Click the "Begin" button on the left to begin the simulation.
This simulation is designed to accompany the case study "Smiles
and Leniency." The experiment consisted of three experimental "smile"
conditions and one control condition.
The idea of the simulation is to see how likely it is that the three findings
that occurred in the experiment (listed below) would occur given various values
of the population parameters. The findings are:
(a) the contrast comparing the average of the three smile means was significantly higher than the neutral condition mean.
(b) Exactly one smile condition was significantly different from the neutral condition (Using Dunnett's test).
(c) None of the differences among the three smile means were significant (Using Bonferroni-corrected t tests).
The 0.05 significance level is used throughout.
When the window opens, the left side of the display will show possible population
values for the means of the four conditions and the within-condition standard deviation.
The standard deviation is assumed to be the same for all conditions. Each population
is assumed to be normally distributed. The initial values represent the case where
the three population means are equal to each other and greater than the neutral mean.
Click the "Start Simulation" button and 100 simulated experiments will
be performed. First look at whether the contrast was significant or not. Using the
initial values of the population parameters, the contrast should be significant somewhat
less than 90% of the time. (The probability of it being significant is the power
of the test). Following the tree diagram, see what percentage of the experiments
found that, in addition to there being a significant contrast, exactly one experimental
condition was significantly different from the control. (It should be slightly above
20%). Finally, note the percentage of the experiments that, in addition to finding
the contrast significant and finding exactly one mean significantly different from
the control, also find no significant differences among the experimental groups.
It should be roughly 20%.
The simulation can be used to determine the probability of the three statistical
outcomes in the study given various states of the real world. For example, based
on the finding that only the false-smile condition was significantly higher than
the control, you should estimate the probability of obtaining the three experimental
outcomes when only the false-smile condition is different from the neutral condition
in the population. Change the values of the means and standard deviations to get
the probability as high as you can.