TS - Testing 2 Samples Lesson

Testing 2 Samples Lesson

Comparative studies are more convincing than single one-sample investigations, so one-sample inference is NOT as common as comparative (two-sample) inference. 

In a comparative study we may want to compare two treatments or we may want to compare two populations.   In either case, the samples must be chosen randomly and independently  in order to perform statistical inference.   When comparing two means, both samples must be a SRS and must be chosen independently.  Also, both populations must be Normally distributed.  Check the data for outliers or skewedness.

Always, before we begin, we must check conditions.   There are conditions required of both samples.   If we can validate the conditions then we conclude that the difference in the samples will be an "unbiased estimator" of the true difference in the population. 

Always, before we begin, we must check conditions.   There are conditions required of both samples.   If we can validate the conditions then we conclude that the difference in the samples will be an "unbiased estimator" of the true difference in the population.   Using mathematical notation that looks like   equals . We then proceed with the statement of hypotheses.

The null hypothesis is that there is no difference between the two parameters.

The alternative hypothesis could be that

The formula for finding variance is quite involved and requires inclusion of both standard deviations and both sample sizes.  

The mean formulas are presented in Chapter 24 and the proportion formulas are presented in Chapter 22.   Since the math is cumbersome, it is best to rely on the calculator for assistance using the option for 2-SampTTest for means or 2-PropZTest for proportions. Nevertheless, you should be familiar with the formulas being used and understand the derivation of each.

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