Hypothesis Test: Mean – Two Independent Samples

This test is used to test a claim about the equality of the means of two independent populations. (If the data are somehow matched or paired, do not use this test; use the hypothesis test for "Mean Matched Pairs.") For example, this test could be used for the claim that "Men have a mean IQ score that is equal to the mean IQ score of women," which would be denoted as "Pop. Mean 1 = Pop. Mean 2."

First select the format of the original claim that is to be tested. Note that there are 6 different choices, which can be viewed by clicking on the small box to the right of the default claim ("Pop. Mean 1= Pop. Mean 2"). Use the up/down arrow keys to highlight the desired choice, then click on that desired choice. STATDISK will determine the appropriate null hypothesis from the claim selected.

Significance (level): Enter a positive value in decimal form, such as 0.05.

For Sample 1, make these entries:
Sample Size, n1: Enter the sample size as a positive whole number.
Sample 1 mean: Enter the sample mean of the first sample.
Sample 1 StDev: Enter the standard deviation of the first sample as a positive number.
Population StDev: Enter the value of the standard deviation of the first POPULATION only if that value is known. In reality, this value is usually not known, so this box is usually left blank. DO NOT ENTER THE VALUE OF THE SAMPLE STANDARD DEVIATION HERE.

For the second sample, make the corresponding entries as described above.

If the two POPULATION standard deviations are entered, the results will be based on calculations using a normal distribution, as described in the textbook. If the two POPULATION standard deviations are not both known (as is usually the case), you must choose among these options:

Not Eq vars: NO POOL (That is, do not assume that the two population variances are equal, and do not use a pooled estimate of a common population variance.)

Eq. vars: POOL (That is, assume that the two population variances are equal, and use a pooled estimate of the common population variance.)

Prelim F-Test (That is, have STATDISK do a preliminary F test to decide whether the two population variances appear to be equal. Then, based on the result, proceed by either assuming that the two population variances are not equal (NO POOL) or by assuming that the two population variances are equal (POOL).)

Among the above three options, the NO POOL option generally yields the best results and it is the recommended option.

Note: If the NO POOL option is used, STATDISK proceeds with calculations using the t distribution with the number of degrees of freedom found from the formula included in the textbook (instead of using the simplified "df = smaller of n1-1 and n2-1"). STADISK displays the number of degrees of freedom. Because STATDISK uses the more accurate formula for df, the results may differ somewhat from those given in the textbook.

Click on the Evaluate button to obtain the results.

Click on the Print button to print the results.

Click on the Plot button to display a graph showing the distribution with the test statistic and critical value(s).

To close the window, click on the X at the top of the module window.