Image: T Test
Image: T Test

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“T-test in Hypothesis Testing”

The final statistical test for comparing two means that may or may not be related is the T-test. Randomly chosen samples from each of the two categories or groups are used in the testing. It is a statistical technique in which samples are selected at random and where the normal distribution is not perfectly normal.

Whether the samples to be studied are from the same category or other categories determines the type of T-test that should be run. The conclusion drawn from the method reflects the likelihood that the mean differences were the result of chance. The test is useful for comparing student grades, population ages, crop lengths from two different species, etc.

Example of T Testing: Samples and Examples

t.test(x, y = NULL,

       mu = 0, var.equal = FALSE)


  • Y: A vector to compute the one-sample t-test
  • Z: A second vector to compute the two-sample t-test

      –  u: Mean of the population- var.equal: Specify if the variance of the two vectors is equal. By default, set to `TRUE`


# H0 : mu = 10

t.test(TRUE, mu = 10

Difference between Z and T testing

A comparison between the z-test and the t-test based on specific conditions is shown here. It is undoubtedly difficult to decide which test statistics to use when.

Since the sample size varies from study to analysis, any sample size can be used with a proper test for hypothesis testing. When the sample size is big, typically n > 30, the z-test is employed, as an example.

When the standard deviation is unknown, the t-test is the statistical test that may be used to determine whether or not the means of two different populations differ.

The parametric test known as the z-test is used to see if the means of two independent datasets differ from one another.

Types of T Testing

T-Test- One-Sample

In this test, the mean or average of one group is contrasted with the predetermined average, which is either the population’s theoretical value or means. For instance, a teacher might want to calculate the class 6 kids’ average height and compare it to a predetermined value of more than 46.

To do this, the teacher first picks a group of pupils at random and records each student’s weight. She then determines the mean weight for that group and determines whether it is greater than the standard figure of 46.

Independent T-Test with Two Samples

When samples from two different groups, species, or populations are analyzed and compared, this test is used. A separate T-test is another name for it. The independent two-sample test, for instance, would be used if a teacher wanted to compare the height of male and female students in class 5.

Test for paired samples

When two groups are members of the same population or group, this type of hypothesis testing is carried out. The groups are examined at two distinct times or under two different circumstances.

T-test with equal variance

When the sample size in each group or population is the same or the variance between the two data sets is comparable, this test is run. It is additionally known as a pooled T-test.

T-Test Explanation in Machine Learning

A T-test analyses a collection of data received from two comparable or dissimilar groups to ascertain the likelihood that the outcome would differ from what is typically found. The test’s accuracy is influenced by a number of variables, including the distribution patterns utilized and the variants affecting the samples that were gathered. The test is run depending on the settings, and a T-value is obtained as the statistical inference of the likelihood that the typical result is the result of chance.

A T-test can be used, for instance, to determine whether the mean length of fruit from two different species is the same. The user can choose randomly from two other species of that fruit. You must know about other machine learning topics from the coding courses online. Some of the tropics are:- 

Some Frequently Asked Questions (FAQs)

Q:- Is the hypothesis test the same as the t-test?

Ans:- The term “t-test” refers to the fact that these hypothesis tests use t-values to evaluate your sample data. T-values are a type of test statistic. Hypothesis tests use the test statistic that is calculated from your sample to compare your sample to the null hypothesis.

Q:- What is the t-test explained with an example?

Ans:- It lets you know if those differences in means could have happened by chance. The t-test is usually used when data sets follow a normal distribution but you don’t know the population variance. For example, you might flip a coin 1,000 times and find the number of heads follows a normal distribution for all trials.

Q:- What are t-tests and their significance?

Ans:- T-test is a hypothesis-testing technique where you are testing the significance of two or more groups and determining the important differences between these groups. It’s a variation of inferential statistics and is mainly used with datasets that have a normal distribution, but unidentified variances.

Q:- What are the properties of the t-test?

Ans:- The t distribution has the following properties: The mean of the distribution is equal to 0. The variance is equal to v / ( v – 2 ), where v is the degrees of freedom (see last section) and v > 2. The variance is always greater than 1, although it is close to 1 when there are many degrees of freedom.

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