Repeated measures ANOVA makes assumptions about your data that are rarely observed in reality (compound sphericity) and cannot deal with missing data. If you have 7 time points, I suggest that you look at growth curve modelling, which has really taken off as a method over the past few years.

A log transformation is typically appropriate for ratio data.

A better question is why do you think that you need to transform your data? Best, David

Repeated measures ANOVA makes assumptions about your data that are rarely observed in reality (compound sphericity) and cannot deal with missing data. If you have 7 time points, I suggest that you look at growth curve modelling, which has really taken off as a method over the past few years.

What is the ' the length ratio of fin ray 4 and 6'?

I agree with Ronán. But, does this mean that repeated measures ANOVA's should be banned completely? Not always, I think. One can test for the sphericity assumptions (Mauchly's test). If there is a lack of homogeneity of the structure of variances and covariances, there are way to inspect this structure, and to model and correct for violations of sphericity assumptions. Missing values, if not too much present (say no more than 5%), can be imputed or can be dealt with, e.g. with the SAS proc mixed on the data in 'long format'. What you could do is to calculate the residuals of the 7 measures as nominators of the ratio on the denominator of these. I assume this denominator is the same for all the 7 time point measures (as nominators) of fin ray. On these residuals you could run a repeated measures ANOVA, provided these are quite normally distributed (inspect the histograms). If these are not normally distributed, you could run the Friedman ranks test (or, even better, the Friedman aligned ranks test). [email protected]

Repeated measures ANOVA is really very old and incompatible. A better analysis would be using a (generalized) linear mixed model for such data without any transformations.

ANOVA is just a special case of regression

https://www.theanalysisfactor.com/why-anova-and-linear-regression-are-the-same-analysis/

Generalized linear models vs ANOVA:

https://stats.stackexchange.com/questions/289226/what-are-the-differences-between-anovas-and-glms

I agree with Mehmet in that you do not need to transform the ratios (in fact you should not). If the ratio data are fairly normally distributed (inspect the histograms and QQ-plots), just run a repeated measures ANOVA on the ratios. Otherwise run the Friedman ranks test. You can model a growth curve by testing for trends, e.g. with the 'polynomial' option in the the SAS proc glm repeated statement.

Dear all,

Thank you very much for your help and guidance! Special thanks to Jos Feys who suggested using Friedman rank test. My data is not normal distribution so I tried to use Friedman test. I think it works!

Once again, many thanks!

Best regards,

Ngoc

If your design is factorial; e.g., between (Groups) x within (repeated measures), then you can use one of the functions of the Brunner non-parametric nparLD R package or SAS macros. For example, f1.LD.f1 if for a 2-way 1 between factor x 1 within factor. f1.LD.f2 is for a 3-way 1 between x 2 within factors.

The Friedman aligned ranks test is somewhat more powerful then the simple Friedman test. With the scmamp R package you can run this test + post hoc tests, see:

https://cran.r-project.org/web/packages/scmamp/scmamp.pdf

To test for trends, you could use the non-parametric Page test for ordered alternatives:

https://www.rdocumentation.org/packages/crank/versions/1.1/topics/page.trend.test

from the crank R package:

https://cran.r-project.org/web/packages/crank/crank.pdf

[email protected]

In addition to Mehmet's answer, see the following notes. They provide the details for Mehmet's comments. Best, David Booth

https://www.stat.ncsu.edu/people/davidian/courses/st790/notes.html

Hello Tran

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 and 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