please help me with this question. the answer should reflect Pearson\'s r, not t

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please help me with this question. the answer should reflect Pearson's r, not t test (question #2). I posted this before but the answer was incorrect.

correlation was judged to be statistcally you say about the nature of the relationship? hether emotional well-being in later life Harker and Keltner (2001) examined w could be predicted from the facial expressions of 141 women in th yearbook photos. The predictor variable of greatest interest was the emotional expression"'in the college yearbook photo. They also had these photo graphs rated on physical attractiveness. They contacted the same wo follow-up psychological assessments at age 52 (and at other ages; data not shown here). Here are the correlations of these two predictors (based on ratings of the yearbook photo) with several of their self-reported social and emotional outcomes at age 52: 1 2. men for In College Photo Physical Attractiveness Positivity of Facial Expression At Age 52 Negative emotionality Nurturance 04 - 06 .27 a. Which of the six correlations above are statistically significant (i) if you test each correlation using = .05, two-tailed, and (ii) if you set Ewa-05 and use Bonferroni-corrected tests? b. How would you interpret their results? c. Can you make any causal inferences from this study? Give reasons. d. Would it be appropriate for the researchers to generalize these findings to other groups, such as men? e. What additional information would be available to you if you were able to sce the scatter plots for these variables? 3. Are there ever any circumstances when a correlation such as Pearson's r can be interpreted as evidence for a causal connection between two variables? If yes what circumstances?

Explanation / Answer

the values in the table detemines the pearson correlation or r between the respective variables. they are represented as x1, x2........... for easy calculations

if r is the correlation r2 represents the probabilty that there could be a causal relationship between two variables .

(x1)2 =   0.0016

(x2)2 =    0.0036

(x3)2 =  0.0009

(x4)2 = 0.0729

(x5)2 = 0.0484

(x6)2 = 0.0729

at alpha/2=0.05/2=0.025(two tailed test), significance level the value of r2 less than 0.025 tells that there is statistically significant correlation between two variables.

b) Based on this, significant variables, to determine the state at age 52 (dependent variable) from college photos parametres(independent variable) are physical attractiveness for negative emotionality, nurturance and well being. other three corelations are rejected to determine causal relationship.

c) coorelation with physical attractiveness are founds statistically signicant whilecorrelation with positivity of facial expression in college photos don't. so we can say that there is causal relationship between physical attractiveness and variables considered at age 52 but not this is not the case with positivity of facial expression in college .

d) No, researchers can not generalise it to other groups having different characteristics which might influence the coreelation coefficient.

e) if we are able to see the scatter plot we will be able to see the pattern how the variables are correlated - linearly, exponentially etc.

physical attractiveness positivitivityof facial expression negative emotionality .04    (x1) -.27         (x4) nurturance -.06     (x2) .22           (x5) well being .03      (x3) .27             (x6)

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