ANOVA is the short-form form for Analysis of Variance, the repeated ANOVA is one of the members of the ANOVA family, it compares the mean of one or more variables taken from a set of repeated observations. The repeated ANOVA model can contain zero or more independent variables, this model also contains a minimum of one dependent variable having at least one observation. The authors used repeated-measures ANOVA because when CIs are derived from multilevel models with more than one variable the results are reliable (Baguley, 2012). Another important aspect of using this approach is its ability to reduce the sphericity assumption by inputting a new model which does not have an unstructured covariance matrix, therefore, estimating both the variances and the covariances between the repeating measured values with different parameters.
Repeated measures ANOVA was the best approach since Cousineau-Morey CIs can also be computed from the standard ANOVA without problems by using various statistical software like Microsoft excel and from the software single-tier plots for CI can be drawn easily. There exist several other packages like SPSS which are advanced and can accommodate multilevel models for inbuilt variables. ANOVA designs can provide the required CIs for the respective average (Baguley, 2012). When it comes to the construction of 2-tier plots, it becomes challenging and to make it simpler, one can choose to use customized macros and functions. Repeated ANOVA is also preferred by researchers because the graphical representation of the interval estimates’ suits most informal inferences, it is also considered important to choose a method that gives intervals that are almost equal to a CI of a known inference.
This test was not the most appropriate choice because as Baguley, 2012 states most people interpret the overlapping ninety-five percent CIs as an equivalent to minimal change between various statistics a scenario that is not always true. After all, it depends on whether the inference is formal or informal and the choice of the range plotted. This problem is often avoided by using the thumbs rule, for example, a fifty percent overlap is equal to some big difference but it will be advisable to plot the margin corresponding to the inference chosen.
Another problem that makes this method challenging is that it does not comprise of multiple testing aspects and when working on errors of multiple testing, it is difficult to remove them in the case of informal inferences and as much as a considerable number of inferences may be constructed and various people ask various questions it will not be to make a prior correction. Another limitation is that the approach adopted in the repeated measures ANOVA makes assumptions on the distribution which sometimes do not hold in practice. When the errors appearing in the statistical structure are big then what follows is a very skewed distribution and where the estimates are based on the t and z distributions then the results are not good approximates.
The authors displayed the results in a figure or table; therefore, I was able to interpret the study because the tables and figures were well constructed. From the study, it can be concluded one can generate a good solution to the plotting when using within-subjects CI that is correct does not violate the sphericity of the variables. The specific variables can be constructed and used to generate a plotting in the software R using the its functions. These estimations of the intervals are very useful in exploratory analysis and informal inferences when data is being reported from a normal ANOVA model, they are also designed to integrate graphical inferences of various patterns under different conditions.
References
Baguley, T. (2012). Calculating and graphing within-subject confidence intervals for ANOVA. Behavior Research Methods, 44(1), pp.158–175.