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PSYC 3002

Analysis of Variance (ANOVA)

Bachelor of Science in Psychology, Walden University

PSYC 3002: Introduction to Basic Statistics

Analysis of Variance (ANOVA)

1. The null hypothesis is that there will not be any significant differences in the group

mean anxiety scores. The alternative hypothesis is that there will be at least one group

with an anxiety reduction mean that is different from at least one other group’s mean.

According to Bjorkman (2015), hypothesis for ANOVA are different; we do not

predict all the means will differ, nor do we predict specific factor-level differences

when stating our null and alternative hypothesis because we are comparing multiple

groups at once.

2. The factor, or independent variable (Heiman, 2015), is the type of therapy the

participants received for their anxiety. The dependent variable is the anxiety levels

measured upon completion of the experiment.

3. The levels of the factor are “the conditions of the independent variable” (Heiman,

2015, Pg. 186). The levels in the provided scenario are the four different types of

therapy the participants received for their anxiety: behavioral, cognitive, biofeedback,

and medication.

4. According to Heiman (2015), to compute the degree of freedom between groups, take

the number of levels in the factors (k) and subtract it by 1 (df=k-1). Since there are

four levels of the factor in this scenario, the equation would look like this 4 – 1 = 3.

Thus, the degree of freedom between groups is 3.

5. According to Heiman (2015), the formula for the degree of freedom within groups is

the total number of participants (N) minus the total number of factors. There are 20

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participants in this study and there are 4 levels of factors. Therefore, 20 – 4 = 16. The

degree of freedom within groups is 16.

6. According to the SPSS output, the F value is equal to 13.749

7. The p value, using SPSS, is less than .001 (.000)

8. In this study, the results of the F test were highly significant with a p value that is less

than the 0.05 level of significance of .000, which means that at least one type of

therapy produced a different level of anxiety than the other three. Therefore, we

should reject the null hypothesis.

9. Prior to post hoc testing, psychologist can only conclude that differences in anxiety

scores do exist amongst the four methods of therapy. When we use a one-way

ANOVA, we are unable to conclude the actual relationships between the different

types of therapy and their anxiety scores. The is because the F statistic cannot indicate

which statistic means differ significantly (Heiman, 2015).

10. In this study, the results were statistically significant; therefore, the psychologist

should perform a post-hoc test. Performing the post hoc testing will allow us to see if

there is only one group that is significantly better than the others, or if differences in

effectiveness exist in all of the groups (Bjorkman, 2015).

The Tukey HSD results calculated in SPSS tell us the following:

First, in the significant levels for the behavioral group, there is not a not a significant

difference between behavioral and biofeedback or medication, but there is a

significant difference between behavioral and cognitive, which means that the

veterans that received cognitive therapy had a significantly different anxiety level

mean than the veterans that received behavioral therapy. Second, we can look at the

biofeedback group and see the only significant differences are between biofeedback

therapy group and cognitive therapy group, and the same goes for the medication

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PSYC 3002 Analysis of Variance (ANOVA) Bachelor of Science in Psychology, Walden University PSYC 3002: Introduction to Basic Statistics Analysis of Variance (ANOVA) 1. The null hypothesis is that there will not be any significant differences in the group mean anxiety scores. The alternative hypothesis is that there will be at least one group with an anxiety reduction mean that is different from at least one other group’s mean. According to Bjorkman (2015), hypothesis for ANOVA are different; we do not predict all the means will differ, nor do we predict specific factor-level differences when stating our null and alternative hypothesis because we are comparing multiple groups at once. 2. The factor, or independent variable (Heiman, 2015), is the type of therapy the participants received for their anxiety. The dependent variable is the anxiety levels measured upon completion of the exper ...
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