Tests of Differences between Means, Dependent Means (3 of 4)

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For this example,



There are 10 - 1 = 9 degrees of freedom (Note that the sample size is the number of difference scores, not the total number of scores.) A t table can be used to find that the probability value is 0.074.

An alternate formula for s_M is:



where s₁ is the standard deviation of Condition 1, s₂ is the standard deviation of Condition 2, n is the number of subjects, and r is the correlation between scores in Conditions 1 and 2. For the example data, s₁ = 87.764, s₂ = 77.719, n = 10, and r = 0.9206 and therefore s_M = 10.88.


An example of a report of this result is shown below.

The mean time to respond to a visual stimulus (M = 319.5) was longer than the mean time to respond to an auditory stimulus (M = 297.5). However, this difference was not statistically significant, t(9) = 2.02, p = 0.074.