Researchers investigated the prevalence of personality disorders among adolescents who were psychiatric inpatients and had one of three diagnoses: (1) diagnosis 1, (2) diagnosis 2, and (3) both diagnosis 1 and diagnosis 2. The mean number of disorders was as follows: diagnosis 1

M=1.1,

diagnosis 2

M=0.7,

both diagnoses

M=1.9.

The researchers reported, "The three study groups differed in the average number of diagnosed personality disorders,

F(2,126)=11.64,

p<0.0001."

Explain this result to someone who is familiar with hypothesis testing with known populations but is unfamiliar with the t test or the analysis of variance.

The null hypothesis is that the three groups are from populations of number of personality disorders with

If this null hypothesis is

the variance of these populations can be estimated in two ways. (i) Estimate from the variation within each of the three groups and then

them. (ii) Estimate from the variation between the three means,

by the size of each sample group. Since the estimates should be approximately equal, the ratio of the two estimates should be approximately 1. If the null hypothesis is

the estimate (ii) is

than the estimate (i) and the ratio, F, of (i) to (ii) is

than 1. The fact that

F=11.64

is much larger than 1 and

p<0.0001

indicates that the null hypothesis

be rejected.

Anwers

a. equal or different

b. false or true

c. sum or average

d. dividing or multiplying

e. false or true

f. less or greater

g. less or greater

h. can or cannot