REPEATED MEASURE ANOVA OR ANCOVA?
I have often read and heard that a) repeated measure ANOVA and b) ANCOVA , the two analyses answer different research questions.
It's not rare seen Researcher disagreeing with the supervisor based on which #Analysis would do the right justice to the research questions!
Please, when the research objective is about the mean gain, growth, or change - comparing two or more groups, particularly in a pre-post test research (or two groups; of intervention and placebo/control). Which of the two Analysis should be used, and what really messure this changes? What other method can I use?
Hi,
in the context of a pre-post test research where two measurements are taken from the same individual at different times, the assumption of independence of observations is violated: the pre and post group are related to each other, since they come from the same subjects. Using ANCOVA you would be comparing the two means (pre vs post) as if they were two completely separate groups, independent from each other. Therefore, the correct approach involves using a repeated measures test, which works on the variations of the individuals. Since you also have a between-subjects factor (intervention group), I suggest using the two-way mixed ANOVA, which includes a within-subjects factor (time), a between-subjects one (group) and the interaction (time*group) to test whether the effect of a factor is dependent on the value of the other (i.e. the longitudinal trend is different between groups).
Please keep in mind that there are many other assumptions that must be met in order to run this analysis, more information here: https://statistics.laerd.com/spss-tutorials/two-way-repeated-measures-anova-using-spss-statistics.php
If you know about ANOVA then you find the similarity with ANCOVA just a covariate extra in ANCOVA.
You can read any good text book please for further clarification.
There is a lot of debate among statisticians about which is the most appropriate test for your design. An analysis of covariance is essentially an analysis of variance in which differences between levels of a factor are tested after controlling for other variables, termend covariates. If you have a randomised trial where, by virtue of randomisation, any real group differences in baseline values are unlikely, then ANCOVA reduces the amount of unexplained variation in the data. This reduces the error variance and makes the F-test of group difference on the final value of the outcome variable more sensitive; the power of the F-test is increased.
In the context of a pre-post design the repeated measures ANOVA and the ANCOVA with pre scores as a covariate have different assumptions and test different, albeit related hypotheses. Daniel Wright has written on this. For example: Article Allocation to groups: Examples of Lord's paradox
Thanks everyone. This could be confusing, but three things were cleared; a two group repeated measure design could be:
A) the two groups are not of same individuals (two independent factors [DVs], both were measure on 3 levels/ conditions (repeated
for each participant). This is a typical 2 by 3 Mixed Factorial Design, and longitudinal study. An Example is seen here, http://eweb.furman.edu/~lpace/SPSS_Tutorials/lesson9.html
B) two groups of same individuals, the first was a pre-test (two factors) and the second group, post-test (two factors, each at three levels). This is mine own case. A two -way (i.e., two factors repeated measure ) ANOVA seems right to me. Am I right?
C. One way, two factor mixed ANOVA; a mixed within subject and between subject factors.
And, for mixed ANOVA using R:
https://www.datanovia.com/en/lessons/mixed-anova-in-r/
Thanks so much Dr Thom Baguley Emanuele Cassioli , the explanation and the 2 way mixed ANOVA 'seems likely to lead to answer to the research objectives'...perhabs similar research references.
Thank you sir, Jos Feys , the insight on ANCOVA (between effect) and the power of the F-test very helpful.
Am so grateful for your contributions.
In some experiments, you need to eliminate possible covariance effects on the independent variables.It provide us to determine the real relationship between independent and dependent variables . In this case, the Ancova test is applied and the result is free from the effect of covariance.
I want to give a classic answer. In the Ancova test, as a difference from anova, the covariance variable that will affect the difference between repeats is controlled and the difference between repeats is measured more accurately.
Haider Raid Talib , thanks so much for following sir. And to all who have contributed and advised, am really grateful... very big and thankfully.
That is very true sir, Fuat Kocyigit , the covariate that would affect the results can be controlled. That is, considering some experiments where we use ANOVA, some of the unexplained variability (i.e. the error or residual from the model) was due to some additional variable, ( a covariate), which is not part of the experiment or model. If we can somehow identify and remove the effect of this covariate-variable, we could reduce the error variance thus enabling us to get a more accurate picture or estimate of the true effect of the independent variables. This is the main goal of Analysis of Covariance (ANCOVA), and funny enough we can approach ANCOVA from the methods of both ANOVA and Regression!
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