Lee et al. (2014) examined whether classic stories about moral behavior influence whether children lie. They studied three moral stories (Pinocchio, The Boy Who Cried Wolf, and George Washington and the Cherry Tree) and one control story (The Tortoise and the Hare). Children ages 3-7 completed a temptation-resistance task and then were asked whether they had peeked. Suppose the results for children who peeked were:
Make sure the story is being used as the explanatory variable or press the (explanatory, response) button. Check the Show Shuffle Options box, enter a large number of shuffles, and press Shuffle.
Use the pull-down menu to set the Statistic choice to the Chi-squared (\(\chi^2\)) statistic. Compute an empirical p-value based on the simulated chi-squared values.
Check the box to Overlay Chi-square distribution. Does the theoretical chi-squared distribution (with \(df=3\)) appear to be a reasonable model for the simulated null distribution? How are you deciding?
Yes. The chi-squared distribution with \(df=3\) is a reasonable model for the simulated null distribution here, and the model-based p-value is close to the simulation p-value.
When data arise from a randomized experiment, the chi-squared model is generally appropriate if at least 80% of expected counts are at least 5 and all are at least 1.
Examine the chi-squared contributions for each cell ("residuals" are square roots of these values). Which cell(s) contribute the most to the overall chi-squared sum? Compare the observed counts to the expected counts for those cells. What do these comparisons reveal about which types of stories seem to make children more likely to confess?
For George Washington, the observed confessed count is larger than expected and the observed did-not-confess count is smaller than expected, suggesting this story may increase confession relative to the others.
Examining the conditional proportions that confessed across the four stories (0.313, 0.500, 0.295, 0.348), we see the children were more likely to confess when read the George Washington story compared to the negative consequences stories or the neutral story. A chi-squared test (valid because all expected cell counts are larger than 5) however does not find these differences to be statistically significant (\(X^2 = 5.202\text{,}\) p-value = 0.158). We do not have convincing evidence that the type of story influences Canadian children’s likelihood of confessing their indiscretion in this situation. Still, the results are in the direction conjectured by the researchers, and larger sample sizes may find significant results if this study was repeated.
