psychology 302

Psychology 302, Winter 2020 Problem Set 2, due Wednesday, Feb 5 IN CLASS

Do all problems except #2 by hand and show your work

1. A researcher wants to study the relationship between extraversion and amount of social interaction. She administers a measure of extraversion that ranges from 1-20, where higher scores mean higher extraversion. She then observes the number of social interactions between participants in a 30 minute period in the lab. The data are as follows:

Participant

Extraversion score (X) Number of social interactions (Y)

1 20 7 2 5 2 3 18 9 4 6 3 5 19 8 6 8 6 7 15 3 8 7 4 9 17 7 10 16 10

Mean: 13.10 5.90 SD: 5.59 2.62

a. Draw a scatterplot for the data b. Calculate the correlation of X and Y using the formula I provided in

class c. What proportion of variance in number of social interactions is

explained by extraversion score? d. Fully describe this relationship in English (not stats-speak). That

means say something about the direction and strength of the relationship and what it means.

2. Re-do problem #1 (a) and (b) using SPSS. Follow the guidelines in your

handout to make an attractive scatterplot. Hand in your SPSS output and circle the values of r on the output.

3. Given the following set of paired scores for 5 subjects:

Sub ID: 1 2 3 4 5 X 6 8 4 8 7 Y 5 6 9 9 11

a. Construct a scatter plot for the data b. Compute the value of the correlation coefficient c. Add the following set of scores from a sixth subject to the data: X =

24, Y = 26 d. Add the new point to your scatterplot from (a) (or make a new plot) e. Compute the correlation for the set of six paired scores f. Explain why there is such a big difference between (b) and (d).

4. As the value of a correlation approaches r1.0 (compared to a correlation close to

zero), what does it indicate about the following:

a. The shape of the scatterplot b. The variability of the Y scores at each value of X c. The accuracy with which we can predict Y if X is known

5. A recent study reported a relationship between anger levels (X) and blood

pressure (Y) in college-age participants. You want to see whether this is true in a sample of 12 friends. You use an anger measure that ranges from 10-100 where higher scores mean more anger. Systolic blood pressure (SBP) is measured in millimeters of mercury, where higher values mean higher blood pressure. I did a lot of the legwork for you on this one. Do the remaining calculations by hand and show your work.

X Y 𝑋 − 𝑋 𝑌 − 𝑌 𝑋 − 𝑋 𝑌 − 𝑌 64 170 25.5 31.5 803.25 27 132 -11.5 -6.5 74.75 37 129 -1.5 -9.5 14.25 39 108 0.5 -30.5 -15.25 17 122 -21.5 -16.5 354.75 29 118 -9.5 -20.5 194.75 36 131 -2.5 -7.5 18.75 34 142 -4.5 3.5 -15.75 44 156 5.5 17.5 96.25 50 168 11.5 29.5 339.25 46 147 7.5 8.5 63.75 39 139 0.5 0.5 0.25

6 = 38.5 138.5 0 0 1929 Sx = 11.49 SY = 18.41

a. Calculate the correlation of anger level (X) and SBP (Y) using the formula I

provided in class b. What proportion of variance in anger is explained by SBP? c. Fully describe this relationship in English (not stats-speak). That means say

something about the direction and strength of the relationship and what it means.