Question

Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a moderate dose of the drug, and a group that received a high dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient.

We are now also interested if a patient's weight has an effect on the drug's effectiveness. Patients were categorized as either underweight, overweight, or 'medium weight'.  These revised data are presented below. Use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 2-way ANOVA test for the data in the following table:

	Placebo	Moderate Dose	High Dose
underweight	42	22	13
underweight	52	19	14
medweight	41	31	12
medweight	41	21	19
overweight	39	8	10
overweight	33	23	0

1. What are your F_crit values?
2. If there is a significant difference between the weights, where specifically are the differences?
3. Is there a significant interaction between weight and dosage? Why/why not?

Answer 1

using excel>data >data analysis>two way anova

we have

Anova: Two-Factor With Replication
SUMMARY	Placebo	Moderate Dose	High Dose	Total
underweight
Count	2	2	2	6
Sum	94	41	27	162
Average	47	20.5	13.5	27
Variance	50	4.5	0.5	260.8
medweight
Count	2	2	2	6
Sum	82	52	31	165
Average	41	26	15.5	27.5
Variance	0	50	24.5	146.3
overweight
Count	2	2	2	6
Sum	72	31	10	113
Average	36	15.5	5	18.83333
Variance	18	112.5	50	234.9667
Total
Count	6	6	6
Sum	248	124	68
Average	41.33333	20.66667	11.33333
Variance	37.86667	55.46667	39.86667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	284.1111	2	142.0556	4.124194	0.053546	4.256495
Factor B	2828.444	2	1414.222	41.05806	2.99E-05	4.256495
Interaction	71.88889	4	17.97222	0.521774	0.722608	3.633089
Within	310	9	34.44444
Total	3494.444	17

1. Fcrit values are 4.257 and 3.633
2. since p value of Factor B (weights) are less than 0.05 so we can say that there is a significant difference between the weights.
3. NO there a not significant interaction between weight and dosage because p value is greater than 0.05