Z-tests, a type of inferential hypothesis test, compares a sample mean (with treatment) to a population mean (without treatment). The z-score tells you how many standard deviations a data point is from the mean of a data set.Ā
Use a Z-test under these conditions
Populationās standard deviation is knownĀ
Sample size is larger than 30; n>30 (if less then use t-test)
Data should be normally distributed (some variation can be justifiable but if itās strongly non-normal then donāt use z-test)
Data was collected randomly and are independent
It should be noted that z-tests are rarely used irl because situations where the population variance Ļ2Ā is known while the population mean is unknown hardly ever happens. Thatās also likely why it isnāt explicitly on SPSS.
Ā Ā Ā 1.State statistical hypothesisĀ
Ā Ā Ā 2.Ā Find critical area
Ā Ā Ā Ā Ā Ā Ā -Find the Z-Critical (which is the cut off point for the critical area)
Ā Ā Ā 3. Calculate test statisticĀ
Ā Ā Ā Ā 4. Make a decision and state APA conclusion
If Zo (Z-observed) is within the critical area then you can reject your null hypothesis because itās significant. If not then you cannot reject your null hypothesis.Ā
If significant (reject null hypothesis):
āA z-test revealed that [*IV] significantly increased/decreased [*DV] in the sample (M=__, SD=__) from the [IV] reported by the population (Ī¼=__,Ā Ļ=__), z=__, p<.05ā³
If not significant (donāt reject null hypothesis):
āA z-test revealed that [sample] (M=__, SD=__) are not significantly different than the general population (Ī¼=__, Ļ=__), z=__, p>.05ā³
*IV- Independent VariableĀ Ā *DV- Dependent Variable
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