Math CentralQuandaries & Queries


Question from a student:

I am writing a paper for a grad class in which I am comparing achievement levels of boys and girls. I have data that shows the average marks for girls and boys in each grade 12 subject for the entire province.
Average marks (%) for SK students, aggregated by gender

My prof want me to show there is a statistical difference. What do I have to do to show this? I don't have access to the raw data, so don't know the SD. Is there anything I can do mathematically with the data that I have? (I can determine n for each set of data, it ranges between 2400 and about 13000 for each subject area.)


Applying the concept of statistical difference to this situation doesn't make sense. Statistical difference or statistical significance only makes sense if you have a sample (part of the population of interest) and you want to use this sample to make an inference about the entire population. You however don't have this situation. You actually have the population values not sample values. In this situation statistical difference doesn't apply. The differences you have are the true differences.

It is obvious that the girls tend to achieve higher average scores than the boys, with the differences greater in the humanities and less in science. Since the averages apply to the entire population, those numbers are an exact picture of the average difference between boys and girls in each subject in this time and place.

The last row of your table is troublesome however. Adding a difference between English scores to a difference in math scores to the difference in history scores is a meaningless undertaking. It would make more sense to say the differences range from 1.5 percentage points to 7.7 percentage points. You could also say the females outperform the males in math scores by approximately 3 percentage points.

We hope this helps,
Chris and Harley

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