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# PY3101 Advanced Behavioural Research Design And Analysis

## Question:

Using an ANOVA…

• We can compare more than two conditions
• We can investigate the effects of two or more independent variables on a dependent variable
• This saves time, and allows us to see how IVs ‘interact’ to affect the DV
• For example, on a memory task, science majors do better after practicing with rote memory but fine arts majors do better with mnemonic training.
• Another example: before being stressed, the RT for young and old individuals is comparable. But, during and after stress, young individuals have a faster RT than old participants.

Why not use lots of t-tests?• Performing repeated t-tests increases the familywise error rate. This refers to the error rate across statistical tests conducted on the same data

In a two-way ANOVA you have two independent nominal level IVs and one interval-or-better DV

• Each IV may have any number of levels or conditions (e.g., Treatment 1, Treatment 2, Treatment 3…… No Treatment)
• In a two-way ANOVA you will obtain 3 F ratios:

– Does the first IV have a significant main effect on the DV

– Does the second IV have a significant main effect?

– Does the interaction of the two independent variables have a significant effect on the DV, that is, if the impact of one IV depends on the level of the other

MANOVA is useful in experimental situations where at least some of the independent variables are manipulated. It has several advantages over ANOVA.

– By measuring several dependent variables in a single experiment, there is a better chance of discovering which factor is truly important.

– It can protect against Type I errors that might occur if multiple ANOVA’s were conducted independently.

– It can reveal differences not discovered by ANOVA tests.

• Consider using the MANOVA when there are several correlated DVs, and you want a single, overall statistical test on this set of variables instead of performing multiple individual tests.
• MANOVA is also useful to explore how independent variables influence some patterning of response on the dependent variables. That is, how the IV differentially predicts the DVs.
• MANOVA is also considered a valid alternative to the repeated measures ANOVA when sphericity (i.e., equal variances of the differences between all possible pairs of groups) is violated.

Main Effects:

• Do the linearly combined DV’s change per level of each IV singularly? (Holding all other effects constant…e.g. inclusion of covariates, other IVs etc.)
• Does change in the linearly-combined DV for one IV depend on the levels of another IV?
• For example: Given three types of treatment, does one treatment work better for men and another work better for women?
• If equal samples in each cell then one interaction is independent of main effects and other interactions

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[Accessed 01 June 2023].

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