Question

(Chapter 15) A psychologist conducts a two-factor study comparing the effectiveness of two different therapy techniques (factor A) for treating mild and severe phobias (factor B). The dependent variable is a measure of fear for each participant. If the study uses n= 9 participants in each of the five conditions, then identify the df values for each of the three F-Ratios.  Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers.

Answer 1

There are two different therapy techniques (Factor A) and two different phobias, mild and severe (factor B)

The data table will look like this,

	Therapy 1	Therapy 2
mild	9 replications	9 replications
severe	9 replications	9 replications

and the two way ANOVA table with replication for the given data values will look like this,

ANOVA
Source of Variation	df	SS	MS	F	P-value
Phobias	r - 1 = 2 - 1 = 1	.	.	.	.
Therapy	c - 1 = 2 - 1 = 2	.	.	.	.
Interaction	(r-1)(c-1) = (2-1)(2-1) = 1	.	.	.	.
Within	n - r*c = 36 - 2*2 = 32	.	.	.	.
Total	n - 1 = 36 - 1 = 35	.	.	.	.

where, r = number of rows, c = number of columns, and n = total data points in 4 treatment conditions.

The F value is obtained using the formula, F = MS (treatment)/ MS (within). hence the numerator degree of freedom is the degree of freedom corresponds to MS (treatment) and the denominator degree of freedom is the degree of freedom corresponds to MS (Within)

For Phobias

numerator df = 1, denominator df = 32

For Therapy

numerator df = 1, denominator df = 32

For interaction

numerator df = 1, denominator df = 32

,