What is T-Test Table and When to Use It?

A t-test can be represented in statistics as a predictive hypothesis test, where the test statistic follows the Student’s t-distribution if a null hypothesis is formed. Therefore, here we use the t-test table. The approaches of two observation groups are evaluated in paired T-test. Each group should obtain the observations randomly. Therefore, it is the protocol and not other variables that are the explanation for the difference in response.

The T-test is used for creating observations regarding a known sample before and after an event has occurred. Such that, in the case of two samples, observations from both these samples are paired with each other for using T-test effectively with precision. In the statistics chapter, this has been discussed in further detail.

The T-Test table is used to identify the ratio for t-statistics and to evaluate the proportions combined with z-scores. Moreover, the probability of t-values can also be deciphered from the t-distribution table for a given value. Therefore, the probability thus obtained gives the area between two t-distribution ordinates, infinity and a given value. NEET entrance exam students must be well-aware of creating T-test table. The significant values for the probabilities of the t-distribution, α to the degrees of freedom(df), are established with the help of a T-Test table. Below, we have attached T-Test tables for both one tail and two tails. 

The formula for independent two-sample t-test is 

$$t=\frac{\overline{X_1}-\overline{X_2}}{\sqrt{\frac{{s_p}^2}{n_1}+\frac{{s_p}^2}{n_2}}}$$Here, 

$\overline{X_1}\text{ and }\overline{X_2}$ are means of 2 groups

n₁ and n₂ are sizes of 2 groups
${s_p}^2$ is pooled variance which is calculated as 

$${s_p}^2=\frac{(n_1-1){s_1}^2+(n_2-1){s_2}^2}{n_1+n_2-2}$$

${s_1}^2\text{ and }{s_2}^2$ are variances of 2 groups

The t-test is used in the following scenarios:

• Comparing Means of 2 Groups: Whenever you want to compare means of continuous variable between two independent groups. In that case, you will use a T-test. For example, if you want to compare the average test scores of 2 different classes, in that case, you will use a T-test. JEE Main entrance exam aspirants must know about such use cases of T-test.
• Pre-post Comparisons: Whenever you have measurements from the same group before and after intervention or treatment. This is called a paired t-test. For instance, you want to measure the blood pressure of patients before and after taking a drug; in this case, a paired t-test will be done.
• Hypothesis Testing: Whenever you want to test the hypothesis about mean of a single group against a known value. In this case, you will use a t-test. For example, if you want to test whether the average weight of a sample of individuals is different from the specified population mean.
• Small Sample Sizes: T-tests are useful while dealing with small sample sizes (where n < 30), as they depend on t-distribution since it accounts for additional uncertainty during estimation of the mean.
• Equal Variances: When you assume that the variances of the two groups are equal. This version of t-test adjusts for unequal variances (Welch's t-test). 

Let us take a look at some of the important questions related to t-test for the IIT JAM exam and the IISER examination:

1. Calculate t-test for the following data.

Solution.

• In the first step, we would be subtracting all the values of score 2 from score 1.
• Then we would be adding up all the values obtained.
• In the third step, we would be squaring up the value obtained from subtracting each subject.
• Then we would be adding up all the values obtained.
• In the final step, we would be using this formula to get the required t-test

Therefore, the required t-test value is -2.74. Thus, we can reject the null hypothesis for this value.

2. There are two sets: (2,7,8,9) and (4,3,2,1). Calculate t-test for the same.

Solution.

• In the first step, we would be subtracting all the values of score 2 from score 1.
• Then we would be adding up all the values obtained.
• In the third step, we would be squaring up the value obtained from subtracting each subject.
• Then we would be adding up all the values obtained.
• In the final step, we would be using this formula to get the required t-test

Therefore, the required t-test value is 2.36

3. Calculate t-test for the following data.

Solution.

• In the first step, we would be subtracting all the values of score 2 from score 1.
• Then we would be adding up all the values obtained.
• In the third step, we would be squaring up the value obtained from subtracting each subject.
• Then we would be adding up all the values obtained.
• In the final step, we would be using this formula to get the required t-test

Therefore, the required t-test value is 4.27

Let us take a look at some important FAQs related to the T-test that students must be well aware of when they plan to take the 12th CBSE board exam: