Tutorials

Transact-SQL

Reinforcement Learning

R Programming

React Native

Python Design Patterns

Python Pillow

Python Turtle

Preparation

Verbal Ability

Company Questions

Trending Technologies

Cloud Computing

Data Science

B.Tech / MCA

Data Structures

Operating System

Computer Network

Compiler Design

Computer Organization

Discrete Mathematics

Ethical Hacking

Computer Graphics

Software Engineering

Web Technology

Cyber Security

C Programming

Data Mining

Data Warehouse

Evaluating Hypotheses in Machine Learning: A Comprehensive Guide

Learn how to evaluate hypotheses in machine learning, including types of hypotheses, evaluation metrics, and common pitfalls to avoid. Improve your ML model's performance with this in-depth guide.

Create an image featuring JavaScript code snippets and interview-related icons or graphics. Use a color scheme of yellows and blues. Include the title '7 Essential JavaScript Interview Questions for Freshers'.

Introduction

Machine learning is a crucial aspect of artificial intelligence that enables machines to learn from data and make predictions or decisions. The process of machine learning involves training a model on a dataset, and then using that model to make predictions on new, unseen data. However, before deploying a machine learning model, it is essential to evaluate its performance to ensure that it is accurate and reliable. One crucial step in this evaluation process is hypothesis testing.

In this blog post, we will delve into the world of hypothesis testing in machine learning, exploring what hypotheses are, why they are essential, and how to evaluate them. We will also discuss the different types of hypotheses, common pitfalls to avoid, and best practices for hypothesis testing.

What are Hypotheses in Machine Learning?

In machine learning, a hypothesis is a statement that proposes a possible explanation for a phenomenon or a problem. It is a conjecture that is made about a population parameter, and it is used as a basis for further investigation. In the context of machine learning, hypotheses are used to define the problem that we are trying to solve.

For example, let's say we are building a machine learning model to predict the prices of houses based on their features, such as the number of bedrooms, square footage, and location. A possible hypothesis could be: "The price of a house is directly proportional to its square footage." This hypothesis proposes a possible relationship between the price of a house and its square footage.

Why are Hypotheses Essential in Machine Learning?

Hypotheses are essential in machine learning because they provide a framework for understanding the problem that we are trying to solve. They help us to identify the key variables that are relevant to the problem, and they provide a basis for evaluating the performance of our machine learning model.

Without a clear hypothesis, it is difficult to develop an effective machine learning model. A hypothesis helps us to:

• Identify the key variables that are relevant to the problem
• Develop a clear understanding of the problem that we are trying to solve
• Evaluate the performance of our machine learning model
• Refine our model and improve its accuracy

Types of Hypotheses in Machine Learning

There are two main types of hypotheses in machine learning: null hypotheses and alternative hypotheses.

Null Hypothesis

A null hypothesis is a hypothesis that proposes that there is no significant difference or relationship between variables. It is a hypothesis of no effect or no difference. For example, let's say we are building a machine learning model to predict the prices of houses based on their features. A null hypothesis could be: "There is no significant relationship between the price of a house and its square footage."

Alternative Hypothesis

An alternative hypothesis is a hypothesis that proposes that there is a significant difference or relationship between variables. It is a hypothesis of an effect or a difference. For example, let's say we are building a machine learning model to predict the prices of houses based on their features. An alternative hypothesis could be: "There is a significant positive relationship between the price of a house and its square footage."

Evaluating Hypotheses in Machine Learning

Evaluating hypotheses in machine learning involves testing the null hypothesis against the alternative hypothesis. This is typically done using statistical methods, such as t-tests, ANOVA, and regression analysis.

Here are the general steps involved in evaluating hypotheses in machine learning:

• Formulate the null and alternative hypotheses : Clearly define the null and alternative hypotheses that you want to test.
• Collect and prepare the data : Collect the data that you will use to test the hypotheses. Ensure that the data is clean, relevant, and representative of the population.
• Choose a statistical method : Select a suitable statistical method to test the hypotheses. This could be a t-test, ANOVA, regression analysis, or another method.
• Test the hypotheses : Use the chosen statistical method to test the null hypothesis against the alternative hypothesis.
• Interpret the results : Interpret the results of the hypothesis test. If the null hypothesis is rejected, it suggests that there is a significant relationship between the variables. If the null hypothesis is not rejected, it suggests that there is no significant relationship between the variables.

Common Pitfalls to Avoid in Hypothesis Testing

Here are some common pitfalls to avoid in hypothesis testing:

• Overfitting : Overfitting occurs when a model is too complex and performs well on the training data but poorly on new, unseen data. To avoid overfitting, use techniques such as regularization, early stopping, and cross-validation.
• Underfitting : Underfitting occurs when a model is too simple and fails to capture the underlying patterns in the data. To avoid underfitting, use techniques such as feature engineering, hyperparameter tuning, and model selection.
• Data leakage : Data leakage occurs when the model is trained on data that it will also be tested on. To avoid data leakage, use techniques such as cross-validation and walk-forward optimization.
• P-hacking : P-hacking occurs when a researcher selectively reports the results of multiple hypothesis tests to find a significant result. To avoid p-hacking, use techniques such as preregistration and replication.

Best Practices for Hypothesis Testing in Machine Learning

Here are some best practices for hypothesis testing in machine learning:

• Clearly define the hypotheses : Clearly define the null and alternative hypotheses that you want to test.
• Use a suitable statistical method : Choose a suitable statistical method to test the hypotheses.
• Use cross-validation : Use cross-validation to evaluate the performance of the model on unseen data.
• Avoid overfitting and underfitting : Use techniques such as regularization, early stopping, and feature engineering to avoid overfitting and underfitting.
• Document the results : Document the results of the hypothesis test, including the statistical method used, the results, and any conclusions drawn.

Evaluating hypotheses is a crucial step in machine learning that helps us to understand the problem that we are trying to solve and to evaluate the performance of our machine learning model. By following the best practices outlined in this blog post, you can ensure that your hypothesis testing is rigorous, reliable, and effective.

Remember to clearly define the null and alternative hypotheses, choose a suitable statistical method, and avoid common pitfalls such as overfitting, underfitting, data leakage, and p-hacking. By doing so, you can develop machine learning models that are accurate, reliable, and effective.

• [1] James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning: With Applications in R. Springer.
• [2] Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
• [3] Han, J., Pei, J., & Kamber, M. (2012). Data Mining: Concepts and Techniques. Morgan Kaufmann.

I hope this helps! Let me know if you need any further assistance.

Best Guesses: Understanding The Hypothesis in Machine Learning

• February 22, 2024
• General , Supervised Learning , Unsupervised Learning

Machine learning is a vast and complex field that has inherited many terms from other places all over the mathematical domain.

It can sometimes be challenging to get your head around all the different terminologies, never mind trying to understand how everything comes together.

In this blog post, we will focus on one particular concept: the hypothesis.

While you may think this is simple, there is a little caveat regarding machine learning.

The statistics side and the learning side.

Don’t worry; we’ll do a full breakdown below.

You’ll learn the following:

What Is a Hypothesis in Machine Learning?

• Is This any different than the hypothesis in statistics?
• What is the difference between the alternative hypothesis and the null?
• Why do we restrict hypothesis space in artificial intelligence?
• Example code performing hypothesis testing in machine learning

In machine learning, the term ‘hypothesis’ can refer to two things.

First, it can refer to the hypothesis space, the set of all possible training examples that could be used to predict or answer a new instance.

Second, it can refer to the traditional null and alternative hypotheses from statistics.

Since machine learning works so closely with statistics, 90% of the time, when someone is referencing the hypothesis, they’re referencing hypothesis tests from statistics.

Is This Any Different Than The Hypothesis In Statistics?

In statistics, the hypothesis is an assumption made about a population parameter.

The statistician’s goal is to prove it true or disprove it.

This will take the form of two different hypotheses, one called the null, and one called the alternative.

Usually, you’ll establish your null hypothesis as an assumption that it equals some value.

For example, in Welch’s T-Test Of Unequal Variance, our null hypothesis is that the two means we are testing (population parameter) are equal.

This means our null hypothesis is that the two population means are the same.

We run our statistical tests, and if our p-value is significant (very low), we reject the null hypothesis.

This would mean that their population means are unequal for the two samples you are testing.

Usually, statisticians will use the significance level of .05 (a 5% risk of being wrong) when deciding what to use as the p-value cut-off.

What Is The Difference Between The Alternative Hypothesis And The Null?

The null hypothesis is our default assumption, which we are trying to prove correct.

The alternate hypothesis is usually the opposite of our null and is much broader in scope.

For most statistical tests, the null and alternative hypotheses are already defined.

You are then just trying to find “significant” evidence we can use to reject our null hypothesis.

These two hypotheses are easy to spot by their specific notation. The null hypothesis is usually denoted by H₀, while H₁ denotes the alternative hypothesis.

Example Code Performing Hypothesis Testing In Machine Learning

Since there are many different hypothesis tests in machine learning and data science, we will focus on one of my favorites.

This test is Welch’s T-Test Of Unequal Variance, where we are trying to determine if the population means of these two samples are different.

There are a couple of assumptions for this test, but we will ignore those for now and show the code.

You can read more about this here in our other post, Welch’s T-Test of Unequal Variance .

We see that our p-value is very low, and we reject the null hypothesis.

What Is The Difference Between The Biased And Unbiased Hypothesis Spaces?

The difference between the Biased and Unbiased hypothesis space is the number of possible training examples your algorithm has to predict.

The unbiased space has all of them, and the biased space only has the training examples you’ve supplied.

Since neither of these is optimal (one is too small, one is much too big), your algorithm creates generalized rules (inductive learning) to be able to handle examples it hasn’t seen before.

Here’s an example of each:

Example of The Biased Hypothesis Space In Machine Learning

The Biased Hypothesis space in machine learning is a biased subspace where your algorithm does not consider all training examples to make predictions.

This is easiest to see with an example.

Let’s say you have the following data:

Happy  and  Sunny  and  Stomach Full  = True

Whenever your algorithm sees those three together in the biased hypothesis space, it’ll automatically default to true.

This means when your algorithm sees:

Sad  and  Sunny  And  Stomach Full  = False

It’ll automatically default to False since it didn’t appear in our subspace.

This is a greedy approach, but it has some practical applications.

Example of the Unbiased Hypothesis Space In Machine Learning

The unbiased hypothesis space is a space where all combinations are stored.

We can use re-use our example above:

This would start to breakdown as

Happy  = True

Happy  and  Sunny  = True

Happy  and  Stomach Full  = True

Let’s say you have four options for each of the three choices.

This would mean our subspace would need 2^12 instances (4096) just for our little three-word problem.

This is practically impossible; the space would become huge.

So while it would be highly accurate, this has no scalability.

More reading on this idea can be found in our post, Inductive Bias In Machine Learning .

Why Do We Restrict Hypothesis Space In Artificial Intelligence?

We have to restrict the hypothesis space in machine learning. Without any restrictions, our domain becomes much too large, and we lose any form of scalability.

This is why our algorithm creates rules to handle examples that are seen in production. 

This gives our algorithms a generalized approach that will be able to handle all new examples that are in the same format.

Other Quick Machine Learning Tutorials

At EML, we have a ton of cool data science tutorials that break things down so anyone can understand them.

Below we’ve listed a few that are similar to this guide:

• Instance-Based Learning in Machine Learning
• Types of Data For Machine Learning
• Verbose in Machine Learning
• Generalization In Machine Learning
• Epoch In Machine Learning
• Inductive Bias in Machine Learning
• Understanding The Hypothesis In Machine Learning
• Zip Codes In Machine Learning
• get_dummies() in Machine Learning
• Bootstrapping In Machine Learning
• X and Y in Machine Learning
• F1 Score in Machine Learning
• Recent Posts

• Exploring How the Government Can Use Open Source Software [Unlock the Possibilities] - August 19, 2024
• The Power of Software Testing for Organizations [Boost Your Success Now!] - August 19, 2024
• What do software account executives make? [Unlock Your Earning Potential Now] - August 19, 2024

• What is hypothesis testing?
• Edit on GitHub

Hypothesis Testing 

Statistical inference is the process of learning about characteristics of a population based on what is observed in a relatively small sample from that population. A sample will never give us the entire picture though, and we are bound to make incorrect decisions from time to time.

We will learn how to derive and interpret appropriate tests to manage this error and how to evaluate when one test is better than another. we will learn how to construct and perform principled hypothesis tests for a wide range of problems and applications when they are not.

What is Hypothesis 

Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

Due to random samples and randomness in the problem, we can different errors in our hypothesis testing. These errors are called Type I and Type II errors.

Type of hypothesis testing 

Let \(X_1, X_2, \ldots, X_n\) be a random sample from the normal distribution with mean \(\mu\) and variance \(\sigma^2\)

Example of random sample after it is observed:

Based on what you are seeing, do you believe that the true population mean \(\mu\) is

This is below 3 , but can we say that \(\mu<3\) ?

This seems awfully dependent on the random sample we happened to get! Let’s try to work with the most generic random sample of size 8:

Let \(\mathrm{X}_1, \mathrm{X}_2, \ldots, \mathrm{X}_{\mathrm{n}}\) be a random sample of size \(\mathrm{n}\) from the \(\mathrm{N}\left(\mu, \sigma^2\right)\) distribution.

The Sample mean is

We’re going to tend to think that \(\mu<3\) when \(\bar{X}\) is “significantly” smaller than 3.

We’re going to tend to think that \(\mu>3\) when \(\bar{X}\) is “significantly” larger than 3.

We’re never going to observe \(\bar{X}=3\) , but we may be able to be convinced that \(\mu=3\) if \(\bar{X}\) is not too far away.

How do we formalize this stuff, We use hypothesis testing

\(\mathrm{H}_0: \mu \leq 3\) <- Null hypothesis \(\mathrm{H}_1: \mu>3 \quad\) Alternate hypothesis

Null hypothesis 

The null hypothesis is a hypothesis that is assumed to be true. We denote it with an \(H_0\) .

Alternate hypothesis 

The alternate hypothesis is what we are out to show. The alternative hypothesis is a hypothesis that we are looking for evidence for or out to show . We denote it with an \(H_1\) .

Some people use the notation \(H_a\) here

Conclusion is either : Reject \(\mathrm{H}_0 \quad\) OR \(\quad\) Fail to Reject \(\mathrm{H}_0\)

simple hypothesis 

A simple hypothesis is one that completely specifies the distribution. Do you know the exact distribution.

composite hypothesis 

You don’t know the exact distribution. Means you know the distribution is normal but you don’t know the mean and variance.

Critical values 

Critical values for distributions are numbers that cut off specified areas under pdfs. For the N(0, 1) distribution, we will use the notation \(z_\alpha\) to denote the value that cuts off area \(\alpha\) to the right as depicted here.

Errors in Hypothesis Testing 

Let \(X_1, X_2, \ldots, X_n\) be a random sample from the normal distribution with mean \(\mu\) and variance \(\sigma^2=2\)

Idea : Look at \(\bar{X}\) and reject \(H_0\) in favor of \(H _1\) if \(\overline{ X }\) is “large”. i.e. Look at \(\bar{X}\) and reject \(H_0\) in favor of \(H _1\) if \(\overline{ X }> c\) for some value \(c\) .

You are a potato chip manufacturer and you want to ensure that the mean amount in 15 ounce bags is at least 15 ounces. \(\mathrm{H}_0: \mu \leq 15 \quad \mathrm{H}_1: \mu>15\)

Type I Error 

The true mean is \(\leq 15\) but you concluded i was \(>15\) . You are going to save some money because you won’t be adding chips but you are risking a lawsuit!

Type II Error 

The true mean is \(> 15\) but you concluded it was \(\leq 15\) . You are going to be spending money increasing the amount of chips when you didn’t have to.

Developing a Test 

Let \(X_1, X_2, \ldots, X_n\) be a random sample from the normal distribution with mean \(\mu\) and known variance \(\sigma^2\) .

Consider testing the simple versus simple hypotheses

level of significance 

Let \(\alpha= P\) (Type I Error) \(= P \left(\right.\) Reject \(H _0\) when it’s true \()\) \(= P \left(\right.\) Reject \(H _0\) when \(\left.\mu=5\right)\)

\(\alpha\) is called the level of significance of the test. It is also sometimes referred to as the size of the test.

Power of the test 

\(1-\beta\) is known as the power of the test

Choose an estimator for μ.

Choose a test statistic or Give the “form” of the test.

We are looking for evidence that \(H _1\) is true.

The \(N \left(3, \sigma^2\right)\) distribution takes on values from \(-\infty\) to \(\infty\) .

\(\overline{ X } \sim N \left(\mu, \sigma^2 / n \right) \Rightarrow \overline{ X }\) also takes on values from \(-\infty\) to \(\infty\) .

It is entirely possible that \(\bar{X}\) is very large even if the mean of its distribution is 3.

However, if \(\bar{X}\) is very large, it will start to seem more likely that \(\mu\) is larger than 3.

Eventually, a population mean of 5 will seem more likely than a population mean of 3.

Reject \(H _0\) , in favor of \(H _1\) , if \(\overline{ X }< c\) for some c to be determined.

Step Three 

If \(c\) is too large, we are making it difficult to reject \(H _0\) . We are more likely to fail to reject when it should be rejected.

If \(c\) is too small, we are making it to easy to reject \(H _0\) . We are more likely reject when it should not be rejected.

This is where \(\alpha\) comes in.

Step Four 

Give a conclusion!

\(0.05= P (\) Type I Error) \(= P \left(\right.\) Reject \(H _0\) when true \()\) \(= P (\overline{ X }< \text{ c when } \mu=5)\)

\( = P \left(\frac{\overline{ X }-\mu_0}{\sigma / \sqrt{ n }}<\frac{ c -5}{2 / \sqrt{10}}\right.\) when \(\left.\mu=5\right)\)

where \(\mu_0\) and \(\mu_1\) are fixed and known.

Composite vs Composite Hypothesis 

Step One Choose an estimator for μ

Step Two Choose a test statistic: Reject \(H_0\) , in favor of \(H_1\) if \(\bar{𝖷}\) > c, where c is to be determined.

Step Three Find c.

One-Tailed Tests 

Let \(X_1, X_2, \ldots, X_n\) be a random sample from the normal distribution with mean \(\mu\) and known variance \(\sigma^2\) . Consider testing the hypotheses

where \(\mu_0\) is fixed and known.

Step four 

Reject \(H _0\) , in favor of \(H _1\) , if $ \( \overline{ X }<\mu_0+ z _{1-\alpha} \frac{\sigma}{\sqrt{ n }} \) $

In 2019, the average health care annual premium for a family of 4 in the United States, was reported to be \(\$ 6,015\) .

In a more recent survey, 100 randomly sampled families of 4 reported an average annual health care premium of \(\$ 6,537\) . Can we say that the true average is currently greater than \(\$ 6,015\) for all families of 4?

Assume that annual health care premiums are normally distributed with a standard deviation of \(\$ 814\) . Let \(\mu\) be the true average for all families of 4.

Step Zero 

Set up the hypotheses.

Decide on a level of significance. \( \alpha=0.10\)

Choose an estimator for \(\mu\) .

Give the form of the test. Reject \(H _0\) , in favor of \(H _1\) , if

for some \(c\) to be determined.

Conclusion. Reject \(H _0\) , in favor of \(H _1\) , if

From the data, where \(\bar{x}=6537\) , we reject \(H _0\) in favor of \(H _1\) . The data suggests that the true mean annual health care premium is greater than \(\$ 6015\) .

Hypothesis Testing with P-Values 

Recall that p-values are defined as the following: A p-value is the probability that we observe a test statistic at least as extreme as the one we calculated, assuming the null hypothesis is true. It isn’t immediately obvious what that definition means, so let’s look at some examples to really get an idea of what p-values are, and how they work.

Let’s start very simple and say we have 5 data points: x = <1, 2, 3, 4, 5>. Let’s also assume the data were generated from some normal distribution with a known variance \(\sigma\) but an unknown mean \(\mu_0\) . What would be a good guess for the true mean? We know that this data could come from any normal distribution, so let’s make two wild guesses:

The true mean is 100.

The true mean is 3.

Intuitively, we know that 3 is the better guess. But how do we actually determine which of these guesses is more likely? By looking at the data and asking “how likely was the data to occur, assuming the guess is true?”

What is the probability that we observed x=<1,2,3,4,5> assuming the mean is 100? Probabiliy pretty low. And because the p-value is low, we “reject the null hypothesis” that \(\mu_0 = 100\) .

What is the probability that we observed x=<1,2,3,4,5> assuming the mean is 3? Seems reasonable. However, something to be careful of is that p-values do not prove anything. Just because it is probable for the true mean to be 3, does not mean we know the true mean is 3. If we have a high p-value, we “fail to reject the null hypothesis” that \(\mu_0 = 3\) .

What do “low” and “high” mean? That is where your significance level \(\alpha\) comes back into play. We consider a p-value low if the p-value is less than \(\alpha\) , and high if it is greater than \(\alpha\) .

From the above example.

This is the \(N\left(6015,814^2 / 100\right)\) pdf.

The red area is \(P (\overline{ X }>6537)\) .

The P-Value is the area to the right (in this case) of the test statistic \(\bar{X}\) .

The P-value being less than \(0.10\) puts \(\bar{X}\) in the rejection region.

The P-value is also less than \(0.05\) and \(0.01\) .

It looks like we will reject \(H _0\) for the most typical values of \(\alpha\) .

Power Functions 

Let \(X_1, X_2, \ldots, X_n\) be a random sample from any distribution with unknown parameter \(\theta\) which takes values in a parameter space \(\Theta\)

We ultimately want to test

where \(\Theta_0\) is some subset of \(\Theta\) .

So in other words, if the null hypothesis was for you to test for an exponential distribution, whether lambda was between 0 and 2, the complement of that is not the rest of the real number line because the space is only non-negative values. So the complement of the interval from 0 to 2 in that space is 2 to infinity.

\(\gamma(\theta)= P \left(\right.\) Reject \(H _0\) when the parameter is \(\left.\theta\right)\)

\(\theta\) is an argument that can be anywhere in the parameter space \(\Theta\) . it could be a \(\theta\) from \(H _0\) it could be a \(\theta\) from \(H _1\)

Two Tailed Tests 

Derive a hypothesis test of size \(\alpha\) for testing

We will look at the sample mean \(\bar{X} \ldots\) \(\ldots\) and reject if it is either too high or too low.

Reject \(H _0\) , in favor of \(H _1\) if either \(\overline{ X }< c\) or \(\bar{X}>d\) for some \(c\) and \(d\) to be determined.

Easier to make it symmetric! Reject \(H _0\) , in favor of \(H _1\) if either

Reject \(H _0\) , in favor of \(H _1\) , if

In a more recent survey, 100 randomly sampled families of 4 reported an average annual health care premium of \(\$ 6,177\) . Can we say that the true average, for all families of 4 , is currently different than the sample mean from 2019? $ \( \sigma=814 \quad \text { Use } \alpha=0.05 \) $

Assume that annual health care premiums are normally distributed with a standard deviation of \(\$ 814\) . Let \(\mu\) be the true average for all families of 4. Hypotheses:

We reject \(H _0\) , in favor of \(H _1\) . The data suggests that the true current average, for all families of 4 , is different than it was in 2019.

Hypothesis Tests for Proportions 

A random sample of 500 people in a certain country which is about to have a national election were asked whether they preferred “Candidate A” or “Candidate B”. From this sample, 320 people responded that they preferred Candidate A.

Let \(p\) be the true proportion of the people in the country who prefer Candidate A.

Test the hypotheses \(H _0: p \leq 0.65\) versus \(H _1: p>0.65\) Use level of significance \(0.10\) . We have an estimate

The Model 

Take a random sample of size \(n\) . Record \(X_1, X_2, \ldots, X_n\) where \(X_i= \begin{cases}1 & \text { person i likes Candidate A } \\ 0 & \text { person i likes Candidate B }\end{cases}\) Then \(X_1, X_2, \ldots, X_n\) is a random sample from the Bernoulli distribution with parameter \(p\) .

Note that, with these 1’s and 0’s, $ \( \begin{aligned} \hat{p} &=\frac{\# \text { in the sample who like A }}{\# \text { in the sample }} \\ &=\frac{\sum_{ i =1}^{ n } X _{ i }}{ n }=\overline{ X } \end{aligned} \) \( By the Central Limit Theorem, \) \hat{p}=\overline{ X }$ has, for large samples, an approximately normal distribution.

So, \(\quad \hat{p} \stackrel{\text { approx }}{\sim} N\left(p, \frac{p(1-p)}{n}\right)\)

In particular, $ \( \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \) \( behaves roughly like a \) N(0,1) \( as \) n$ gets large.

\(n >30\) is a rule of thumb to apply to all distributions, but we can (and should!) do better with specific distributions.

\(\hat{p}\) lives between 0 and 1.

The normal distribution lives between \(-\infty\) and \(\infty\) .

However, \(99.7 \%\) of the area under a \(N(0,1)\) curve lies between \(-3\) and 3 ,

Go forward using normality if the interval $ \( \left(\hat{p}-3 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+3 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right) \) \( is completely contained within \) [0,1]$.

Choose a statistic. \(\widehat{p}=\) sample proportion for Candidate \(A\)

Form of the test. Reject \(H _0\) , in favor of \(H _1\) , if \(\hat{ p }> c\) .

Use \(\alpha\) to find \(c\) Assume normality of \(\hat{p}\) ? It is a sample mean and \(n>30\) .

The interval $ \( \left(\hat{p}-3 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+3 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right) \) \( is \) (0.5756,0.7044)$

Reject \(H _0\) if

What is a t-test, and when do we use it? A t-test is used to compare the means of one or two samples, when the underlying population parameters of those samples (mean and standard deviation) are unknown. Like a z-test, the t-test assumes that the sample follows a normal distribution. In particular, this test is useful for when we have a small sample size, as we can not use the Central Limit Theorem to use a z-test.

There are two kinds of t-tests:

One Sample t-tests

Two Sample t-tests

Let \(X_1, X_2, \ldots, X_n\) be a random sample from the normal distribution with mean \(\mu\) and unknown variance \(\sigma^2\) .

Consider testing the simple versus simple hypotheses $ \( H _0: \mu=\mu_0 \quad H _1: \mu<\mu_0 \) \( where \) \mu_0$ is fixed and known.

unknown!This is a useless test!

It was based on the fact that

What is we use the sample standard deviation \(S =\sqrt{ S ^2}\) in place of \(\sigma\) ?

Conclusion! Reject \(H _0\) , in favor of \(H _1\) , if

In a more recent survey, 15 randomly sampled families of 4 reported an average annual health care premium of \(\$ 6,033\) and a sample variance of \(\$ 825\) .

Can we say that the true average is currently greater than \(\$ 6,015\) for all families of 4 ?

Use \(\alpha=0.10\)

Assume that annual health care premiums are normally distributed. Let \(\mu\) be the true average for all families of 4.

Choose a test statistic

Give the form of the test. Reject 𝖧0 , in favor of h1, if 𝟢 𝖧𝟣 𝖷 > 𝖼 where c is to be determined.

Conclusion. Rejection Rule: Reject \(H _0\) , in favor of \(H _1\) if

We had \(\bar{x}=6033\) so we reject \(H_0\) .

There is sufficient evidence (at level \(0.10\) ) in the data to suggest that the true mean annual healthcare premium cost for a family of 4 is greater than \(\$ 6,015\) .

Two Sample Tests for Means 

Fifth grade students from two neighboring counties took a placement exam.

Group 1, from County 1, consisted of 57 students. The sample mean score for these students was \(7 7 . 2\) and the true variance is known to be 15.3. Group 2, from County 2, consisted of 63 students and had a sample mean score of \(75.3\) and the true variance is known to be 19.7.

From previous years of data, it is believed that the scores for both counties are normally distributed.

Derive a test to determine whether or not the two population means are the same.

Suppose that \(X _{1,1}, X _{1,2}, \ldots, X _{1, n _1}\) is a random sample of size \(n_1\) from the normal distribution with mean \(\mu_1\) and variance \(\sigma_1^2\) . Suppose that \(X_{2,1}, X_{2,2}, \ldots, X_{2, n_2}\) is a random sample of size \(n_2\) from the normal distribution with mean \(\mu_2\) and variance \(\sigma_2^2\) .

Suppose that \(\sigma_1^2\) and \(\sigma_2^2\) are known and that the samples are independent.

Think of this as $ \( \begin{gathered} \theta=0 \text { versus } \theta \neq 0 \\ \text { for } \\ \theta=\mu_1-\mu_2 \end{gathered} \) $

Choose an estimator for \(\theta=\mu_1-\mu_2\)

Give the “form” of the test. Reject \(H _0\) , in favor of \(H _1\) if either \(\hat{\theta}>c\) or \(\hat{\theta}<-c\) for some c to be determined.

Find \(c\) using \(\alpha\) Will be working with the random variable

We need to know its distribution…

Find c using \(\alpha\) .

\(\bar{X}_1-\bar{X}_2\) is normally distributed

Suppose that \(\alpha=0.05\) . $ \( \begin{aligned} & z _{\alpha / 2}= z _{0.025}=1.96 \\ & z _{\alpha / 2} \sqrt{\frac{\sigma_1^2}{ n _1}+\frac{\sigma_2^2}{ n _2}}=1.49 \end{aligned} \) $

and we reject \(H _0\) . The data suggests that the true mean scores for the counties are different!

Two Sample t-Tests for a Difference of Means 

Group 1, from County A, consisted of 8 students. The sample mean score for these students was \(77.2\) and the sample variance is \(15.3\) .

Group 2, from County B, consisted of 10 students and had a sample mean score of \(75.3\) and the sample variance is 19.7.

Pooled Variance 

Since \(\bar{x}_1-\bar{x}_2=1.9\) is not above \(5.840\) , or below \(-5.840\) we fail to reject \(H _0\) , in favor of \(H _1\) at \(0.01\) level of significance.

The data do not indicate that there is a significant difference between the true mean scores for counties \(A\) and \(B\) .

Welch’s Test and Paired Data 

Two Populations: Test

Suppose that \(X_{1,1}, X_{1,2}, \ldots, X_{1, n_1}\) is a random sample of size \(n_1\) from the normal distribution with mean \(\mu_1\) and variance \(\sigma_1^2\) .

Suppose that \(X_{2,1}, X_{2,2}, \ldots, X_{2, n}\) is a random sample of size \(n_2\) from the normal distribution with mean \(\mu_2\) and variance \(\sigma_2^2\) .

Suppose that \(\sigma_1^2\) and \(\sigma_2^2\) are unknown and that the samples are independent. Don’t assume that \(\sigma_1^2\) and \(\sigma_2^2\) are equal!

Welch says that:

has an approximate t-distribution with \(r\) degrees of freedom where

rounded down.

A random sample of 6 students’ grades were recorded for Midterm 1 and Midterm 2. Assuming exam scores are normally distributed, test whether the true (total population of students) average grade on Midterm 2 is greater than Midterm 1. α = 0.05

The Hypotheses: Let \(\mu\) be the true average difference for all students.

This is simply a one sample t-test on the differences.

3.5 > 4.6

Conclusion: We fail to reject h0 , in favor of h1 , at 0.05 level of significance.

These data do not indicate that Midterm 2 scores are higher than Midterm 1 scores

Comparing Two Population Proportions 

A random sample of 500 people in a certain county which is about to have a national election were asked whether they preferred “Candidate A” or “Candidate B”. From this sample, 320 people responded that they preferred Candidate A.

A random sample of 400 people in a second county which is about to have a national election were asked whether they preferred “Candidate A” or “Candidate B”.

From this second county sample, 268 people responded that they preferred Candidate \(A\) .

Estimate \(p_1-p_2\) with \(\hat{p}_1-\hat{p}_2\) For large enough samples,

Use estimators for p1 and p2 assuming they are the same.

Call the common value p.

Estimate by putting both groups together.

Two-tailed test with z-critical values…

qnorm(1-0.05/2)

\(Z=-0.9397\) does not fall in the rejection region!

Hypothesis Tests for the Exponential 

Suppose that \(X_1, X_2, \ldots, X_n\) is a random sample from the exponential distribution with rate \(\lambda>0\) . Derive a hypothesis test of size \(\alpha\) for

What statistic should we use?

Test 1: Using the Sample Mean 

Choose a statistic.

Give the form of the test Reject 𝖧0 , in favor of h1 , if 𝖷_bar < 𝖼

for some c to be determined.

\(\chi_{\alpha, n }^2\) In R, get \(\chi_{0.10,6}^2\)

by typing qchisq(0.90,6)

Best Test 

Ump tests .

Suppose that \(X_1, X_2, \ldots, X_n\) is a random sample from the exponential distribution with rate \(\lambda>0\) .

Derive a uniformly most powerful hypothesis test of size \(\alpha\) for

Consider the simple versus simple hypotheses

for some fixed \(\lambda_1>\lambda_0\) .

###Steps Two, Three, and Four

Find the best test of size \(\alpha\) for

for some fixed \(\lambda_1>\lambda_0\) . This test is to reject \(H _0\) , in favor of \(H _1\) if

Note that this test does not depend on the particular value of \(\lambda_1\) . -It does, however, depend on the fact that \(\lambda_1>\lambda_0\)

The “UMP” test for

is to reject \(H_0\) , in favor of \(H_1\) if

Test for the Variance of the Normal Distribution 

Suppose that \(X_1, X_2, \ldots, X_n\) is a random sample from the normal distribution with mean \(\mu\) and variance \(\sigma^2\) . Derive a test of size/level \(\alpha\) for

Choose a statistic/estimator for \(\sigma^2\)

Give the form of the test. Reject \(H_0\) , in favor of \(H_1\) , if

find c using alpha

A lawn care company has developed and wants to patent a new herbicide applicator spray nozzle. Example: For safety reasons, they need to ensure that the application is consistent and not highly variable. The company selected a random sample of 10 nozzles and measured the application rate of the herbicide in gallons per acre

The measurements were recorded as

\(0.213,0.185,0.207,0.163,0.179\) \(0.161,0.208,0.210,0.188,0.195\)

Assuming that the application rates are normally distributed, test the following hypotheses at level \(0.04\) .

Get sample variance in \(R\) .

Hit and then input numbers, one by one, hitting in between and <Enter \(>\) at the end.

Compute variance by typing

or \(\left(\left(\operatorname{sum}\left(x^{\wedge} 2\right)-\left(\operatorname{sum}(x)^{\wedge} 2\right) / 10\right) / 9\right.\) Result: \(0.000364\)

Reject \(H_0\) , in favor of \(H_1\) , if \(S^2>c\) .

Reject \(H _0\) , in favor of \(H _1\) , if \(S ^2> c\)

Reject \(H_0\) , in favor of \(H_1\) , if \(S^2>c\)

Fail to reject \(H _0\) , in favor of \(H _1\) , at level 0.04. There is not sufficient evidence in the data to suggest that \(\sigma^2>0.01\) .

• > Machine Learning
• > Statistics

What is Hypothesis Testing? Types and Methods

• Soumyaa Rawat
• Jul 23, 2021

Hypothesis Testing  

Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not. 

In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number. 

In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true. 

Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started! 

Types of Hypotheses

In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.

Alternative Hypothesis

Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing. 

It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence. 

When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.

Null Hypothesis

The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it. 

The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis. 

(Must read: What is ANOVA test? )

Non-Directional Hypothesis

The Non-directional hypothesis states that the relation between two variables has no direction. 

Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa. 

Directional Hypothesis

The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables. 

Herein, the hypothesis clearly states that variable A affects variable B, or vice versa. 

Statistical Hypothesis

A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics. 

By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not. 

(Related blog: z-test vs t-test )

Performing Hypothesis Testing  

Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner. 

In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure. 

To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test. 

A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful. 

At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%. 

(Read also: Types of data sampling techniques )

Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.

Establish the hypotheses

First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing. 

These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis. 

Generate a testing plan

Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size. 

All these factors are very important while one is working on hypothesis testing.

Analyze data samples

As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples. 

While analyzing the data samples, a researcher needs to determine a set of things -

Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.

Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples. 

Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.

P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis. 

Infer the results

The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible. 

Methods of Hypothesis Testing

As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -

Frequentist Hypothesis Testing

The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data. 

The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST). 

The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s. 

Bayesian Hypothesis Testing

A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis. 

The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand. 

On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis. 

The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.  

(Also read - Introduction to Bayesian Statistics ) 

To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach. 

Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing. 

(Also read: Introduction to probability distributions )

A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis. 

Share Blog :

Be a part of our Instagram community

Trending blogs

5 Factors Influencing Consumer Behavior

Elasticity of Demand and its Types

An Overview of Descriptive Analysis

What is PESTLE Analysis? Everything you need to know about it

What is Managerial Economics? Definition, Types, Nature, Principles, and Scope

5 Factors Affecting the Price Elasticity of Demand (PED)

6 Major Branches of Artificial Intelligence (AI)

Scope of Managerial Economics

Dijkstra’s Algorithm: The Shortest Path Algorithm

Different Types of Research Methods

Latest Comments

• Trending Categories

• Selected Reading
• UPSC IAS Exams Notes
• Developer's Best Practices
• Questions and Answers
• Effective Resume Writing
• HR Interview Questions
• Computer Glossary

What is hypothesis in Machine Learning?

The hypothesis is a word that is frequently used in Machine Learning and data science initiatives. As we all know, machine learning is one of the most powerful technologies in the world, allowing us to anticipate outcomes based on previous experiences. Moreover, data scientists and ML specialists undertake experiments with the goal of solving an issue. These ML experts and data scientists make an initial guess on how to solve the challenge.

What is a Hypothesis?

A hypothesis is a conjecture or proposed explanation that is based on insufficient facts or assumptions. It is only a conjecture based on certain known facts that have yet to be confirmed. A good hypothesis is tested and yields either true or erroneous outcomes.

Let's look at an example to better grasp the hypothesis. According to some scientists, ultraviolet (UV) light can harm the eyes and induce blindness.

In this case, a scientist just states that UV rays are hazardous to the eyes, but people presume they can lead to blindness. Yet, it is conceivable that it will not be achievable. As a result, these kinds of assumptions are referred to as hypotheses.

Defining Hypothesis in Machine Learning

In machine learning, a hypothesis is a mathematical function or model that converts input data into output predictions. The model's first belief or explanation is based on the facts supplied. The hypothesis is typically expressed as a collection of parameters characterizing the behavior of the model.

If we're building a model to predict the price of a property based on its size and location. The hypothesis function may look something like this −

$$\mathrm{h(x)\:=\:θ0\:+\:θ1\:*\:x1\:+\:θ2\:*\:x2}$$

The hypothesis function is h(x), its input data is x, the model's parameters are 0, 1, and 2, and the features are x1 and x2.

The machine learning model's purpose is to discover the optimal values for parameters 0 through 2 that minimize the difference between projected and actual output labels.

To put it another way, we're looking for the hypothesis function that best represents the underlying link between the input and output data.

Types of Hypotheses in Machine Learning

The next step is to build a hypothesis after identifying the problem and obtaining evidence. A hypothesis is an explanation or solution to a problem based on insufficient data. It acts as a springboard for further investigation and experimentation. A hypothesis is a machine learning function that converts inputs to outputs based on some assumptions. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. Several machine learning theories are as follows −

1. Null Hypothesis

A null hypothesis is a basic hypothesis that states that no link exists between the independent and dependent variables. In other words, it assumes the independent variable has no influence on the dependent variable. It is symbolized by the symbol H0. If the p-value falls outside the significance level, the null hypothesis is typically rejected (). If the null hypothesis is correct, the coefficient of determination is the probability of rejecting it. A null hypothesis is involved in test findings such as t-tests and ANOVA.

2. Alternative Hypothesis

An alternative hypothesis is a hypothesis that contradicts the null hypothesis. It assumes that there is a relationship between the independent and dependent variables. In other words, it assumes that there is an effect of the independent variable on the dependent variable. It is denoted by Ha. An alternative hypothesis is generally accepted if the p-value is less than the significance level (α). An alternative hypothesis is also known as a research hypothesis.

3. One-tailed Hypothesis

A one-tailed test is a type of significance test in which the region of rejection is located at one end of the sample distribution. It denotes that the estimated test parameter is more or less than the crucial value, implying that the alternative hypothesis rather than the null hypothesis should be accepted. It is most commonly used in the chi-square distribution, where all of the crucial areas, related to, are put in either of the two tails. Left-tailed or right-tailed one-tailed tests are both possible.

4. Two-tailed Hypothesis

The two-tailed test is a hypothesis test in which the region of rejection or critical area is on both ends of the normal distribution. It determines whether the sample tested falls within or outside a certain range of values, and an alternative hypothesis is accepted if the calculated value falls in either of the two tails of the probability distribution. α is bifurcated into two equal parts, and the estimated parameter is either above or below the assumed parameter, so extreme values work as evidence against the null hypothesis.

Overall, the hypothesis plays a critical role in the machine learning model. It provides a starting point for the model to make predictions and helps to guide the learning process. The accuracy of the hypothesis is evaluated using various metrics like mean squared error or accuracy.

The hypothesis is a mathematical function or model that converts input data into output predictions, typically expressed as a collection of parameters characterizing the behavior of the model. It is an explanation or solution to a problem based on insufficient data. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. A two-tailed hypothesis is used when there is no prior knowledge or theoretical basis to infer a certain direction of the link.

• Related Articles
• What is Machine Learning?
• What is momentum in Machine Learning?
• What is Epoch in Machine Learning?
• What is Standardization in Machine Learning
• What is Q-learning with respect to reinforcement learning in Machine Learning?
• What is Bayes Theorem in Machine Learning
• What is field Mapping in Machine Learning?
• What is Parameter Extraction in Machine Learning
• What is Tpot AutoML in machine learning?
• What is Projection Perspective in Machine Learning?
• What is Grouped Convolution in Machine Learning?
• What is a Neural Network in Machine Learning?
• What is corporate fraud detection in machine learning?
• What is Linear Algebra Application in Machine Learning
• What is Continuous Kernel Convolution in machine learning?

Kickstart Your Career

Get certified by completing the course

Evaluating Hypotheses: Estimating hypotheses Accuracy

For estimating hypothesis accuracy, statistical methods are applied. In this blog, we’ll have a look at evaluating hypotheses and estimating it’s accuracy. 

Evaluating hypotheses: 

Whenever you form a hypothesis for a given training data set, for example, you came up with a hypothesis for the EnjoySport example where the attributes of the instances decide if a person will be able to enjoy their favorite sport or not. 

Now to test or evaluate how accurate the considered hypothesis is we use different statistical measures. Evaluating hypotheses is an important step in training the model. 

To evaluate the hypotheses precisely focus on these points: 

When statistical methods are applied to estimate hypotheses, 

• First, how well does this estimate the accuracy of a hypothesis across additional examples, given the observed accuracy of a hypothesis over a limited sample of data?
• Second, how likely is it that if one theory outperforms another across a set of data, it is more accurate in general?
• Third, what is the best strategy to use limited data to both learn and measure the accuracy of a hypothesis?

Motivation: 

There are instances where the accuracy of the entire model plays a huge role in the model is adopted or not. For example, consider using a training model for Medical treatment. We need to have a high accuracy so as to depend on the information the model provides. 

When we need to learn a hypothesis and estimate its future accuracy based on a small collection of data, we face two major challenges:

Bias in the estimation

There is a bias in the estimation. Initially, the observed accuracy of the learned hypothesis over training instances is a poor predictor of its accuracy over future cases.

Because the learned hypothesis was generated from previous instances, future examples will likely yield a skewed estimate of hypothesis correctness.

Estimation variability.  

Second, depending on the nature of the particular set of test examples, even if the hypothesis accuracy is tested over an unbiased set of test instances independent of the training examples, the measurement accuracy can still differ from the true accuracy. 

The anticipated variance increases as the number of test examples decreases.

When evaluating a taught hypothesis, we want to know how accurate it will be at classifying future instances.

Also, to be aware of the likely mistake in the accuracy estimate. There is an X-dimensional space of conceivable scenarios. We presume that different instances of X will be met at different times. 

Assume there is some unknown probability distribution D that describes the likelihood of encountering each instance in X. This is a convenient method to model this.

A trainer draws each instance separately, according to the distribution D, and then passes the instance x together with its correct target value f (x) to the learner as training examples of the target function f.

The following two questions are of particular relevance to us in this context, 

• What is the best estimate of the accuracy of h over future instances taken from the same distribution, given a hypothesis h and a data sample containing n examples picked at random according to the distribution D?
• What is the margin of error in this estimate of accuracy?

True Error and Sample Error: 

We must distinguish between two concepts of accuracy or, to put it another way, error. One is the hypothesis’s error rate based on the available data sample. 

The hypothesis’ error rate over the complete unknown distribution D of examples is the other. These will be referred to as the sampling error and real error, respectively.

The fraction of S that a hypothesis misclassifies is the sampling error of a hypothesis with respect to some sample S of examples selected from X.

Sample Error:

It is denoted by error s (h) of hypothesis h with respect to target function f and data sample S is 

Where n is the number of examples in S, and the quantity  is 1 if f(x) != h(x), and 0 otherwise. 

True Error: 

It is denoted by error D (h) of hypothesis h with respect to target function f and distribution D, which is the probability that h will misclassify an instance drawn at random according to D.

Confidence Intervals for Discrete-Valued Hypotheses:

“How accurate are error s (h) estimates of error D (h)?” – in the case of a discrete-valued hypothesis (h).

To estimate the true error for a discrete-valued hypothesis h based on its observed sample error over a sample S, where

• According to the probability distribution D, the sample S contains n samples drawn independently of one another and of h. 
• Over these n occurrences, hypothesis h commits r mistakes error s (h) = r/n

Under these circumstances, statistical theory permits us to state the following:

• If no additional information is available, the most likely value of error D (h) is error s (h).
• The genuine error error D (h) lies in the interval with approximately 95% probability.

A more precise rule of thumb is that the approximation described above works well when

What is Hypothesis in Machine Learning? How to Form a Hypothesis?

Hypothesis Testing is a broad subject that is applicable to many fields. When we study statistics, the Hypothesis Testing there involves data from multiple populations and the test is to see how significant the effect is on the population.

Top Machine Learning and AI Courses Online

This involves calculating the p-value and comparing it with the critical value or the alpha. When it comes to Machine Learning, Hypothesis Testing deals with finding the function that best approximates independent features to the target. In other words, map the inputs to the outputs.

By the end of this tutorial, you will know the following:

• What is Hypothesis in Statistics vs Machine Learning
• What is Hypothesis space?

Process of Forming a Hypothesis

Trending machine learning skills.

Hypothesis in Statistics

A Hypothesis is an assumption of a result that is falsifiable, meaning it can be proven wrong by some evidence. A Hypothesis can be either rejected or failed to be rejected. We never accept any hypothesis in statistics because it is all about probabilities and we are never 100% certain. Before the start of the experiment, we define two hypotheses:

1. Null Hypothesis: says that there is no significant effect

2. Alternative Hypothesis: says that there is some significant effect

In statistics, we compare the P-value (which is calculated using different types of statistical tests) with the critical value or alpha. The larger the P-value, the higher is the likelihood, which in turn signifies that the effect is not significant and we conclude that we fail to reject the null hypothesis .

In other words, the effect is highly likely to have occurred by chance and there is no statistical significance of it. On the other hand, if we get a P-value very small, it means that the likelihood is small. That means the probability of the event occurring by chance is very low. 

Join the   ML and AI Course  online from the World’s top Universities – Masters, Executive Post Graduate Programs, and Advanced Certificate Program in ML & AI to fast-track your career.

Significance Level

The Significance Level is set before starting the experiment. This defines how much is the tolerance of error and at which level can the effect can be considered significant. A common value for significance level is 95% which also means that there is a 5% chance of us getting fooled by the test and making an error. In other words, the critical value is 0.05 which acts as a threshold. Similarly, if the significance level was set at 99%, it would mean a critical value of 0.01%.

A statistical test is carried out on the population and sample to find out the P-value which then is compared with the critical value. If the P-value comes out to be less than the critical value, then we can conclude that the effect is significant and hence reject the Null Hypothesis (that said there is no significant effect). If P-Value comes out to be more than the critical value, we can conclude that there is no significant effect and hence fail to reject the Null Hypothesis.

Now, as we can never be 100% sure, there is always a chance of our tests being correct but the results being misleading. This means that either we reject the null when it is actually not wrong. It can also mean that we don’t reject the null when it is actually false. These are type 1 and type 2 errors of Hypothesis Testing. 

Example  

Consider you’re working for a vaccine manufacturer and your team develops the vaccine for Covid-19. To prove the efficacy of this vaccine, it needs to statistically proven that it is effective on humans. Therefore, we take two groups of people of equal size and properties. We give the vaccine to group A and we give a placebo to group B. We carry out analysis to see how many people in group A got infected and how many in group B got infected.

We test this multiple times to see if group A developed any significant immunity against Covid-19 or not. We calculate the P-value for all these tests and conclude that P-values are always less than the critical value. Hence, we can safely reject the null hypothesis and conclude there is indeed a significant effect.

Read:  Machine Learning Models Explained

Hypothesis in Machine Learning

Hypothesis in Machine Learning is used when in a Supervised Machine Learning, we need to find the function that best maps input to output. This can also be called function approximation because we are approximating a target function that best maps feature to the target.

1. Hypothesis(h): A Hypothesis can be a single model that maps features to the target, however, may be the result/metrics. A hypothesis is signified by “ h ”.

2. Hypothesis Space(H): A Hypothesis space is a complete range of models and their possible parameters that can be used to model the data. It is signified by “ H ”. In other words, the Hypothesis is a subset of Hypothesis Space.

In essence, we have the training data (independent features and the target) and a target function that maps features to the target. These are then run on different types of algorithms using different types of configuration of their hyperparameter space to check which configuration produces the best results. The training data is used to formulate and find the best hypothesis from the hypothesis space. The test data is used to validate or verify the results produced by the hypothesis.

Consider an example where we have a dataset of 10000 instances with 10 features and one target. The target is binary, which means it is a binary classification problem. Now, say, we model this data using Logistic Regression and get an accuracy of 78%. We can draw the regression line which separates both the classes. This is a Hypothesis(h). Then we test this hypothesis on test data and get a score of 74%. 

Checkout:  Machine Learning Projects & Topics

Now, again assume we fit a RandomForests model on the same data and get an accuracy score of 85%. This is a good improvement over Logistic Regression already. Now we decide to tune the hyperparameters of RandomForests to get a better score on the same data. We do a grid search and run multiple RandomForest models on the data and check their performance. In this step, we are essentially searching the Hypothesis Space(H) to find a better function. After completing the grid search, we get the best score of 89% and we end the search. 

FYI: Free nlp course !

Now we also try more models like XGBoost, Support Vector Machine and Naive Bayes theorem to test their performances on the same data. We then pick the best performing model and test it on the test data to validate its performance and get a score of 87%. 

Popular AI and ML Blogs & Free Courses

Before you go

The hypothesis is a crucial aspect of Machine Learning and Data Science. It is present in all the domains of analytics and is the deciding factor of whether a change should be introduced or not. Be it pharma, software, sales, etc. A Hypothesis covers the complete training dataset to check the performance of the models from the Hypothesis space.

A Hypothesis must be falsifiable, which means that it must be possible to test and prove it wrong if the results go against it. The process of searching for the best configuration of the model is time-consuming when a lot of different configurations need to be verified. There are ways to speed up this process as well by using techniques like Random Search of hyperparameters.

If you’re interested to learn more about machine learning, check out IIIT-B & upGrad’s  Executive PG Programme in Machine Learning & AI  which is designed for working professionals and offers 450+ hours of rigorous training, 30+ case studies & assignments, IIIT-B Alumni status, 5+ practical hands-on capstone projects & job assistance with top firms.

Pavan Vadapalli

Something went wrong

Machine Learning Skills To Master

• Artificial Intelligence Courses
• Tableau Courses
• NLP Courses
• Deep Learning Courses

Our Popular Machine Learning Course

Our Trending Machine Learning Courses

• Advanced Certificate Programme in Machine Learning and NLP from IIIT Bangalore - Duration 8 Months
• Master of Science in Machine Learning & AI from LJMU - Duration 18 Months
• Executive PG Program in Machine Learning and AI from IIIT-B - Duration 12 Months

Frequently Asked Questions (FAQs)

There are many reasons to do open-source projects. You are learning new things, you are helping others, you are networking with others, you are creating a reputation and many more. Open source is fun, and eventually you will get something back. One of the most important reasons is that it builds a portfolio of great work that you can present to companies and get hired. Open-source projects are a wonderful way to learn new things. You could be enhancing your knowledge of software development or you could be learning a new skill. There is no better way to learn than to teach.

Yes. Open-source projects do not discriminate. The open-source communities are made of people who love to write code. There is always a place for a newbie. You will learn a lot and also have the chance to participate in a variety of open-source projects. You will learn what works and what doesn't and you will also have the chance to make your code used by a large community of developers. There is a list of open-source projects that are always looking for new contributors.

GitHub offers developers a way to manage projects and collaborate with each other. It also serves as a sort of resume for developers, with a project's contributors, documentation, and releases listed. Contributions to a project show potential employers that you have the skills and motivation to work in a team. Projects are often more than code, so GitHub has a way that you can structure your project just like you would structure a website. You can manage your website with a branch. A branch is like an experiment or a copy of your website. When you want to experiment with a new feature or fix something, you make a branch and experiment there. If the experiment is successful, you can merge the branch back into the original website.

Explore Free Courses

Learn more about the education system, top universities, entrance tests, course information, and employment opportunities in Canada through this course.

Advance your career in the field of marketing with Industry relevant free courses

Build your foundation in one of the hottest industry of the 21st century

Master industry-relevant skills that are required to become a leader and drive organizational success

Build essential technical skills to move forward in your career in these evolving times

Get insights from industry leaders and career counselors and learn how to stay ahead in your career

Kickstart your career in law by building a solid foundation with these relevant free courses.

Stay ahead of the curve and upskill yourself on Generative AI and ChatGPT

Build your confidence by learning essential soft skills to help you become an Industry ready professional.

Learn more about the education system, top universities, entrance tests, course information, and employment opportunities in USA through this course.

Suggested Blogs

by Pavan Vadapalli

29 Jul 2024

09 Jul 2024

07 Jul 2024

04 Jul 2024

03 Jul 2024

01 Jul 2024

26 Jun 2024

by MK Gurucharan

24 Jun 2024

• School Guide
• Mathematics
• Number System and Arithmetic
• Trigonometry
• Probability
• Mensuration
• Maths Formulas
• Class 8 Maths Notes
• Class 9 Maths Notes
• Class 10 Maths Notes
• Class 11 Maths Notes
• Class 12 Maths Notes

Hypothesis | Definition, Meaning and Examples

Hypothesis is a hypothesis is fundamental concept in the world of research and statistics. It is a testable statement that explains what is happening or observed. It proposes the relation between the various participating variables.

Hypothesis is also called Theory, Thesis, Guess, Assumption, or Suggestion . Hypothesis creates a structure that guides the search for knowledge.

In this article, we will learn what hypothesis is, its characteristics, types, and examples. We will also learn how hypothesis helps in scientific research.

Table of Content

What is Hypothesis?

Characteristics of hypothesis, sources of hypothesis, types of hypothesis, functions of hypothesis, how hypothesis help in scientific research.

Hypothesis is a suggested idea or an educated guess or a proposed explanation made based on limited evidence, serving as a starting point for further study. They are meant to lead to more investigation.

It’s mainly a smart guess or suggested answer to a problem that can be checked through study and trial. In science work, we make guesses called hypotheses to try and figure out what will happen in tests or watching. These are not sure things but rather ideas that can be proved or disproved based on real-life proofs. A good theory is clear and can be tested and found wrong if the proof doesn’t support it.

Hypothesis Meaning

A hypothesis is a proposed statement that is testable and is given for something that happens or observed.

• It is made using what we already know and have seen, and it’s the basis for scientific research.
• A clear guess tells us what we think will happen in an experiment or study.
• It’s a testable clue that can be proven true or wrong with real-life facts and checking it out carefully.
• It usually looks like a “if-then” rule, showing the expected cause and effect relationship between what’s being studied.

Here are some key characteristics of a hypothesis:

• Testable: An idea (hypothesis) should be made so it can be tested and proven true through doing experiments or watching. It should show a clear connection between things.
• Specific: It needs to be easy and on target, talking about a certain part or connection between things in a study.
• Falsifiable: A good guess should be able to show it’s wrong. This means there must be a chance for proof or seeing something that goes against the guess.
• Logical and Rational: It should be based on things we know now or have seen, giving a reasonable reason that fits with what we already know.
• Predictive: A guess often tells what to expect from an experiment or observation. It gives a guide for what someone might see if the guess is right.
• Concise: It should be short and clear, showing the suggested link or explanation simply without extra confusion.
• Grounded in Research: A guess is usually made from before studies, ideas or watching things. It comes from a deep understanding of what is already known in that area.
• Flexible: A guess helps in the research but it needs to change or fix when new information comes up.
• Relevant: It should be related to the question or problem being studied, helping to direct what the research is about.
• Empirical: Hypotheses come from observations and can be tested using methods based on real-world experiences.

Hypotheses can come from different places based on what you’re studying and the kind of research. Here are some common sources from which hypotheses may originate:

• Existing Theories: Often, guesses come from well-known science ideas. These ideas may show connections between things or occurrences that scientists can look into more.
• Observation and Experience: Watching something happen or having personal experiences can lead to guesses. We notice odd things or repeat events in everyday life and experiments. This can make us think of guesses called hypotheses.
• Previous Research: Using old studies or discoveries can help come up with new ideas. Scientists might try to expand or question current findings, making guesses that further study old results.
• Literature Review: Looking at books and research in a subject can help make guesses. Noticing missing parts or mismatches in previous studies might make researchers think up guesses to deal with these spots.
• Problem Statement or Research Question: Often, ideas come from questions or problems in the study. Making clear what needs to be looked into can help create ideas that tackle certain parts of the issue.
• Analogies or Comparisons: Making comparisons between similar things or finding connections from related areas can lead to theories. Understanding from other fields could create new guesses in a different situation.
• Hunches and Speculation: Sometimes, scientists might get a gut feeling or make guesses that help create ideas to test. Though these may not have proof at first, they can be a beginning for looking deeper.
• Technology and Innovations: New technology or tools might make guesses by letting us look at things that were hard to study before.
• Personal Interest and Curiosity: People’s curiosity and personal interests in a topic can help create guesses. Scientists could make guesses based on their own likes or love for a subject.

Here are some common types of hypotheses:

Simple Hypothesis

Complex hypothesis, directional hypothesis.

• Non-directional Hypothesis

Null Hypothesis (H0)

Alternative hypothesis (h1 or ha), statistical hypothesis, research hypothesis, associative hypothesis, causal hypothesis.

Simple Hypothesis guesses a connection between two things. It says that there is a connection or difference between variables, but it doesn’t tell us which way the relationship goes. Example: Studying more can help you do better on tests. Getting more sun makes people have higher amounts of vitamin D.

Complex Hypothesis tells us what will happen when more than two things are connected. It looks at how different things interact and may be linked together. Example: How rich you are, how easy it is to get education and healthcare greatly affects the number of years people live. A new medicine’s success relies on the amount used, how old a person is who takes it and their genes.

Directional Hypothesis says how one thing is related to another. For example, it guesses that one thing will help or hurt another thing. Example: Drinking more sweet drinks is linked to a higher body weight score. Too much stress makes people less productive at work.

Non-Directional Hypothesis

Non-Directional Hypothesis are the one that don’t say how the relationship between things will be. They just say that there is a connection, without telling which way it goes. Example: Drinking caffeine can affect how well you sleep. People often like different kinds of music based on their gender.

Null hypothesis is a statement that says there’s no connection or difference between different things. It implies that any seen impacts are because of luck or random changes in the information. Example: The average test scores of Group A and Group B are not much different. There is no connection between using a certain fertilizer and how much it helps crops grow.

Alternative Hypothesis is different from the null hypothesis and shows that there’s a big connection or gap between variables. Scientists want to say no to the null hypothesis and choose the alternative one. Example: Patients on Diet A have much different cholesterol levels than those following Diet B. Exposure to a certain type of light can change how plants grow compared to normal sunlight.

Statistical Hypothesis are used in math testing and include making ideas about what groups or bits of them look like. You aim to get information or test certain things using these top-level, common words only. Example: The average smarts score of kids in a certain school area is 100. The usual time it takes to finish a job using Method A is the same as with Method B.

Research Hypothesis comes from the research question and tells what link is expected between things or factors. It leads the study and chooses where to look more closely. Example: Having more kids go to early learning classes helps them do better in school when they get older. Using specific ways of talking affects how much customers get involved in marketing activities.

Associative Hypothesis guesses that there is a link or connection between things without really saying it caused them. It means that when one thing changes, it is connected to another thing changing. Example: Regular exercise helps to lower the chances of heart disease. Going to school more can help people make more money.

Causal Hypothesis are different from other ideas because they say that one thing causes another. This means there’s a cause and effect relationship between variables involved in the situation. They say that when one thing changes, it directly makes another thing change. Example: Playing violent video games makes teens more likely to act aggressively. Less clean air directly impacts breathing health in city populations.

Hypotheses have many important jobs in the process of scientific research. Here are the key functions of hypotheses:

• Guiding Research: Hypotheses give a clear and exact way for research. They act like guides, showing the predicted connections or results that scientists want to study.
• Formulating Research Questions: Research questions often create guesses. They assist in changing big questions into particular, checkable things. They guide what the study should be focused on.
• Setting Clear Objectives: Hypotheses set the goals of a study by saying what connections between variables should be found. They set the targets that scientists try to reach with their studies.
• Testing Predictions: Theories guess what will happen in experiments or observations. By doing tests in a planned way, scientists can check if what they see matches the guesses made by their ideas.
• Providing Structure: Theories give structure to the study process by arranging thoughts and ideas. They aid scientists in thinking about connections between things and plan experiments to match.
• Focusing Investigations: Hypotheses help scientists focus on certain parts of their study question by clearly saying what they expect links or results to be. This focus makes the study work better.
• Facilitating Communication: Theories help scientists talk to each other effectively. Clearly made guesses help scientists to tell others what they plan, how they will do it and the results expected. This explains things well with colleagues in a wide range of audiences.
• Generating Testable Statements: A good guess can be checked, which means it can be looked at carefully or tested by doing experiments. This feature makes sure that guesses add to the real information used in science knowledge.
• Promoting Objectivity: Guesses give a clear reason for study that helps guide the process while reducing personal bias. They motivate scientists to use facts and data as proofs or disprovals for their proposed answers.
• Driving Scientific Progress: Making, trying out and adjusting ideas is a cycle. Even if a guess is proven right or wrong, the information learned helps to grow knowledge in one specific area.

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

• Initiating Investigations: Hypotheses are the beginning of science research. They come from watching, knowing what’s already known or asking questions. This makes scientists make certain explanations that need to be checked with tests.
• Formulating Research Questions: Ideas usually come from bigger questions in study. They help scientists make these questions more exact and testable, guiding the study’s main point.
• Setting Clear Objectives: Hypotheses set the goals of a study by stating what we think will happen between different things. They set the goals that scientists want to reach by doing their studies.
• Designing Experiments and Studies: Assumptions help plan experiments and watchful studies. They assist scientists in knowing what factors to measure, the techniques they will use and gather data for a proposed reason.
• Testing Predictions: Ideas guess what will happen in experiments or observations. By checking these guesses carefully, scientists can see if the seen results match up with what was predicted in each hypothesis.
• Analysis and Interpretation of Data: Hypotheses give us a way to study and make sense of information. Researchers look at what they found and see if it matches the guesses made in their theories. They decide if the proof backs up or disagrees with these suggested reasons why things are happening as expected.
• Encouraging Objectivity: Hypotheses help make things fair by making sure scientists use facts and information to either agree or disagree with their suggested reasons. They lessen personal preferences by needing proof from experience.
• Iterative Process: People either agree or disagree with guesses, but they still help the ongoing process of science. Findings from testing ideas make us ask new questions, improve those ideas and do more tests. It keeps going on in the work of science to keep learning things.

People Also View:

Mathematics Maths Formulas Branches of Mathematics

Hypothesis is a testable statement serving as an initial explanation for phenomena, based on observations, theories, or existing knowledge . It acts as a guiding light for scientific research, proposing potential relationships between variables that can be empirically tested through experiments and observations.

The hypothesis must be specific, testable, falsifiable, and grounded in prior research or observation, laying out a predictive, if-then scenario that details a cause-and-effect relationship. It originates from various sources including existing theories, observations, previous research, and even personal curiosity, leading to different types, such as simple, complex, directional, non-directional, null, and alternative hypotheses, each serving distinct roles in research methodology .

The hypothesis not only guides the research process by shaping objectives and designing experiments but also facilitates objective analysis and interpretation of data , ultimately driving scientific progress through a cycle of testing, validation, and refinement.

Hypothesis – FAQs

What is a hypothesis.

A guess is a possible explanation or forecast that can be checked by doing research and experiments.

What are Components of a Hypothesis?

The components of a Hypothesis are Independent Variable, Dependent Variable, Relationship between Variables, Directionality etc.

What makes a Good Hypothesis?

Testability, Falsifiability, Clarity and Precision, Relevance are some parameters that makes a Good Hypothesis

Can a Hypothesis be Proven True?

You cannot prove conclusively that most hypotheses are true because it’s generally impossible to examine all possible cases for exceptions that would disprove them.

How are Hypotheses Tested?

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data

Can Hypotheses change during Research?

Yes, you can change or improve your ideas based on new information discovered during the research process.

What is the Role of a Hypothesis in Scientific Research?

Hypotheses are used to support scientific research and bring about advancements in knowledge.

Please Login to comment...

Similar reads.

• Geeks Premier League
• School Learning
• Geeks Premier League 2023
• Maths-Class-12

Improve your Coding Skills with Practice

What kind of Experience do you want to share?