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