﻿ Two-Way Full Repeated Analysis of Variance

# Two-Way Full Repeated Analysis of Variance

### Statistics > ANOVA > Two-Way Two

Performs a balanced two-way analysis of variance with repeated measures on both factors.

### Dialog box items

Response:
Enter the column containing the response variable.

Factor A:
Enter one of the factor level columns.

Factor B:
Enter the other factor level column

Report:
The display of outputs of VisualStat.

### Data

The response variable must be numeric and in one column. You must have a single factor level column for each of the two factors. These can be numeric, or text.

### Charts

Displays a histogram, a histogram with a normal curve, and a boxplot.

Histogram:
Choose to display a histogram for each variable

Histogram with Normal Curve:
Choose to display a histogram with a normal curve for each variable

Boxplot of data:
Choose to display a boxplot for each variable

Options:
Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.

### Options

Display means for Factor A:
Check to compute marginal means and confidence intervals for each level of the row factor

Display means for Factor B:
Check to compute marginal means and confidence intervals for each level of the column factor

Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

### Example

The file Look contains data for the following study:

A researcher was interested in whether frequency of exposure to a picture of an ugly or attractive person would influence one's liking for the photograph. In order to find out the researcher, at the start of each class he taught, pinned a large photograph of an ugly and attractive person in front of the class. At the end of the class period the students in the class were asked to rate on a 7 point liking scale the extent to which they found the persons depicted in the photos to be likeable on a scale similar to the one below.

unlikeable -3 -2 -1 0 1 2 3 likeable

The psychologist posted the pictures at the start of each class period and had the students rate their liking for the two pictures at the end of the lst class, again after 5 classes and finally again after 10 classes. Thus each student gave 3 ratings for each of the two photographs (after 1 exposure, 5 exposures and 10 exposures).

1.Open the DataBook anova.vstz

2.Select the sheet Look

3.Choose the tab Statistics, the group Anova and the command Two-Way Two

4.In Response, select Rating. In Factor A, select Photo. In Factor B, select Day.

5.Click Options page

6.Check Display means for Factor A and check Display means for Factor B

7.Click OK

Report window output

Two-Way Full Repeated Analysis of Variance

-=-=-=-= Rating / Photo / Day =-=-=-=-

ANOVA TABLE

df  SumOfSquares  Mean Square          F          P

Photo                        1          73.5      73.5000   147.0000     0.0012

Day                          2        0.3333       0.1667     0.6000     0.5787

Interaction                  2             12       6.0000    18.0000     0.0029

Day, Subject Interaction     6        1.6667       0.2778

Photo, Subject Interaction   3           1.5       0.5000

Error                        6             2       0.3333

Total                       23        93.3333

Photo        N     Mean   StDev  SE Mean   Effect  95% LCL  95% UCL  Minimum  Maximum

attractive  12   1.9167  0.7930   0.2289   1.7500   1.4128   2.4205   1.0000   3.0000

ugly        12  -1.5833  1.0836   0.3128  -1.7500  -2.2718  -0.8948  -3.0000   0.0000

<total>     24   0.1667  2.0144   0.4112   0.0000  -0.6840   1.0173  -3.0000   3.0000

Day       N    Mean   StDev  SE Mean   Effect  95% LCL  95% UCL  Minimum  Maximum

1         8  0.2500  1.4880   0.5261   0.0833  -0.9940   1.4940  -2.0000   2.0000

10        8  0.0000  2.9761   1.0522  -0.1667  -2.4881   2.4881  -3.0000   3.0000

5         8  0.2500  1.4880   0.5261   0.0833  -0.9940   1.4940  -2.0000   2.0000

<total>  24  0.1667  2.0144   0.4112   0.0000  -0.6840   1.0173  -3.0000   3.0000