Z-Test two sample for means in Excel using the QI Macros
When to use the Z-Test two sample for means
- To compare population and sample means to determine if there is a significant difference.
- To compare means between two samples.
- To compare the mean of one sample to a given constant.
The Z-test is typically used in evaluating the results of standardized tests. Are the results from a sample of students outside of or within the standard test performance? Consider the following example taken from Statistical Analysis in Excel for Dummies by Joseph Schmuller.
Imagine a new training technique designed to increase IQ. Take a sample of 25 people and train them using the new technique. Take another sample of 25 people and give them no special training.
Now, conduct a test with the two samples and input their scores into Excel:
Then, select the data with the mouse and click on the QI Macros Menu to select the Z-Test two sample for means test:
The QI Macros will prompt for a significance level (default = 0.05):
a hypothesized mean difference (in this case 0 ):
and variances for variables 1 and 2
The QI Macros Z-Test will perform the calculations and interpret the results for you:
What's Cool About Z-Test Calculations in the QI Macros?
When you run the Z-Test, the QI Macros will compare the p-value (0.192) to the significance level (0.05) and interpret the results for you. "Cannot Reject the Null Hypothesis because p > 0.05" and that the "Means are the same."
Interpreting the Z-Test results manually
- The null hypothesis H0 is that the mean difference = 0
or in other words the means are the same
- The alternative hypothesis Ha is that the mean difference is > 0
or in other words that the mean of the trained population is larger
|test statistic > critical value
(i.e. z> zcrit)
|Reject the null hypothesis|
|test statistic < critical value
(i.e. z< zcrit)
|Cannot Reject the null hypothesis|
|p value < a||Reject the null hypothesis|
|p value > a||Cannot Reject the null hypothesis|
Since the null hypothesis is that the means are the same this is a two-sided test. Therefore, use the two-tail values for your analysis.
Since the z statistic < zcritical (1.305 < 1.960) and p value > a ( 0.192> 0.05) , we cannot reject the null hypothesis that the means are the same.
Since the p-value is < 0.05, we can reject the null hypothesis.