Question

1.ANova Problem

Imagine that you are a research psychologist who is interested in studying the effects of a new drug for treating moderate depression. You are interested not only in the efficacy of the new drug, but also how effective it is in conjunction with therapy. You expect that patients who are treated with the new drug and therapy together would show the lowest scores on the Beck Depression Inventory (BDI), indicating the greatest relief from their depressive symptoms, but you also think that treatment with the drug itself will show improvement relative to the placebo condition. Thirty-six patients (20 Female, 16 Male) are recruited for the study and are randomly assigned to the four conditions below. They receive the treatment assigned for 12 weeks, and then are given the BDI to assess their current level of depression.

Here are the scores for each participant in each group after the 12 week treatment:

New Drug	New Drug + Therapy	Therapy Only	Placebo
18	18	18	23
20	17	19	24
21	15	22	27
22	16	21	30
24	15	15	16
17	19	16	18
18	16	20	26
16	16	22	21
19	19	23	23

You are not expected to produce any tables or figures for Results assignment #2, but you may if you wish. See the instructions document for details on how to complete the write-up for this study.

Here, you should describe the results only – there should be no interpretation of what those results “mean” in the larger theoretical context (but you should indicate whether or not they support or fail to support your hypothesis). Generally, you should discuss results in terms of operational definitions, not conceptual variables, because the results are specific to what you did in the study being reported. Be sure to refer the reader to any tables or figures that you include in the paper (see assignment for details on this).

Whenever you report a mean, you must also include standard deviation or standard error. The mean may be reported in the subject or object of the sentence and the SD/SE reported parenthetically following, or both may be reported parenthetically.

Example: “The mean shoe size was 9.5 (SD = 1.2) for males, and 7.5 (SD = 1.1) for females.” OR “The mean shoe size was larger for males (M = 9.5, SD = 1.2) than for females (M = 7.5, SD = 1.1).”

Results:

You must include all relevant information about the statistical test that you have conducted. Including the types of test, the value of the test, the p-value, and in most cases, the df. Also be sure that you are clearly identifying the direction of the effect, and which groups/conditions are different than others. The following example shows statistics reported in correct APA format.

Example: “We hypothesized that what people eat for breakfast before taking an exam would influence exam performance. We predicted that people who ate eggs would do better than both other groups and that the cupcake group would do better than those who ate nothing. We conducted a one-way ANOVA to compare the means between the no breakfast group, the cupcake group, and the eggs group, and discovered an overall significant effect of type of food eaten on exam performance, F (2, 57) = 4.32, p = .02. Post-hoc tests conducted using the Tukey HSD test showed that the cupcake group had significantly higher exam scores (M = 88, SD = 4) than both other groups. The eggs breakfast group (M = 83, SD = 3) also scored significantly higher than the no breakfast group (M = 75, SD = 5). Our prediction was partially supported as the cupcake group and the eggs group had better exam performance than the no breakfast group.”

NOTE: For the Beck Depression Inventory (BDI), a total score of 0-13 is considered minimal range, 14-19 is mild, 20-28 is moderate, and 29-63 is severe. This may help you in your write up.

Answer 1

In the given experiment we have to study the effects of new drug for treating moderate depression. To do this we made four groups of treatments viz. New Drug(1), New Drug + Therapy(2), Therapy Only(3) and Placebo(4). The summary statistics for all 4 groups are given below:

Summary Statistics of data

SUMMARY
Groups	Count	Sum	Average	Variance	Standard Deviation
New Drug(1)	9	175	19.44	6.53	2.55
New Drug + Therapy(2)	9	151	16.78	2.44	1.56
Therapy Only(3)	9	176	19.56	7.78	2.79
Placebo(4)	9	208	23.11	19.11	4.37

Now we have to test the null hypothesis

H0: there is no difference in the mean effects of any treatment groups.

Ha: there is difference in the mean effects of at least one treatment group.

To test this hypothesis, we conducted one-way ANOVA and the result of ANOVA is given below

Single Factor ANOVA of the data

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	182.333	3	60.778	6.78	0.001147	2.90
Within Groups	286.889	32	8.965
Total	469.222	35

From the results of ANOVA we can see that F statistic and its p-value is highly significant which suggests that we have enough evidence against H0 to reject it and conclude that there is difference in the mean effects of at least one treatment group. Since our ANOVA is significant, we can go for post hoc test to know which pair of treatment is significant.

Post-hoc pairwise comparison

Tukey Multiple comparison of means
95 % family-wise confidence level
Treatment pairs	diff	lwr	upr	p adj
2-1	-2.667	-6.491	1.158	0.25269
3-1	0.111	-3.713	3.935	0.99982
4-1	3.667	-0.158	7.491	0.06405
3-2	2.778	-1.046	6.602	0.22117
4-2	6.333	2.509	10.158	0.00049
4-3	3.556	-0.269	7.380	0.07592

We hypothesized that the new drug introduced will have significant effect for treatment of moderate depression. We also hypothesized that the combination of new drug and therapy will have the highest effect for treating moderate depression. We conducted a one-way ANOVA to compare the means between New Drug, New Drug + Therapy, Therapy Only and Placebo and discovered an overall significant effect of Drug for the treatment of depression with F(3,32)=6.78 and p=0.00115. Post-hoc tests conducted using the Tukey HSD test showed that the New Drug + Therapy (M=16.78, SD=1.56) have significantly lower BDI scores than Placebo (M=23.11, SD=4.37) with p-value=0.00049 . Other treatment pairs were not significantly different. Our hypothesis of highest effect of combination of new drug and therapy is supported by this analysis