Two-Sample T-Test
The two-sample t-test, also known as an independent t-test, is used to determine whether there is a significant difference between the means of two independent (unrelated) groups. It is typically used when you have two separate groups and want to assess whether their means are statistically different from each other.
The formula for the Two-Sample t-test is given by:
where
- and are the sample means,
- n1 and n2 are the sample sizes,
- degree of freedom = n1 + n2 – 2
- and where sp is calculated as:
Here are some key characteristics of the two-sample t-test:
Assumptions:
- The data in each group should follow a normal distribution.
- The variances of the two groups should be approximately equal (homogeneity of variances).
Use Cases:
- Comparing the average test scores of students from two different schools.
- Assessing whether there is a significant difference in the average salaries of employees in two different departments.
Hypotheses:
Null Hypothesis (H0): There is no significant difference between the means of the two groups.
Alternative Hypothesis (Ha): There is a significant difference between the means of the two groups.
Differences Between two-sample, t-test and paired t-test
Statistical tests are essential tools in data analysis, helping researchers make inferences about populations based on sample data. Two common tests used to compare the means of different groups are the two-sample t-test and the paired t-test. Both tests are based on the t-distribution, but they have distinct use cases and assumptions. In this article, we’ll explore the differences between these two tests in R, when to use each one, and how to conduct them in practice.
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