Question

1. An experimenter who is interested in the effects of pharmaceutical commercials on mood randomly assigns participants to three groups: a depression medication commercial condition, an anxiety medication commercial condition, and a faucet commercial condition. After viewing the commercials, participants report their level of sadness. Higher scores indicate more sadness. Conduct an analysis of variance and report the obtained F-ratio below.  

Depression	Anxiety	Faucet
8	4	3
6	5	4
5	6	5
8	3	6
7	5	5
6	2	2
8	5	1

2. If the results of the ANOVA from question 1 are statistically significant, conduct Tukey's HSD post hoc test to determine which conditions are significantly different from each other. Which statement below best describes the differences detected from Tukey's HSD?

	a.	The depression commercial group reported significant higher levels of sadness than the anxiety commercial group and the faucet group, and the faucet group reported significant lower levels of sadness than the anxiety group.
	b.	The depression commercial group reported higher level of sadness than the anxiety and faucet commercial group, but the anxiety and faucet commercial groups were not significantly different.
	c.	The depression commercial condition had significantly lower levels of depression than the faucet commercial group, but all other pairwise differences were not statistically significant.
	d.	A post-hoc test was not necessary because the F-ratio was not statistically significant.

Answer 1

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

Column	n	Mean	Std. Dev.	Std. Error
Depression	7	6.8571429	1.2149858	0.45922146
Anxiety	7	4.2857143	1.3801311	0.52164053
Faucet	7	3.7142857	1.7994708	0.68013604

ANOVA table

Source	DF	SS	MS	F-Stat	P-value
Columns	2	39.238095	19.619048	8.8920863	0.0021
Error	18	39.714286	2.2063492
Total	20	78.952381

Tukey HSD results (95% level)
Depression subtracted from

	Difference	Lower	Upper	P-value
Anxiety	-2.5714286	-4.5977649	-0.54509221	0.0121
Faucet	-3.1428571	-5.1691935	-1.1165208	0.0025

Anxiety subtracted from

	Difference	Lower	Upper	P-value
Faucet	-0.57142857	-2.5977649	1.4549078	0.7552

Fom the above output, we can see that the p - value for difference between Depression from each of the two components are less than 0.05 and hence, these differences are significant.

So,

The depression commercial group reported higher level of sadness than the anxiety and faucet commercial group, but the anxiety and faucet commercial groups were not significantly different.

Option B is correct.