The t test for repeated measures is a hypothesis-testing procedure in which there are two separate groups at people tested and the population variance is not known
To clarify, the t test for repeated measures is actually designed for a different scenario. It is used to compare the means of related variables or conditions within the same group of participants, rather than comparing two separate groups.
However, if you are referring to the independent samples t-test, which compares the means of two separate groups, while assuming the population variance is unknown, here's how you can conduct it:
1. Formulate the null and alternative hypotheses:
- Null Hypothesis (H0): There is no difference between the means of the two groups.
- Alternative Hypothesis (Ha): There is a significant difference between the means of the two groups.
2. Gather the required data:
- Collect data for both groups, ensuring they are independent of each other.
- Determine the sample sizes, means, and sample standard deviations of each group.
3. Calculate the t-statistic:
- Use the following formula to calculate the t-statistic:
t = (mean1 - mean2) / √((s1^2 / n1) + (s2^2 / n2))
where mean1 and mean2 are the means of group 1 and 2, s1 and s2 are the sample standard deviations of group 1 and 2, and n1 and n2 are the sample sizes of group 1 and 2.
4. Determine the degrees of freedom:
- Calculate the degrees of freedom (df) using the following formula: df = n1 + n2 - 2.
5. Determine the critical value:
- Consult a t-distribution table or use statistical software to find the critical value corresponding to your desired significance level (e.g., 0.05).
6. Compare the t-statistic with the critical value:
- If the absolute value of the t-statistic is greater than the critical value, reject the null hypothesis in favor of the alternative hypothesis. This suggests a significant difference between the two groups.
- If the absolute value of the t-statistic is less than or equal to the critical value, fail to reject the null hypothesis. This suggests no significant difference between the two groups.
7. Interpret the results:
- If the null hypothesis is rejected, you can conclude that there is evidence to support the alternative hypothesis, indicating a significant difference between the means of the two groups.
- If the null hypothesis is not rejected, you cannot conclude that there is a significant difference between the means of the two groups.
Please note that this explanation assumes you have the necessary data and statistical knowledge to conduct the t-test. If not, it's advisable to consult a statistician or use statistical software to perform the analysis accurately. Additionally, remember to consider the assumptions of the t-test, such as the independence of observations and normality of the data.