Z-test for samples
Z-test for samples
What is it?
The z-test for one sample uses a similar formula to the z-score for an individual, and it is used to find significant differences between a sample mean and a population mean. It indicates how likely it is that a sample with a certain mean and standard deviation came from the population being studied—that it has a population mean. Essentially, it asks: Given a population with a certain mean, how likely is it I could draw a sample with my given sample mean?
Calculation
and:
For a 95% confidence interval, if the z is greater than 1.96 or less than -1.96, it means that p<.05, and the difference is statistically significant. That is, it is so unlikely that the sample came from this population (5% chance or less) that we reject the null hypothesis and say that the sample is different from the population. For a 99% confidence interval, if the z is greater than 2.58 or less than -2.58, it means that p<.01, and the difference is even more significant—the null hypothesis can be rejected with greater confidence.
Computer
Excel
1. Go to the F(x) bar at the top of the screen and click it
2. Select the STATISTICS category
3. Select “Z-test”
4. Under “ARRAY,” highlight the data set against which you’re testing one of the scores
5. Under “X,” highlight (or type in) the score you’re testing
“SIGMA” is used if you know the standard deviation of your population. If you don’t, Excel simply uses the standard deviation of the sample (and you can leave this window blank)
6. This will give you a z-value. If it is more than +1.96 or less than -1.96, p<.05 and you may reject the null hypothesis. If not, you should not reject the null hypothesis.
Z-test: two sample for means on Excel
1. Go to TOOLS> DATA ANALYSIS
Note: if there is no option for "data analysis," you need to add it in. Under TOOLS, click on ADD-INS...
A window will open up. Check "data analysis" and it will automatically install for you (for free)
2. Select "Z-test: 2-sample for means
3. Enter your variable ranges and variances. The variances are the standard deviations of each variable.
4. Hitting OK will put all the information on a new sheet in your workbook.
SPSS
Back to Inferential Page
References:
Patten, Mildred L. (2002). Understanding research methods: An Overview of the essentials (3rd ed.). Los Angeles: Pyrczak Publishing.
Pavkov, Thomas W., & Pierce, Kent A. (2003). Ready, set, go! A Student guide to SPSS(R) 11.0 for Windows. Boston: McGraw-Hill.
Pyrczak, Fred. (2002). Success at statistics: A Worktext with humor (2nd ed.). Los Angeles: Pyrczak Publishing.
