Below are the case:
30 students to answered 4 types of questions : spelling, reading, writing and phonology test. I need to know which instrument is the most correct answered and the most worst instrument? My data have a few outlier due to 0 marks in a few instruments which resulted non-normalize distribution. Therefore I cannot simply use the mean ans the SD as in normal distribution. Then what types of statistical test should I used?
The alternative to Mean and SD when your data is skewed is to report Median and IQR (and the direction of skewing--left or right).
Just curious however, why would you want to report Mean & SD for a data that appears to be categorical, in which case n(%) would be more appropriate?
Anyway, IF indeed your data is categorical, then Fischer's test (the non-parametric alternative to chi-square test) would be appropriate. And if numerical, then Kruskal Wallis (the no-parametric alternative to one-way ANOVA) would do fine.
Best wishes!
As suggested above for each group you can provide median and Interquartile range.
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Also you can go for kruskal Wallis test for the comparison between the groups, and then further you can do pairwise comparisons also for each pair so that you can see which pair is differing.
In the case where the same 30 students were allocated marks for the four tests, and you want to compare the four tests, the Friedman test will be appropriate; it is a type of repeated measures setup.
your experiment appears to be related to the IRT (Item Response Theory) and/or the models related to the Rasch Model.
You may google the names to obtain more information.
Or you may let your data available, after "anonymisation" if necessary, to get some help from the community.
Dear Siti
Your question is not very clear, please add the total number of observations of the group and the total number of observation in each sub group.
I think that your data contains several related subgroups. In order to analyses the data and testing the significance between the subgroups , you need to apply the Model of ANOVA for correlated scores, which may be explained by:
The correlated/related analysis of variance indicates whether several (two or more) sets of scores have very different means. However, it assumes that a single sample of individuals has contributed scores to each of the different sets of scores and that the correlation coefficients between sets of scores are large. It is also used in designs where matching has taken place.
Regards,
Zuhair
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