This issue came up recently in other questions and has me wondering about it. If you have sequential measurements of a continuous variable on the same subjects over time then you can do repeated-measures ANOVA. But what if the same individuals are not necessarily measured at each time point, in other words if you instead measure the available population (or a sample from it) at each time point sequentially, would it still be valid to use a repeated-measures ANOVA?
If you're trying to see how a quality changes in a population over time and you sample different individuals each time, you would not be able to use a repeated-measure ANOVA. Afterall, you didn't repeatedly measure something in the individuals. You could use a repeated-measure ANOVA if your participants are "yoked" together across time as a within-subject variable. For example, let's say that rather than sampling the same participants at each time interval, you might be sampling 500 voters from each congressional district each time and using that to estimate a quality at each time of each district. Then you could use a repeated-measure ANOVA because your unit of analysis is the congressional district (rather than the individual). That is, even though it's different people, you repeatedly measured the district. Hope that helps. Best wishes with your project, Jerry! ~ Kevin
If you're trying to see how a quality changes in a population over time and you sample different individuals each time, you would not be able to use a repeated-measure ANOVA. Afterall, you didn't repeatedly measure something in the individuals. You could use a repeated-measure ANOVA if your participants are "yoked" together across time as a within-subject variable. For example, let's say that rather than sampling the same participants at each time interval, you might be sampling 500 voters from each congressional district each time and using that to estimate a quality at each time of each district. Then you could use a repeated-measure ANOVA because your unit of analysis is the congressional district (rather than the individual). That is, even though it's different people, you repeatedly measured the district. Hope that helps. Best wishes with your project, Jerry! ~ Kevin
If the groups are matched on e.g. age, sex, culture, disorders and you can call them dependent groups, then you can have repeated measure
Dear Jerry
In the case the multiple measurements taken for the same individuals we can calculate the repeatability coefficient of individual for certain trait, but in the case of another individuals for each measurements may be refer also to the variation result from sampling.
Good Luck
Dear Jerry
" the same individuals are not necessarily measured at each time point" and You know which measurement belongs to certain individual (person) - there are more flexible models than RM ANOVA called general linear mixed models (GLMM).
GLMM are able to estimate individuals errors ( within-error) and between errors related to different timepoints, different treatments and so on.
Hope it may by useful.
Thank you Olga - I'm also exploring mixed models, which are a bit more complicated. But I'm leaning towards RM ANOVA because: 1) in my dataset, I can impute missing values by taking an average of the prior and succeeding time points, which makes biological sense with my data; and 2) I feel this would allow the most use of the data than using Mixed Models because it would use all the (actual + imputed) data. Mixed models will not discard cases with missing values the way regular RM ANOVA does, but I still find it intuitively weak to use mixed models when so many datapoints are missing; and 3) my data appear to meet the required assumptions for using RM ANOVA; 4) the output for repeated measures ANOVA seems to cover every aspect of what I want to explain, whereas the Mixed Models output is a little more vague; and finally, 5) Mixed Models are extremely complicated with the software I use. I may do it both ways and compare results. Using Mixed Models seems to be the fad nowadays but I wonder if the method is truly any better.
Has anyone here used both Mixed Models and Repeated-Measures ANOVA?
Jerry, if You want compare the results, it is interesting to compare the results of various imputing methods too (along with GLMM results).
Clinical longitudinal data are often biased (for example: after severe treatment, certain patients miss the second visit, those who feels bad).
May be there are some reasons execute two analysis: Intention-to-treat (RM ANOVA with imputing or GLMM) and per-protocol (RM ANOVA without missing values).
I know nothing of Your research and data, so it's only my weak assumptions about design and data....
> Has anyone here used both Mixed Models and Repeated-Measures ANOVA?
Yes, but no imputing. In that case the results are very much the same.
Good luck!
Hi Jerry
1. Repeated measures test has to be applied for each survey.
2. The assumptions of Repeated measures test have to be investigated carefully.
3. Repeated measures ANOVA is the equivalent of the one-way ANOVA, but for related, not independent groups, and is the extension of the dependent t-test. A repeated measures ANOVA is also referred to as a within-subjects ANOVA or ANOVA for correlated samples.
4. We can analyse data using a repeated measures ANOVA for two types of study design. Studies that investigate either (1) changes in mean scores over three or more time points, or (2) differences in mean scores under three or more different conditions.
5. One of the major assumptions of this type of repeated measure analysis is that of sphericity. If this assumption of sphericity is violated, then the value of F statistic will come out with severely biased results. In other words, if the assumption of sphericity is violated, then the researcher might end up committing Type I error.
6. There are options available for the researcher to override this violation of assumptions while performing this type of repeated measure analysis. The researcher can do an adjusted degree of freedom test or use the Green house-Geisser method to overcome the effects of violation.
7. Wilcoxon signed rank test is the appropriate non-parametric alternative.
8. For more details in theoretical side, please refer to:
i. William G. Cochran, Gertrude M. Cox (1977). Experimental Design, Wiley.
ii. Snedecor, W.G. and Cochran,W.G. (1989). Statistical Methods, Blackwell.
iii.Geoffrey Keppel Professor Emeritus, Thomas D. Wickens (2004). Design and
Analysis: A Researcher's Handbook (4th Edition). International Edition.
9. For practical side, please refer to:
iv. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.
v.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.
Regards,
Zuhair
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