Question

2. Use the Chi-Square test procedure to solve the following research question: A psychologist seeks to examine whether certain mental health issues are more prevalent in a sample of violent criminal offenders (1,000) compared to the average population.

	Observed	Expected
Anxiety disorder	152	146 (14.6 x 1000)
Mood disorder	112	80 (8.0 x 1000)
Personality disorder	195	90 (9.0 x 1000)
Schizophrenia	75	15 (1.5 x 1000)
None	521	669 (66.9 x 1000)

2a. Calculate and provide the chi-square statistic for this data (4 pts)

2b. State the degrees of freedom and determine if the test is significant (2 pts)

2c. Calculate and provide the Effect size (phi coefficient) for the test (2 pts)

Answer 1

Q2) a) The chi square test statistic here is computed as:

Therefore 408.29 is the required chi square test statistic here.

b) The degrees of freedom here is computed as:

Therefore for 4 degrees of freedom, we get the p-value from the chi square distribution tables here as:

As the p-value here is approx 0, therefore the test is significant and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the given frequencies are not according to expected frequencies.

c) The effect size for the test is computed here as:

Therefore 9.0365 is the required effect size value here.