When did there is a requirement of uniform class size in statistics?
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Answer:
Class size is the average number of students per class, calculated by dividing the number of students enrolled by the number of classes. In order to ensure comparability between countries, special needs programmes have been excluded.
ANSWER.
It is most important to understand that the requirement for the majority of parametrical tests is the normality of the distribution of the mean, not of the original data! Of course, if the original data is normally distributed, so the mean distribution is certainly normal. But means of samples from an uniform distribution also presents normal distributions, since sample size is at least five or six. This property comes from the central limit theory.
As a general rule, the more skewed the data distribution, the greater the sample size needed to garantee the normality of mean distribution. If you have big samples (at least 30, but better greater than 50), you don't need to worry about normality, unless you have very skewed distribution.
To think about central limit theory and use visual inspection of histograms, as sugested above, is better than to use normality tests as Kolmogorov-Smirnov or Chi-squared. The first has no power to reject null hypothesis with small sample sizes and is focused in only one point of the distribution. The second is usefull only with great sample sizes, where you don't need to worry about it.
So, forget about normality tests and focus on the visual examination. If you have data aproximately simetrically distributed, go futher with parametric tests!
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