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Children born in the summer perform weaker in school tests than autumn born children (mostly due to them being younger in their school year/grade). I have the test data for a class of 30 children and I have found the mean grade in science, reading, writing, and maths for the autumn and the summer born children in the class. I have subtracted the mean autumn grades from the mean summer grades for each subject, giving 4 'Gap Sizes' (my dependent variable).

My first question is: what statistical test could I use to test if there is a significant difference in the season gap size between the 4 subjects? I also have the data for the grades of the children from their first year of school. My second question is: How could I, for example, test to see if the gap size in science in the first year/grade of school is significantly different from their current year?

The fact that my dependent variable is simply the difference between 2 means (1 for each subject) is what has confused me.

Any help would be much appreciated.

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I think this is a simple situation but you are just confused because your dependent variable "gap size" is created by subtraction. You calculate gap size before undertaking any statistical test. Once you obtain the gap size, you just need to proceed with statistics as usual.

To answer your first question, to test whether there is a significant difference in gap size between school subjects, you simply perform a 1-way ANOVA, with school subject as the independent variable and gap size as the dependent variable.

To answer the second question, whether there is a change in a student's gap size from year to year, first please clarify whether you are interested in change within an individual student (i.e. do students' gap sizes increase over time) or the average gap size. If you are interested in the change within the individual student, you would use a paired t-test testing time 1 against time 2. If you are interested in a change in the average, you would use a unpaired t-test testing time 1 against time 2.

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  • $\begingroup$ Hi! I think my issue with the 1-way ANOVA is that I have no raw 'gap size' data to enter, seeing as it I just have 4 pieces of data for it - one for reading (autumn reading test score average - summer reading test score average), and one for each of writing, maths and science (the mean autumn scores - the mean summer scores). Is a 1-way ANOVA still appropriate and, if so, what data would I be entering? Thanks again for your help. $\endgroup$ Mar 7, 2018 at 11:00
  • $\begingroup$ Harry, you don't test the averages themselves. You test the gap size between each student's individual score. $\endgroup$
    – Bosley
    Mar 12, 2018 at 11:30

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