A Repeated Measures Analysis of Covariance (ANCOVA) is a statistical technique that combines elements of repeated measures analysis (or repeated measures ANOVA - Analysis of Variance) and analysis of covariance (ANCOVA). It is used when you have a study design with multiple repeated measurements on the same subjects and you want to examine the effects of one or more independent variables on the dependent variable while controlling for the effects of one or more covariates.
Here's a breakdown of the key components:
Use Cases:
- Repeated Measures ANCOVA is commonly used in research involving longitudinal studies, clinical trials, or any study where subjects are measured at multiple time points.
- It's used when you want to assess the effect of an independent variable (or variables) while controlling for the influence of covariates that might affect the dependent variable.
Thank you for the answer. Please highlight assumptions to be met before the ANCOVA and how to go about it. I do not have the statistical background and have been referring to Andy Field's book for the analysis but could not find the details about this in this book. Uzair Essa Kori
The first assumption is 1-Normality, which necessitates that the residuals from the model are normally distributed; this can be tested using the Shapiro-Wilk test, Kolmogorov-Smirnov test, or graphical methods like Q-Q plots or histograms. The second assumption, 2-Homogeneity of variance, requires that the variances of the residuals are equal across groups, and can be tested using Levene’s test or Bartlett’s test. The third assumption is 3-Independence, which mandates that the observations are independent of each other; this can be verified by reviewing the study design and data collection method. The fourth assumption is 4-Linearity, which requires a linear relationship between the dependent variable and the covariates and can be tested using scatter plots or Pearson correlation coefficients. Lastly, the fifth assumption, 5-Homogeneity of regression slopes, necessitates that the relationship between the covariates and the dependent variable is the same for each group; testing for interaction terms in the ANCOVA model, where a significant interaction term indicates a violation of this assumption.
As for resources, depending on your preferred learning method and the software you are using, you might find one of these resources helpful: Real Statistics Using Excel for step-by-step guidance on testing ANCOVA assumptions using Excel (https://real-statistics.com/analysis-of-covariance-ancova/assumptions-ancova/), SPSS Tutorials for software-specific guidance if you are using SPSS (https://www.spss-tutorials.com/spss-ancova-analysis-of-c), or The Analysis Factor for dealing with violations of ANCOVA assumptions (https://www.theanalysisfactor.com/assumptions-of-ancova/). As for books “Biostatistical Analysis” by Jerrold H. Zar covers ANCOVA in Chapter 12, while "ANOVA and ANCOVA: A GLM Approach" offers these techniques from a linear model perspective. Hope this helps.
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