# Everything you need to know about Hypothesis Testing in Machine Learning

Akansha 09 Sep, 2021

This article was published as a part of the Data Science Blogathon

## What is Hypothesis Testing?

Any data science project starts with exploring the data. When we perform an analysis on a sample through exploratory data analysis and inferential statistics we get information about the sample. Now, we want to use this information to predict values for the entire population.

Hypothesis testing is done to confirm our observation about the population using sample data, within the desired error level. Through hypothesis testing, we can determine whether we have enough statistical evidence to conclude if the hypothesis about the population is true or not.

## How to perform hypothesis testing in machine learning?

To trust your model and make predictions, we utilize hypothesis testing. When we will use sample data to train our model, we make assumptions about our population. By performing hypothesis testing, we validate these assumptions for a desired significance level.

Let’s take the case of regression models: When we fit a straight line through a linear regression model, we get the slope and intercept for the line. Hypothesis testing is used to confirm if our beta coefficients are significant in a linear regression model. Every time we run the linear regression model, we test if the line is significant or not by checking if the coefficient is significant. I have shared details on how you can check these values in python, towards the end of this blog.

Key steps to perform hypothesis test are as follows:

1. Formulate a Hypothesis
2. Determine the significance level
3. Determine the type of test
4. Calculate the Test Statistic values and the p values
5. Make Decision

Now let’s look into the steps in detail:

## Formulating the hypothesis

One of the key steps to do this is to formulate the below two hypotheses:

The null hypothesis represented as H₀ is the initial claim that is based on the prevailing belief about the population.
The alternate hypothesis represented as H₁ is the challenge to the null hypothesis. It is the claim which we would like to prove as True

One of the main points which we should consider while formulating the null and alternative hypothesis is that the null hypothesis always looks at confirming the existing notion. Hence, it has sign >= or , < and ≠

## Determine the significance level also known as alpha or α for Hypothesis Testing

The significance level is the proportion of the sample mean lying in critical regions. It is usually set as 5% or 0.05 which means that there is a 5% chance that we would accept the alternate hypothesis even when our null hypothesis is true

Based on the criticality of the requirement, we can choose a lower significance level of 1% as well.

## Determine the Test Statistic and calculate its value for Hypothesis Testing

Hypothesis testing uses Test Statistic which is a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

## Select the type of Hypothesis test

We choose the type of test statistic based on the predictor variable – quantitative or categorical. Below are a few of the commonly used test statistics for quantitative data

 Type of predictor variable Distribution type Desired Test Attributes Quantitative Normal Distribution Z – Test Large sample size Population standard deviation known Quantitative T Distribution T-Test Sample size less than 30 Population standard deviation unknown Quantitative Positively skewed distribution F – Test When you want to compare 3 or more variables Quantitative Negatively skewed distribution NA Requires feature transformation to perform a hypothesis test Categorical NA Chi-Square test Test of independence Goodness of fit

#### Z-statistic – Z Test

Z-statistic is used when the sample follows a normal distribution. It is calculated based on the population parameters like mean and standard deviation.
One sample Z test is used when we want to compare a sample mean with a population mean

Two sample Z test is used when we want to compare the mean of two samples

#### T-statistic – T-Test

T-statistic is used when the sample follows a T distribution and population parameters are unknown. T distribution is similar to a normal distribution, it is shorter than normal distribution and has a flatter tail.

If the sample size is less than 30 and population parameters are not known, we use T distribution. Here also, we can use one Sample T-test and a two-sample T-test.

#### F-statistic – F test

For samples involving three or more groups, we prefer the F Test. Performing T-test on multiple groups increases the chances of Type-1 error. ANOVA is used in such cases.

Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means.

F-statistic is used when the data is positively skewed and follows an F distribution. F distributions are always positive and skewed right.

F = Variation between the sample means/variation within the samples

For negatively skewed data we would need to perform feature transformation

#### Chi-Square Test

For categorical variables, we would be performing a chi-Square test.

Following are the two types of chi-squared tests:

1. Chi-squared test of independence – We use the Chi-Square test to determine whether or not there is a significant relationship between two categorical variables.
2. Chi-squared Goodness of fit helps us determine if the sample data correctly represents the population.

Test Statistic is then used to calculate P-Value. A P-value measures the strength of evidence in support of a null hypothesis. If the P-value is less than the significance level, we reject the null hypothesis.

if the p-value < α, then we have statistically significant evidence against the null hypothesis, so we reject the null hypothesis and accept the alternate hypothesis

if the p-value > α then we do not have statistically significant evidence against the null hypothesis, so we fail to reject the null hypothesis.

As we make decisions, it is important to understand the errors that can happen while testing.

## Errors while making decisions

There are two possible types of error we could commit while performing hypothesis testing.

1) Type1 Error – This occurs when the null hypothesis is true but we reject it.The probability of type I error is denoted by alpha (α). Type 1 error is also known as the level of significance of the hypothesis test

2) Type 2 Error – This occurs when the null hypothesis is false but we fail to reject it. The probability of type II error is denoted by beta (β)

## Hypothesis testing in python

The stats model library has the unique ability to perform and summarize the outcomes of hypothesis tests on your model. Based on your feature variables, you can determine which test value is relevant for your model and make decisions accordingly.

`import statsmodels.api as sm`

To create a fitted model, I have used Ordinary least squares

`lr = sm.OLS(y_train, X_train_lm).fit()`

Once we have trained the model, we can see the summary of the tests using the command

`print(lr.summary())`

The model summary will look something like below.

From a hypothesis testing standpoint, you need to pay attention to the following values decide if you need to refine your model

• Prob (F-statistic) –  F-statistic tells us the goodness of fit of regression. You want the probability of F-statistic to be as low as possible to reject the null hypothesis.
• P-value is given in the column P>|t| – As mentioned above, for a good model, we want this value to be less than the significance level.

Image source: All images in this blog have been created by the author

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Akansha 09 Sep, 2021

balaji 17 Oct, 2023

such a good article easy to understand

Aashi 16 Jun, 2024

What does the p value for each variable represent?