Based on my scores, they are not normally distributed, Thus, I have conducted Friedman Test and also ANOVA and ANCOVA repeated measures based on the absolute means scores in order to identify changes within five sessions in a group. Can I use these both parametric tests although my scores are not normally distributed please?
If you coded the scores as numeric values then you can use these tests. However, you should not do it because the interpretation of the results will likely be misleading.
Generally, my anwer to your question is: No.
And this answer has at least 99% confidence ;)
Thank you for the reply Dr.Jochen. How about the Friedman Test? Is there any other alternatives to analyze? How if I have based on the absolute mean scores in ANCOVA repeated measures?
Friedman Test is ok for ordinal variables. Ordered logistic regression models can also be used, but they will be cumbesome if there are many levels/categories.
If a score is measured on an ordinal scale, taking differences, sum or averages is simply not meaningful. For instance, there is nothing like the average between the values "agree" and "strongly agree". If one simply uses numeric values to represent these categories, one can calculate a mean of these values, but it is not very meaningful, because the choise of the numbers is arbitrary.
In your last post you wrote that the scores are on a continuous scale. This is uncommon for "scores". But if this is really correct, then the scale is at least an interval scale, and on such a scale calculations like differences, sums etc. make sense. In this case I suspect that the scores-scale is bounded (it hat a minimal and maximal possible value). If data gets close to one of the boundaries (relative to the "noise") it cannot have a symmetric distribution. Distributions on such bounded scales can better be described using the beta-distribution, and there are beta-regression techniques available. A possible work-around would then be to use a normal regression model with the logit-transformed data.
Respected researcher,
I have conducted a research on the impact of toys on reading comprehension where the children were assessed in terms of free and cued recall measures. There were five sessions in a group. each session carries a different strategy. Since my scores are in continuous variable and not normally distributed, I have conducted the Friedman test. Am I in the right track Dr?
So your scores should represent "reading comprehension". What is meant by "assessed in terms of free and cued recall measures"? Can you explain how exactly a score value is measured/determined?
Since the scores are not normally distributed, First, I have conducted the Mann-Whitney test to identify the scores differences between the two groups. Then, I have conducted the Kruskal wallis test to identify the scores difference between three types of learners in a group itself. Now, I need to identify which session works the best for the children and i need to analyse the mean scores within the five sessions dr.
Respected researcher
there are two measures involved in my research; free and cues recall. Free recall is a measure which needs the students to tell everything that they remember fro the story that they have read after they move the given toys. Hoever, cued recall requires the children to answer the questions based on the story that they have read. The both scores will be evaluated by two different examiners by looking into the scoring criteria given by the key players
It is impossible from your description to understand how a score-value is constructed. In order to help you we will need the detailed operationalization rules for the "score" variable.
Just to give three examples:
a) The score is determined as the number of key aspects of a story correctly listed by a student, where the key aspects (and their total number) are fixed and their number is constant for all stories (or may be story-specific).
b) The score is determined as the time a student needs to correctly recall all key aspects of a story, where the key aspects are ...(like in a)
c) The score is a value in the range [0,100] given by an examiner to judge the recall performance of a student re-telling a story where 0 means no recall at all and 100 means the student could retell the whole story exactly (or tell all details of the story).
etc.
For a) the scores were counts, and a Poisson- or beta-binomial model would be ok.
For b) the scores were times, and some "survival"-model (rate-model/exponential model) could be appropriate.
For c) the score is in fact ordinal, so some ordered-logistic model would work.
These are just examples out of my head. I have no idea how your scores are operationalized and these examples can be completely off the mark. But they hopefully demonstrate what kind of information I requested.
Cued recall measure
1 point- exact answer
1/2 point- partially correct
0 point-wrong answer
Free Recall measure
1 point- exact answer or relevant main idea
1/2 point-partially correct
0 point-wrong answer
Is the total number of correct answers given, known, limited? Is it the same for all stories or different between stories? Were the answers "free" or "multiple choice"? If the asnwers were "free": is listed (before the experiment) which answers are to be calssified as "correct"?
1. the total number of correct answers are known and within the story.
2. no, the answers differ for each session as the stories used are different
3. the answers were free
4. if the answers are free, the correct answers derived from the actual correct proposition recalled by the students like in the story. we have developed a list of idea units.
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