Split plot ANOVA is mostly used by SPSS researchers when the two fixed factors (predictors) are nested. This means the two groupings of the treatments interact influencing the predicted. In this case either of the treatment can be used as whole or sub plots showing that they interact

In split-plot ANOVA test, you have 2 independent variables:
a. Between-Subjects Factor – Composed of two or more groups of completely different people.
b. Within-Subjects Factor – Composed of two or more groups that consist of the same people.
It is used when two independent variables have been manipulated using different participants in all conditions. Assumptions of split-plot comprise the following:
i. Random Sampling
ii. Normality
iii. Null Hypothesis
iv. Homogeneity of Variance

Homogeneity of Variance
a)Of the Between-Group Means- The Variance of the means is equal for each group between subjects. This can be tested by doing a one-way ANOVA on these subject means and looking at Levene’s test results.

b)Equality of the Variance-Covariance Matrix across treatment levels of Between Groups Factor- Tells you if the variance/covariance matrices associated with each Between-groups factor is the same. This is tested using the Box’s M test.

c)Circularity of the Pooled Variance/Covariance Matrix- Tests whether all the variances apost hocare equal, and all the covariances are equal for the pooled matrix. If not, then the Type I error rate is inflated. (Rejecting the null hypothesis when the null hypothesis is true) It is tested using Mauchly’s W test.
We will look at a comprehensive illustration that’ll help us appreciate the application of split-plot ANOVA in SPSS research.
Case Study
EABL, a leading Brewery in East Africa had a panel of statisticians in close synergy with a leading psychologist unit in the city who were interested in the effects of alcohol on mate selection at night-clubs. The hypothesis was that after alcohol had been consumed, subjective feelings of physical attractiveness would get more inaccurate. They were also interested in whether this effect was different for males and females. They picked a sample of 48 people, 24 men and 24 women. They then took groups of participants to a night-club and gave them no alcohol (participants got placebo drinks of alcohol-free lager, 2 pints of strong lager, or 4 pints of strong lager). At the end of the evening they took a photograph of the person that the participant was chatting up with. They then got a pool of independent raters to assess the attractiveness of the person in each photograph out of 100.

Inputting Data
It’s important to note that levels of between group variables go in a single column of the SPSS data editor. We are therefore going to need to create 2 different coding variables in the data editor which will represent gender and alcohol consumption. So create a variable called Gender in the data editor and activate the labels dialog box. You should define value labels to represent the two genders. I’ll use Male=0 and Female=1. After this is done, you can enter a code of 0 or 1 in this column indicating to which group the participant belonged. Create a second variable called Alcohol and assign group codes by using the labels dialog box. I recommend you code this variable using three variables with three values: Placebo (no Alcohol)=1, 2 Pints=2, and 4 Pints=3. You can now enter 1, 2 or 3 into this column to represent the amount of alcohol consumed by the participant.
Once the two coding variables are created, you can create a third variable in which to place the values of the dependent variable. Call this variable attract and use the labels option to give it the fuller name of ‘Attractiveness of Date’. In our example, there are two independent variables and different participants were used in each condition, therefore we can use the general factorial ANOVA procedure in SPSS. This procedure is designed for analysing between-group factorial designs:
1. Enter the data into SPSS
2. Save the data onto a disk in a file called Beer.sav
3. Plot an error graph of the mean attractiveness of mates across the different levels of alcohol
4. Plot an error bar graph of the mean attractiveness of mates selected by males and females

The Main Dialog Box
To access the main dialog box, use the file path Analyze-General Linear Model-Univariate. The resulting dialog box will be displyed. First, select the dependent variable Attractiveness from the variables list on the left-hand side of the dialog box and drag it to the space labelled Dependent Variable. Select Alcohol and Gender in the variables list and drag them to the Fixed Factor(s) box .

Graphing Interactions
Click on Plots to access the dialog box. The plots dialog box allows you to select line graphs of your data and these graphs are very useful for interpreting interaction effects. We have only two independent variables, and the most useful plot is one that shows the interaction between the two variables. In this case, the interaction graph wil help us to interpret the combined effect of gender and alcohol consumption. Select Alcohol from the variables list on the left—hand side of the dialog box and drag it to the space labelled Horizontal Axis. In the space labelled Seperate Lines place the remaining independent variable, Gender. Click on Add and this plot will be added to the list at the bottom of the box. Click on Continue to return to the main dialog box.

Post Hoc Tests
This dialog box is obtained by clicking on Post Hoc tab in the main dialog box. The variable Gender has only two levels and so we don’t need to select post hoc tests for that variable (because any significant tests can reflect only the difference between males and females). However, there were three levels of the Alcohol variable (no alcohol, 2 pints and 4 pints); hence we can conduct post hoc tests. First, you should select the variable Alcohol from the box labelled Factors and transfer it to the box labelled Post Hoc Tests for. Click on Continue to return to the main dialog box.

Options
Click on Define to activate another dialog box. First, you can ask for some descriptive statistics, which will display a table of the means and standard deviations. This is a useful option to select as it helps in interpreting the final results. A vital option to select is the homogeneity of variance tests. Once these options have been selected, click on Continue to return to the main dialog box, then click on OK to run the analysis.

Output from Factorial ANOVA
Output from the Preliminary Analysis
It shows the initial output from factorial ANOVA. This table of descriptive statistics is produced since we asked for descriptives in the options dialog box and it displays the means, standard deviations and number of participants in all conditions of the experiment.

Levene’s Test
Here, a non-significant result is indicative of the homogeneity of variance assumption being met.

Main ANOVA Table
This is the most important part of the output because it tells us whether any of the independent variables have had an effect. The important things to look at in the table are the significance values of the independent variables. The F ratio is highly significant as well. To intepret both F ratio and significance values comprehensively, we look at the bar chart that we plotted of the average mark for each level of alcohol (ignoring gender completely). While reporting, both for the interaction effect and the main effects, it’s important to quote both the F ratio and significance values. An example would be: ‘’There was a significant interaction/main effect between the amount of alcohol consumed and the gender of the person selecting a mate, on the attractiveness of the partner selected, F(a,b)=10.1, p<0.001’’

Post Hoc Analysis
The post hoc tests break down the main effect of alcohol and can be interpreted as if a one-way ANOVA has been conducted on the alcohol variable. The Bonferroni and Games-Howell tests show the same pattern of results. The R-E-G-W-Q test confirms facts with relation to the means of the two groups of variables tested. It should be noted that these post hoc tests ignore the interactive effect of gender and alcohol.

APPLYING SPLIT-PLOT ANOVA TEST IN SPSS RESEARCH

Split plot ANOVA is mostly used by SPSS researchers when the two fixed factors (predictors) are nested. This means the two groupings of the treatments interact influencing the predicted. In this case either of the treatment can be used as whole or sub plots showing that they interact

In split-plot ANOVA test, you have 2 independent variables:

a. Between-Subjects Factor – Composed of two or more groups of completely different people.

b. Within-Subjects Factor – Composed of two or more groups that consist of the same people.

It is used when two independent variables have been manipulated using different participants in all conditions. Assumptions of split-plot comprise the following:

i. Random Sampling

ii. Normality

iii. Null Hypothesis

iv. Homogeneity of Variance

Homogeneity of Variance

a)Of the Between-Group Means- The Variance of the means is equal for each group between subjects. This can be tested by doing a one-way ANOVA on these subject means and looking at Levene’s test results.

b)Equality of the Variance-Covariance Matrix across treatment levels of Between Groups Factor- Tells you if the variance/covariance matrices associated with each Between-groups factor is the same. This is tested using the Box’s M test.

c)Circularity of the Pooled Variance/Covariance Matrix- Tests whether all the variances apost hocare equal, and all the covariances are equal for the pooled matrix. If not, then the Type I error rate is inflated. (Rejecting the null hypothesis when the null hypothesis is true) It is tested using Mauchly’s W test.

We will look at a comprehensive illustration that’ll help us appreciate the application of split-plot ANOVA in SPSS research.

Case Study

EABL, a leading Brewery in East Africa had a panel of statisticians in close synergy with a leading psychologist unit in the city who were interested in the effects of alcohol on mate selection at night-clubs. The hypothesis was that after alcohol had been consumed, subjective feelings of physical attractiveness would get more inaccurate. They were also interested in whether this effect was different for males and females. They picked a sample of 48 people, 24 men and 24 women. They then took groups of participants to a night-club and gave them no alcohol (participants got placebo drinks of alcohol-free lager, 2 pints of strong lager, or 4 pints of strong lager). At the end of the evening they took a photograph of the person that the participant was chatting up with. They then got a pool of independent raters to assess the attractiveness of the person in each photograph out of 100.

Inputting Data

It’s important to note that levels of between group variables go in a single column of the SPSS data editor. We are therefore going to need to create 2 different coding variables in the data editor which will represent gender and alcohol consumption. So create a variable called Gender in the data editor and activate the labels dialog box. You should define value labels to represent the two genders. I’ll use Male=0 and Female=1. After this is done, you can enter a code of 0 or 1 in this column indicating to which group the participant belonged. Create a second variable called Alcohol and assign group codes by using the labels dialog box. I recommend you code this variable using three variables with three values: Placebo (no Alcohol)=1, 2 Pints=2, and 4 Pints=3. You can now enter 1, 2 or 3 into this column to represent the amount of alcohol consumed by the participant.

Once the two coding variables are created, you can create a third variable in which to place the values of the dependent variable. Call this variable attract and use the labels option to give it the fuller name of ‘Attractiveness of Date’. In our example, there are two independent variables and different participants were used in each condition, therefore we can use the general factorial ANOVA procedure in SPSS. This procedure is designed for analysing between-group factorial designs:

1. Enter the data into SPSS

2. Save the data onto a disk in a file called Beer.sav

3. Plot an error graph of the mean attractiveness of mates across the different levels of alcohol

4. Plot an error bar graph of the mean attractiveness of mates selected by males and females

The Main Dialog Box

To access the main dialog box, use the file path Analyze-General Linear Model-Univariate. The resulting dialog box will be displyed. First, select the dependent variable Attractiveness from the variables list on the left-hand side of the dialog box and drag it to the space labelled Dependent Variable. Select Alcohol and Gender in the variables list and drag them to the Fixed Factor(s) box .

Graphing Interactions

Click on Plots to access the dialog box. The plots dialog box allows you to select line graphs of your data and these graphs are very useful for interpreting interaction effects. We have only two independent variables, and the most useful plot is one that shows the interaction between the two variables. In this case, the interaction graph wil help us to interpret the combined effect of gender and alcohol consumption. Select Alcohol from the variables list on the left—hand side of the dialog box and drag it to the space labelled Horizontal Axis. In the space labelled Seperate Lines place the remaining independent variable, Gender. Click on Add and this plot will be added to the list at the bottom of the box. Click on Continue to return to the main dialog box.

Post Hoc Tests

This dialog box is obtained by clicking on Post Hoc tab in the main dialog box. The variable Gender has only two levels and so we don’t need to select post hoc tests for that variable (because any significant tests can reflect only the difference between males and females). However, there were three levels of the Alcohol variable (no alcohol, 2 pints and 4 pints); hence we can conduct post hoc tests. First, you should select the variable Alcohol from the box labelled Factors and transfer it to the box labelled Post Hoc Tests for. Click on Continue to return to the main dialog box.

Options

Click on Define to activate another dialog box. First, you can ask for some descriptive statistics, which will display a table of the means and standard deviations. This is a useful option to select as it helps in interpreting the final results. A vital option to select is the homogeneity of variance tests. Once these options have been selected, click on Continue to return to the main dialog box, then click on OK to run the analysis.

Output from Factorial ANOVA

Output from the Preliminary Analysis

It shows the initial output from factorial ANOVA. This table of descriptive statistics is produced since we asked for descriptives in the options dialog box and it displays the means, standard deviations and number of participants in all conditions of the experiment.

Levene’s Test

Here, a non-significant result is indicative of the homogeneity of variance assumption being met.

Main ANOVA Table

This is the most important part of the output because it tells us whether any of the independent variables have had an effect. The important things to look at in the table are the significance values of the independent variables. The F ratio is highly significant as well. To intepret both F ratio and significance values comprehensively, we look at the bar chart that we plotted of the average mark for each level of alcohol (ignoring gender completely). While reporting, both for the interaction effect and the main effects, it’s important to quote both the F ratio and significance values. An example would be: ‘’There was a significant interaction/main effect between the amount of alcohol consumed and the gender of the person selecting a mate, on the attractiveness of the partner selected, F(a,b)=10.1, p<0.001’’

Post Hoc Analysis

The post hoc tests break down the main effect of alcohol and can be interpreted as if a one-way ANOVA has been conducted on the alcohol variable. The Bonferroni and Games-Howell tests show the same pattern of results. The R-E-G-W-Q test confirms facts with relation to the means of the two groups of variables tested. It should be noted that these post hoc tests ignore the interactive effect of gender and alcohol.