Psychological statistics: methods and applications

Z Test in Psychology

Stating the research question

The z test is being used to test whether watching a film about the conditions of institutionalized mentally ill patients will influence viewers' attitude towards the mentally ill. Evaluations are accomplished using a questionnaire and the scores for viewers and non-viewers will be compared using the z test.

The test subjects are students. The variable being tested by the z test is the mean scores obtained by the two groups on the survey instrument. The scores represent discrete numerical data. The z test will compare the survey score distributions between the two groups: viewers and non-viewers.

Specifying the null and alternative hypotheses

The null hypothesis (H0) for this experiment is that the mean survey scores of the two groups, viewers and non-viewers, will not be significantly different using the probability cutoff value of 0.05 (alpha). The alternative hypothesis (HA) is that the mean survey scores are significantly different using alpha = 0.05.

HO: = 75

HA: 75.

Step 3: Calculating the test statistic

The mean (M) scores for viewers (V) and non-viewers (NV) is 70 and 75, respectively. The standard deviation (SD) for both samples is 12. Using the z test formula for comparing the means of two normally distributed means, the z score can be calculated thus: z = (MNV -- MV)/{?[(SDNV/?NNV) + (SCV/?NV)]}. Entering the provided values gives: (75-70)/?[(12/?36) + (12/?36)] = 5/2 = 2.5 = z.

Step 4: Probability Calculation

What is being tested is whether the students' attitudes towards the mentally ill change as a result of viewing the film, thus it does not matter if the students' attitudes are better or worse, only if they changed significantly from students who did not view the film. Since the attitudes could be worse or better, this is a two-tailed test. If the Z score falls within 95% of control scores, then we have to retain the null hypothesis and reject the alternative hypothesis.