Question

Harker and Keltner examined whether emotional well-being in later life could be predicted by the facial expression of 141 women in their college yearbook photo. The predictor variable of greatest interest was the “positivity of emotional expression” in the college yearbook photo. They also had these photographs rated on physical attractiveness. They contracted the same women for follow-up psychosocial assessment at age 52 (and at other ages; data not shown here). Here is the correlation of these two predictors (based on the rating of the yearbook photo) with several of their self-reported social and emotional outcomes at age 52

In College photo

At age 54                           Physical Attractiveness              Positivity of Facial Expression

Negative emotionality                    .04                                               - .27

Nurturance                                     - .06                                                 .22

Well-being                                       .03                                                 .27

Which of the six correlations above are statistically significant (i) if you test each correlation using = .05, two-tailed, and (ii) if you set EWα = .05 and use Bonferroni-corrected test?

How would you interpret their results?

Can you make any causal inference from this study? Give reason.

Would it be appropriate for the researcher to generalize these findings to other groups, such as men?

What would additional information be available to you if you were able to see the scatter plots for these variables?

Answer 1

Given that

Harker and Keltner (2001) examined wheather emotional well-being in later life could be predicated from the facial expressions of 141 women in their college year book. They contracted the same women for flow up psychologyical assessments at age 52.

a)Testing at the significance level of 0.05,we have to calculate first the t-value for each of the correlation coefficient and then compare it with the critical t-value at the given significance level.

For sample size =141,degree of freedom =141-2= 139

critical t-value = > 1.98,Using excel function , T.INV.2T(0.05,139)

t=\sqrt{\frac{r^{2}\times df}{n-2}}

The t-value for each of the correlation coefficient is shown below

The correlation between positivity of facial expression and self-reported social and emotional outcomes was found to be significant at the significance level of 0.05 as the t-value found using the formula was greater than the critical t-value of 1.98.

Using Bonferroni corrected test,the p-value would be 0.05/6 =.0083

The critical t-value in this case is 2.68.From the above table still the correlation between positivity of facial expression and self-reported social and emotional outcomes ,as the t-value is greater than the critical t-value.

b)It can be said that the correlation between positivity of facial expression and self-reported social and emotional outcomes are significant ,whereas physical attrativeness do not show any significant correlation with self-reported social and emotional outcomes.

c)As we know that correlation between two variables does not imply causation,therefore causal relation between two variables cannot be made based on this study.

d)It would not be appropriate to generalize these findings to men as the result relates to study for only female person .Statistical inference results can be generalised to the same population and not different population.

e)The scatter plot would have provided the visual interpretation and the nature of the relationship between these variables.Based on scatter plot we can make whether a linear or non-linear relationship exists between these variables.