Two-Sample Z-Test

                The Two-Sample Z-test is used to compare the means of two samples to see if it is feasible that they come from the same population. The null hypothesis is: the population means are equal. The Z-test is preferred to the t-test for large samples (N > 30)  or when the variance is known, otherwise, the sample standard deviation is a more biased estimate of a population standard deviance than is allowable, and using a two-sample t-test should be considered (see the Comparing Means command).


1.       Normal but independent populations.

2.       Variances for populations are known.

How To

Run: Statistics→Basic Statistics→Two-Sample Z-Test for Means...

Select two variables.

Enter variances for both populations (known).

Enter the hypothesized means difference. A value of 0 (zero) indicates that the means are hypothesized to be equal.


Mean, Variance, Sample Size – the mean, variance and size of an input variable. See the Descriptive Statistics procedure for more information. 

Mean Difference – difference between the means.

Standard Error - estimated standard error for the difference between means.

z (Test statistic)z-score, the distance between means in units of the standard error.  

Z critical value for z.

P(Z<=z)  p-level – probability of observing the sample statistic as extreme as the test statistic. If the null hypothesis is   and the two-tailed p-value is less than  (0.05), the conclusion is that, statistically, the means are significantly different.


Sprinthall, R. C. (2011). Basic Statistical Analysis (9th ed.). Pearson Education.