Pearson's r example
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Problem: Ernestein Extroversion predicts that there is a significant negative relationship between sympathetic nervous system activation (e.g., heart rate and respiration) and extroversion. (High scores on extroversion will be associated with low scores in sympathetic activation). She administers her extroversion scale to eight participants (high scores represent higher levels of extroversion), and also administers a compsite measure of sympathetic nervous system activation (high scores represent greater activation). Her results follow:

 measure/subject 1 2 3 4 5 6 7 8 extroversion (x) 2 3 3 4 6 6 7 9 ANS (y) 9 8 7 5 5 4 1 1

 x (x-Mx)2 y (y - My)2 xy 2 9 9 16 18 3 4 8 9 24 3 4 7 4 21 4 1 5 0 20 6 1 5 0 30 6 1 4 1 24 7 4 1 16 7 9 16 1 16 9 Sx=40 S(x-Mx)2=40 Sy=40 S(y-My)2=62 Sxy=153 Mx=5 My=5

*(according to the r sig/probability table with df = 6, r must be at least .707 to reach p < .05, so this is statistically signfificant)

Interpretation: Ernestein's hypothesis was confirmed. She found that there was indeed a negative and statistically significant relationship between scores on extroversion and sympathetic nervous system activation.

Practice by creating your own data and then check your work with the Virtual Statistician Pearson Correlation Calculator
(Only works with n = 8)

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