Question

Mary wants to know the impact of medication and therapy on depression rates. She recruits 16 people who want treatment for depression she randomly assigns them to receive therapy or no therapy and to receive Medication or Placebo. After two months in the study, these are participants’ scores for depression as assessed by the Hamilton Depression inventory.

	Medication	Placebo
Therapy	3	5
	3	6
	5	3
	7	3
No Therapy	9	10
	9	12
	10	7
	13	11

1. What statistical test should you conduct?
2. Explain how this question meets or does not meet the assumptions for this statistical test.
3. What are the null and alternative hypotheses?
4. Create and present a completed source table.
5. Conduct a Tukey if necessary, explain if it is not necessary.
6. Report the effect size for effects if appropriate. Explain when it is not appropriate to conduct an effect size.

Answer 1

1. What statistical test should you conduct?

Two-Way ANOVA test

1. Explain how this question meets or does not meet the assumptions for this statistical test.

• The populations from which the samples were obtained must be normally or approximately normally distributed.
• The samples must be independent.
• The variances of the populations must be equal.
• The groups must have the same sample size.

1. What are the null and alternative hypotheses?

H₀: There is no impact of medication and therapy on depression rates.

H_a: There is an impact of medication and therapy on depression rates.

1. Create and present a completed source table.

ANOVA table
Source	SS	df	MS	F	p-value
Factor 1	132.25	1	132.250	37.34	.0001
Factor 2	0.25	1	0.250	0.07	.7950
Interaction	0.00	1	0.000	0.00	1.0000
Error	42.50	12	3.542
Total	175.00	15

1. Conduct a Tukey if necessary, explain if it is not necessary.

A Tukey test is not necessary because we do not have any significant interaction.

1. Report the effect size for effects if appropriate. Explain when it is not appropriate to conduct an effect size.

Source	effect size
Factor 1	0.7557143
Factor 2	0.0014286
Interaction	0

Please give me a thumbs-up if this helps you out. Thank you!