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What effect does having different sample sizes have on the data?

If there are different amounts of data in two samples being compared, will this greatly affect the data? Will it make the data unfair?

That is certainly worth mentioning. For example, a bigger sample may have fairly normal distribution while it could be hard to make a definite conclusion about the shape of distribution for another group as the sample is too small. However, if both groups have at least 30 points that should be good enough for making a conclusion, even if one of the groups has just 30 points and another 300.