Repeated Measures MANOVA Planned Comparisons & Profile Analysis
Introduction
Repeated measures MANOVA is a statistical technique used to analyze the relationship between multiple dependent variables (DVs) and one or more independent variables (IVs) when the same participants are measured under different conditions. In this article, we will discuss how to conduct planned comparisons and profile analysis after a significant repeated measures MANOVA.
Understanding the Design
In your study, you have a repeated measures design with one IV (4 conditions) and 2 DVs. This means that each participant has been exposed to each of the 4 conditions, and you have measured 2 outcomes for each condition. The repeated measures MANOVA will help you to determine if there are significant differences between the conditions for both DVs.
Assuming Significance
Assuming that the MANOVA and univariate tests are significant, you would like to conduct planned comparisons and profile analysis to further explore the results. Planned comparisons involve comparing specific pairs of conditions to determine if there are significant differences between them. Profile analysis, on the other hand, involves examining the pattern of means across the conditions to identify any trends or patterns.
Planned Comparisons
Planned comparisons are a type of post-hoc analysis that involves comparing specific pairs of conditions to determine if there are significant differences between them. There are several types of planned comparisons that you can conduct, including:
- Simple comparisons: These involve comparing two specific conditions to determine if there is a significant difference between them.
- Contrast comparisons: These involve comparing a set of conditions to determine if there is a significant difference between them.
- Polynomial comparisons: These involve comparing a set of conditions to determine if there is a significant difference between them, based on a polynomial trend.
Conducting Planned Comparisons
To conduct planned comparisons, you will need to use a statistical software package, such as SPSS or R. The specific steps will depend on the software you are using, but the general process is as follows:
- Determine the planned comparisons: Decide which pairs of conditions you would like to compare.
- Specify the contrast: Specify the contrast that you would like to use for each planned comparison.
- Conduct the planned comparison: Use the statistical software to conduct the planned comparison.
Profile Analysis
Profile analysis involves examining the pattern of means across the conditions to identify any trends or patterns. This can be done using a variety of techniques, including:
- Linear trend analysis: This involves examining the pattern of means to determine if there is a linear trend across the conditions.
- Quadratic trend analysis: This involves examining the pattern of means to determine if there is a quadratic trend across the conditions.
- Non-linear trend analysis: This involves examining the pattern of means to determine if there is a non-linear trend across the conditions.
Conducting Profile Analysis
To conduct profile analysis, you will need to use a statistical software package, such as SPSS or R. The specific steps will depend on the software you are using, but the general process is as follows:
- Examine the pattern of means: Examine the of means across the conditions to identify any trends or patterns.
- Specify the trend: Specify the trend that you would like to examine (e.g. linear, quadratic, non-linear).
- Conduct the profile analysis: Use the statistical software to conduct the profile analysis.
Interpreting Results
When interpreting the results of planned comparisons and profile analysis, it is essential to consider the following:
- Effect size: Consider the effect size of the planned comparison or profile analysis to determine the practical significance of the results.
- Multiple testing: Consider the issue of multiple testing, as planned comparisons and profile analysis can involve multiple tests.
- Confidence intervals: Consider using confidence intervals to provide a range of values for the planned comparison or profile analysis.
Conclusion
Introduction
In our previous article, we discussed how to conduct planned comparisons and profile analysis after a significant repeated measures MANOVA. In this article, we will answer some of the most frequently asked questions about planned comparisons and profile analysis.
Q: What is the difference between planned comparisons and post-hoc tests?
A: Planned comparisons and post-hoc tests are both types of post-hoc analyses, but they serve different purposes. Planned comparisons are used to test specific hypotheses about the relationships between the conditions, while post-hoc tests are used to identify any significant differences between the conditions.
Q: How do I determine which planned comparisons to conduct?
A: To determine which planned comparisons to conduct, you should consider the following:
- Research question: Consider the research question that you are trying to answer. What specific hypotheses do you want to test?
- Theoretical background: Consider the theoretical background of your study. What are the expected relationships between the conditions?
- Practical significance: Consider the practical significance of the planned comparison. Will it provide useful information about the relationships between the conditions?
Q: What is the difference between a simple comparison and a contrast comparison?
A: A simple comparison involves comparing two specific conditions to determine if there is a significant difference between them. A contrast comparison involves comparing a set of conditions to determine if there is a significant difference between them.
Q: How do I specify a contrast for a planned comparison?
A: To specify a contrast for a planned comparison, you should consider the following:
- Theoretical background: Consider the theoretical background of your study. What are the expected relationships between the conditions?
- Practical significance: Consider the practical significance of the planned comparison. Will it provide useful information about the relationships between the conditions?
- Statistical software: Consider the statistical software that you are using. Different software packages may have different procedures for specifying contrasts.
Q: What is the difference between linear trend analysis and quadratic trend analysis?
A: Linear trend analysis involves examining the pattern of means to determine if there is a linear trend across the conditions. Quadratic trend analysis involves examining the pattern of means to determine if there is a quadratic trend across the conditions.
Q: How do I determine if there is a significant trend in the data?
A: To determine if there is a significant trend in the data, you should consider the following:
- Visual inspection: Examine the pattern of means to determine if there is a trend.
- Statistical analysis: Use statistical software to conduct a trend analysis.
- Effect size: Consider the effect size of the trend to determine the practical significance of the results.
Q: What is the issue with multiple testing in planned comparisons and profile analysis?
A: The issue with multiple testing in planned comparisons and profile analysis is that it can lead to Type I errors. This is because each planned comparison or profile analysis is a separate test, and the probability of a Type I error increases with the of tests.
Q: How can I control for multiple testing in planned comparisons and profile analysis?
A: To control for multiple testing in planned comparisons and profile analysis, you can use the following strategies:
- Bonferroni correction: Divide the alpha level by the number of tests to control for multiple testing.
- Holm-Bonferroni method: Use a more conservative method to control for multiple testing.
- False discovery rate (FDR) correction: Use a method that controls for the false discovery rate.
Conclusion
In conclusion, planned comparisons and profile analysis are essential tools for further exploring the results of a significant repeated measures MANOVA. By understanding the differences between planned comparisons and post-hoc tests, and by using the correct statistical procedures, you can gain a deeper understanding of the relationships between the conditions and the DVs.