Tests of Linear Combinations of Means, Independent Groups (5 of 7)

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  1. The probability computed in Step 4 is compared to the significance level stated in Step 2. Since the probability value (0.045) is less than the significance level (0.05), the effect is significant.

  2. Since the effect is significant, the null hypothesis is rejected. It is concluded that the average relief provided by the two drugs is greater than the relief provided by the placebo.

  3. An example of how the results of the experiment could be described in a report is shown below.
    Both aspirin (M = 4) and Tylenol (M = 3) provided more pain relief than the placebo (M = 2). A planned comparison of the mean of the two experimental groups with the placebo control was significant, t(9) = 2.33, p = 0.045. The means of the two experimental groups were not significantly different from each other, t(9) = 1.34, p = 0.213.
    It is important to state that the combination of means was planned in advance since a different procedure is used if the comparison is decided on after viewing the data.

    The expression "t(9) = 2.33, p = 0.045" means that a t test with 9 degrees of freedom was conducted and that the probability value was 0.045. The test for the difference between the two experimental groups was conducted using the coefficients: a1 = 1, a2 = -1, a3 = 0.

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