Sampling Distribution, Difference between Independent Means (2 of 5)

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Sample n₁ scores from the population of people taking the drug and compute the mean. This mean will be designated as M₁. Then, sample n₂ scores from the population of people not taking the drug and compute the mean. This mean will be designated as M₂. Finally compute the difference between M₁ and M₂. This difference will be called M_d where the "d" stands for "difference." This is the statistic whose sampling distribution is of interest.

The sampling distribution could be approximated by repeating the above sampling procedure over and over while plotting each value of M_d. The resulting frequency distribution would be an approximation to the sampling distribution. The mean and the variance of the sampling distribution of M_d are:



and

.

If and n₁ = n₂= n then

.


For the present example,

= 50 - 40 = 10 and
.