First select just the young people, by clicking on "Data", "Select cases", "If condition is satisfied". Now tell SPSS you have two factors, sex and text type.
Ignore the main effects. If this two way interaction is significant, you can try to obtain information about its interpretation just as you did in module 2 by analyzing the effect of e. Now to select the relevant cases you would have to set the selection condition to e.
Having analyzed the two-way interaction for young people, you would test the two-way interaction for middle-aged people. If that interaction was significant, you would look at simple effects to interpret it. Notice the logic of the procedure here. To interpret a three-way interaction, you break it down into several two-way interactions.
These are called partial interactions, because they are interactions calculated on only part of the data. To interpret a two-way interaction, you break it down into several one-way effects i. In general, an n-way interaction can be interpreted by breaking it down into its component n - 1 -way partial interactions. These partial interactions can be interpreted in turn by breaking them down into n - 2 -way partial interactions, and so on.
However, in case you decide it would be interesting to interpret the two-way interaction. You break down the two-way into 1 a simple effect of text type for women averaging over both ages and 2 a simple effect of text type for men averaging over both ages. To test 1 use select cases to select just the women. To test 2 , use select cases to select just the men, and repeat the procedure. Note what you have done: You have interpreted a two-way interaction by breaking it down into two one-ways.
For your third-year project bear the following in mind: A rule of thumb in analyzing n-way designs is that you are allowed to analyze n - 1 -way partial interactions ONLY IF the n-way interaction is significant. The analyses that you perform only when some other analysis is significant are called post-hoc analyses.
Newman-Keuls is an example of a post hoc analysis. For example, following this rule for the current data set, you could only test the two-way interaction sex by text type for just young people if the three-way interaction was significant. In a similar way, you can only test for simple effects if the two-way interaction was significant. This interaction also needs to be understood.
We will once again have to use the correct error term and compute the F-ratio manually. We will continue to use a critical value based on the per family error rate. The critical value with 2 and 12 degrees of freedom is about 5. With real data we would do that but, for now, it is a topic for another page. Which looks something like this. If you would like more details on how to implement these tests following a significant three-way interaction, there are more detailed pages for SPSS and Stata.
Reference Kirk, Roger E. View Larger Image. Assumptions In order to run a three-way repeated measures ANOVA, there are five assumptions that need to be considered. The first two relate to your choice of study design, whilst the other three reflect the nature of your data: Assumption 1: You have one dependent variable that is measured at the continuous level i. Examples of continuous variables include revision time measured in hours , intelligence measured using IQ score , exam performance measured from 0 to , weight measured in kg , and so forth.
Assumption 2: You have three within-subjects factors where each within-subjects factor consists of two or more categorical levels. Both terms are explained below: A factor is another name for an independent variable. For now, all you need to know is that a within-subjects factor is another name for an independent variable in a three-way repeated measures ANOVA where the same cases e.
Assumption 3: There should be no significant outliers in any cell of the design. Outliers are simply data points within your data that do not follow the usual pattern e. The problem with outliers is that they can have a negative impact on the three-way repeated measures ANOVA by: a distorting the differences between cells of the design; and b causing problems when generalizing the results of the sample to the population.
Due to the effect that outliers can have on your results, you have to choose whether you want to: a keep them in your data; b remove them; or c alter their value in some way. Assumption 4: Your dependent variable should be approximately normally distributed for each cell of the design.
The assumption of normality is necessary for statistical significance testing using a three-way repeated measures ANOVA. This means that some violation of this assumption can be tolerated and the test will still provide valid results.
Therefore, you will often hear of this test only requiring approximately normally distributed data. Furthermore, as sample size increases, the distribution can be very non-normal and, thanks to the Central Limit Theorem, the three-way repeated measures ANOVA can still provide valid results. Also, it should be noted that if the distributions are all skewed in a similar manner e. Therefore, in this example, you need to investigate whether strength scores are normally distributed for each cell of the design.
Assumption 5: The variance of the differences between groups should be equalThis assumption is referred to as the assumption of sphericity. It is sometimes described as the repeated measures equivalent of the homogeneity of variances and refers to the variances of the differences between the levels rather than the variances within each level.
This assumption is necessary for statistical significance testing in the three-way repeated measures ANOVA. This assumption is very important and violation of sphericity can lead to invalid results. STEP 1: Do you have a statistically significant three-way interaction? A three-way interaction is when one or more simple two-way interactions are different at the level of a third factor on the dependent variable. Which of your three factors make up the simple two-way interaction and which acts as the third factor will depend of your study design.
In other words, is the effect of the interaction between weights and time on strength scores affected by whether cardiovascular training is present?
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