# Two independent samples

Description of activity and Excel instructions:Two independent samples

Dataset: sleep.xls

## Always look at the data

Even though the sample sizes are large and OLI does not instruct you to create descriptive statistics, it's a good idea to do so anyway:

- At a minimum, calculate means and standard deviations for each sample.
- Create a histogram for each sample.

## Calculate t-test value and p-value

Excel has a built in data analysis package that runs basic statistical analyses, which Calc does not have. However, it's only a few extra steps in Calc to do the calculations for this test.

It is important to review the summary statistics for the two samples of data.

- Calculate the mean and standard deviation for each group.

Calc does not report the t-test value. You can program the formula in Calc, but I don't recommend taking the time to do so unless you are interested in this kind of thing. The formula for this test is:

- [math]t = {\overline{y}_1 - \overline{y}_2 \over s_{\overline{y}_1 - \overline{y}_2}}[/math]

where

- [math]s_{\overline{y}_1 - \overline{y}_2} = \sqrt{{s_1^2 \over n_1} + {s_2^2 \over n_2}}. [/math]

The calculated t-test statistic for this data is -1.23042.

Calc provides a formula for calculating the p-value which can be used with a few types of t-tests. Type=3 is for use in this situation: unequal samples sizes and unequal variances. Note that Mode=1 indicates a one-sided test:

- To calculate the p-value, enter the formula "=TTEST([range y1],[range y2],1,3)".

Return to the OLI Two Independent Samples page to complete the interpretive exercises.