Question

Dr. Grey wanted to see if doctors prescribed different treatments for OCD for male patients compared to females. Please use the following frequency tables for the data collected by Dr. Grey. SHOW ALL STEPS PLEASE

Contingency table of Observed and Expected Frequencies of the different treatments (Drug vs. Cognitive Therapy) prescribed for patients with OCD.
Therapy Totals		Drug		Cognitive Therapy		Total
Gender of Patient		Observed	Expected	Observed	Expected
	Man	20		10		30
	Woman	15		15		30
	Total	35		25		60

What is your Conclusion?

A) The frequency of OCD diagnosis is the same for men and women, neither get drug or cognitive therapies more than the other

B) There are no significant differences

C) There are significant differences

D) Different frequencies of treatments for OCD are given to women and men, more drugs are given to men whereas Cognitive therapies are given to women.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis:

For Drug: P_Male = P_Female

For Cognitive therapy: P_Male = P_Female

Alternative hypothesis: At least one of the null hypothesis statements is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for homogeneity.

Analyze sample data. Applying the chi-square test for homogeneity to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1)

D.F = (2 - 1) * (2 - 1)
D.F = 1
E_r,c = (n_r * n_c) / n

Χ² = 1.714

where DF is the degrees of freedom, r is the number of populations, c is the number of levels of the categorical variable, n_r is the number of observations from population r, n_c is the number of observations from level c of the categorical variable, n is the number of observations in the sample, E_r,c is the expected frequency count in population r for level c, and O_r,c is the observed frequency count in population r for level c.The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 1.714.

We use the Chi-Square Distribution Calculator to find P(Χ² > 1.714) = 0.191

Interpret results. Since the P-value (0.191) is greater than the significance level (0.05), we failed to reject the null hypothesis.

A) The frequency of OCD diagnosis is the same for men and women, neither get drug or cognitive therapies more than the other