Interpretation

Summarizing the results: (a) the average of the three smile conditions is significantly different from the neutral control condition, (b) the three smile conditions are not significantly different from each other, and (c) only the false smile condition is significantly different from the neutral control.

At first glance, these findings appear to be inconsistent. If the three smile conditions are equal, how can it be that only one is different from the control? The paradox is a false one because the failure to reject the null hypothesis does not mean it should be accepted. A failure to find a significant difference between the felt and control conditions does not mean there is no difference in the population. Similarly, the non-significant differences among the smiling conditions does not mean that there are no differences in the population.

Among the possible states of the population are: (a) All three smile conditions are different from the neutral condition and (b) Only the false-smile condition is different from the neutral condition. The former possibility appears more likely than the latter because there were at least hints of differences between the felt and neutral conditions and between the miserable and neutral conditions whereas there was no evidence of differences among the three smile conditions.

A simulation was developed to explore the relatively likelihood of the two possibilities. In this simulation, you specify population means for the four conditions and conduct simulated experiments. Each experiment is analyzed in the same way as the actual experiment. The goal is to see what pattern(s) of population means are likely to produce results comparable to those actually obtained.

Try the simulation