# Sandbox

Smile Intensity and Divorce

Is there a connection between positive expressive behavior, as seen by facial photographs, and success in avoiding divorce? According to http://www.livescience.com/culture/090414-smile-marriage.html Moskowitz], “If you want to know whether your marriage will survive, look at your spouse's yearbook photos. Psychologists have found that how much people smile in old photographs can predict their later success in marriage.” This claim is based on a study headed by Matthew Hertenstein detailed in the April 5 issue of the journal Motivation and Emotion. The table below is taken from Hertenstein’s publication. Study 1, Sample 1 involves alumni who were psychology majors at a particular university; Study 1, Sample 2 involves alumni from the same university who were not psychology majors. In each instance, the participants submitted yearbook photos which were judged for smile intensity and whether or not the participants were divorced or still married. Study 2 is similar but involved older members of the community who submitted photos from decades past.

Discussion

1. In the above table, a two sample t-test of means (“M”) is carried out for each row. Pick a row and verify degrees of freedom (“df”), the value of t and the p-value (“p”). Note that “p values are one-tailed given the directional hypothesis of the studies.”

2. While p-value is useful to some extent, “effect size” may be of more interest. The last column, “r” signifies that some sort of correlation is taking place; it is sometimes called the point-biserial correlation coefficient. This correlation is between the independent dichotomous variable and the dependent variable (smile intensity). According to the psychology literature, it is given by

Where: rpbi = point-biserial correlation coefficient Mp = whole-test mean for those who stay married Mq = whole-test mean for those who get divorced St = standard deviation for all concerned p = proportion of those who stay married (i.e., those coded as 1s) q = proportion of those who get divorced (i.e., those coded as 0s)

Use this formula and Pick a row to verify the value in the table for “r”—ignore the sign.

3. Clearly, these results are for a sample. Speculate on what you would need to know of the characteristics of the participants in order to infer to a larger population.

4. Although the table is informative as to means and standard deviations, why would boxplots for each row be useful?

5. According to Moskowitz, but not mentioned in the paper itself by Hertenstein, “Overall, the results indicate that people who frown in photos are five times more likely to get a divorce than people who smile.” This comes about by looking at the highest scorers--who turn out to be mostly still married--compared to the lowest scorers who turn out usually to be those who are divorced. Why is this quotation featured rather than the above table? 6. For those who would like to improve their “smile intensity” of their photos, here is what the paper itself says the measurement process is: