Calculation Assignment

2-Way ANOVA

Researchers were interested in whether a cognitive-behavioral group therapy intervention would reduce symptoms of depression among male students in a particular high school. Thirty students were randomly assigned to either the intervention group or the control group, with 15 in each group. The depression level of all students was measured at the beginning of the study (Time 1) and again at the end (Time 2). A two-way mixed ANOVA was used to determine the impact of the intervention. The two independent variables were time of assessment (Time 1 vs. Time 2) and treatment (intervention group vs. control group). (Note that this is considered a “mixed” ANOVA because treatment is a between-group variable, and time of assessment is a within-group/repeated measures variable.)

3171825748665From the data table, notice that “Treatment” is represented by columns and “Time” is represented by rows. Also note that what we call “Rows,” Excel calls “Sample.”

400000From the data table, notice that “Treatment” is represented by columns and “Time” is represented by rows. Also note that what we call “Rows,” Excel calls “Sample.”

Use the data below to calculate a two-way ANOVA in Excel. Answer the questions that follow and include a copy of your results.

Intervention Group Control Group

Time 1 7 17

12 7

10 16

15 14

18 7

12 11

12 9

11 10

18 12

9 9

13 15

9 9

9 10

10 10

8 9

Time 2 9 16

12 8

10 15

9 9

7 16

6 14

6 9

10 11

10 10

14 8

10 17

7 9

9 18

8 12

10 19

Instructions:

Copy the data table above into Excel.

From the Data tab, click on Data Analysis. (If the Data Analysis option does not appear, add it by clicking File, Options, Add-Ins, Analysis ToolPak, Go, OK, as detailed in previous assignments.)

Select Anova: Two-Factor With Replication and then click on OK.

Click in the Input Range Box

Select the entire data set, including all labels, by clicking on the top-left cell and dragging the mouse to the bottom-left cell before releasing the click.

“Rows per sample” is the number of participants in each group, which in this case is 15.

Select .05 as the alpha level.

Under Output options, select Output Range button and then click in the Output Range box.

Click on the cell where you want your results to begin.

Click OK

Answer the questions below.

Copy and paste the results (screen print, Snippit, or whatever works for you) to the bottom of the assignment.

QUESTIONS:

This is a 2×2, 2-way ANOVA. How many cells are there?

The Excel table provides a column for the degrees of freedom. Tell how many df there are for each of the following:

df Time ________________

df Treatment _____________

df Interaction ____________

df Within______________

df Total___________

Notice that the results table (source table) from Excel gives the three values of F – one each for the main effect of time, the main effect of treatment and the interaction of treatment X time. For each, report the calculated value of F, it’s associated p-value, and the critical value of F for the stated degrees of freedom. Then determine if each effect is statistically significant.

Effect The calculated value of F P-value Critical Value of F

(F crit) Is this result statistically significant? (yes or no)

Time (“Sample”) Treatment (“Columns”) Interaction For any statistically significant effect, write the results in APA format. Remember to include both values of df in parenthesis.

In one or two sentences, describe the results of the study.

Explain how the graph below (created from the data) illustrates an interaction effect.

Copy of Excel results: