Instructions

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.