Table of Contents

**Introduction Hypothesis Testing using T-test**

The t-test tells you how significant the differences between groups. It means that it lets you know if those differences (measured in means/averages) could have happened by chance.

**What Is Mean By Hypothesis Testing using T-test?**

The T-Test is ratio of the difference between the two groups and the difference within the groups. The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. A t-score of 4 means that the groups are four times as different from each other as they are within each other. When you run a t-test, the bigger the t-value, the more likely it is that the results are repeatable.

**Types of T-test**

There are three main types of t-test:

- An independent sample t-test
- A Paired sample t-test
- A One sample t-test

**A Paired sample-test**

A paired t-test also called a paired samples t-test or dependent samples t-test. Where you run a t-test on dependent samples. Dependent samples are essentially connected.

For example:

- MRI costs at two different hospitals,
- Two tests on the same person before and after training,
- Two sugar measurements on the same person using different equipment.

**When choosing t-test:**

Choose the paired t-test if you have two measurements on the same item, person, or thing. You should choose a t-test when you measure anything that is unique condition.

For Example: measuring a metal strength. Although the manufacturers are different, you might be subjecting them to the same conditions. Two sample t-test it means you comparing two different samples.

Another Example: test two different groups, means-testing an interview from the company. If you take a random sampling from each group separately and they have different conditions, then samples are independent and should run independent samples t-test.

In hypothesis testing, the independent sample t-test is μ_{1} = μ_{2}. It means, assumes the means are equal. With the paired t-test, the null hypothesis is that the pairwise difference between the two tests is equal (H_{0}: µ_{d} = 0).

**Steps of t-test:**

Step 1: Subtract each Y score from each X score.

Step 2: Add up all of the values from Step 1.

Set this number aside for a moment.

Step 3: Square the differences from Step 1.

Step 4: Add up all of the squared differences from Step 3.

Step 5: Use the following formula to calculate the t-score:

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ΣD: Sum of the differences (Sum of X-Y from Step 2)

ΣD^{2}: Sum of the squared differences (from Step 4)

(ΣD)^{2}: Sum of the differences (from Step 2), squared.

Step 6: Subtract 1 from the sample size to get the degrees of freedom. We have 11 items, so 11-1 = 10.

Step 7: Find the p-value in the t-table, using the degrees of freedom in Step 6. If you don’t have a specified alpha level, use 0.05 (5%). For this sample problem, with df=10, the t-value is 2.228.

Step 8: Compare your t-table value from Step 7 (2.228) to your calculated t-value (-2.74). The calculated t-value is greater than the table value at an alpha level of .05. The p-value is less than the alpha level: p <.05. We can reject the null hypothesis that there is no difference between means.

**Conclusion:**

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You are learn about when to use the t-test and how to calculate. Also, learn what is means by t-test and uses of t-test.