Two sample t test measures whether the means for two groups are significantly different from each other. For example, if we try to assess if mean weight of males and females have statistically significant difference between them.

## Types of T-test

- Independent Ttest - When the groups are independent and have no relation between them.
- Paired Ttest - When the groups are dependent. Paired t-test is used in 'before-after' or 'case-control' studies. For example checking average cholesterol levels of same patients before and after dose.

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## Assumptions of Two Sample t-test

- Scores are normally distributed within each of the two groups
- For independent Ttest - Each score is sampled independently and randomly. Whereas Only the paired groups can be used to perform the paired test.
- Data must be continuous

## Examples of Two Sample t-test

**Pharmaceutical**: A pharmaceutical company wants to test the effectiveness of a new drug. They give the new drug to a group of patients and a placebo to another group of patients. After a certain amount of time, they measure the blood pressure of both groups of patients. Two sample t-test can be used to see if the mean blood pressure of the patients who took the new drug is significantly lower than the mean blood pressure of the patients who took the placebo.**Education**: A professor wants to see if there is a difference in the test scores of students who attend a private college and students who attend a public college. He gives the same test to a group of students from each type of college. Two sample t-test can be used to see if the mean test scores of the students who attend private colleges are significantly different from the mean test scores of the students who attend public colleges.**Marketing**: In marketing, a two-sample t-test can be used to determine if there is a significant difference between two groups of data. For example, a company may want to launch a new product and test the effectiveness of two different advertising campaigns. To determine which campaign is more effective, they could collect data on the ratings of each campaign from a sample of customers and perform a two-sample t-test to determine if there is a significant difference between the mean ratings of the two campaigns.