PSY 0371 Week 1 Assignment 5

PSY 0371  Week 1 Assignment 5 | San Francisco State University | Assignment Help

Homework 5

Continue to record the following information every day (up through December 1, 2020):

1.     the number of hours of sleep you got;

2.     the number of cups of caffeine drinks you had;

3.     the number of cups of non-caffeinated drinks you had;

4.     the number of hours you spent looking at a phone, computer screen, TV, etc.

(NOTE: round hours to the nearest half hour ; count each drink - however big or small - as one drink.  And remember to report the date on which you recorded your data.)

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For the fifth homework assignment, we will look at two variables and see how they are related by computing the Pearson product-moment correlation coefficient, r.  Let's use (1) the number of hours of sleep you got, and (4) the number of hours you spent looking at a phone, computer screen, TV, etc.  You will have to do a lot of the same computations that you did for Homework 4, but this time you'll have to do them twice -- once for number of hours of sleep, and once for the number of hours you spent looking at a phone, computer screen, TV, etc.

Part I: Calculate the hours of sleep

Let's start by doing this for the number of hours of sleep you got last week from Monday, October 12 through Friday, October 16 (N=5):

1.     Report the number of hours of sleep you got last week and the date for each.  (If you slept the same number of hours for each of these nights, please change one of the numbers just so there is some variability among the scores, and indicate which number you changed in this way.)

2.     Compute the mean of the number of hours of sleep you got in (1) above. 

3.     Compute the variance of the number of hours of sleep you got in (1) above.

4.     Compute the standard deviation of the number of hours of sleep you got in (1) above.

5.     Compute the z-scores for each of the original N=5 scores in (1) above.

Part II: Calculate screen time

Now do the same for the number of hours you spent looking at a phone, computer screen, TV, etc. (i.e., a device) last week from Monday, October 12 through Friday, October 16 (N=5). 

1.     Report the number of hours you spent looking at a device last week and the date for each.  (If the number of hours you spent looking at a device is exactly the same for each day last week, please change two of the numbers just so there is some variability among the scores, and indicate which scores you changed in this way.)

2.     Compute the mean of the number of hours you spent looking at a device in (1) above. 

3.     Compute the variance of the number of hours you spent looking at a device in (1) above.

4.     Compute the standard deviation of the number of hours you spent looking at a device in (1) above.

5.     Compute the z-scores for each of the original N=5 scores in (1) above.

Part III: Draw a scatterplot

For the sake of brevity, use the variable X for number of hours of sleep and use the variable Y for  number of hours you spent looking at a device.  Now make a scatterplot of your data by following these steps: 

1.     First draw a vertical line on the left side of your paper; this will be your y-axis. 

2.     Then, starting at the bottom of the y-axis, draw a horizontal line toward the right side of your paper; this will be your x-axis.  (You should now have something that looks like a large letter "L" on your paper.)

3.     Make 11 evenly spaced hatch marks on the x-axis and put the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 immediately under the hatch marks, with 0 under the leftmost hatch mark and 10 under the rightmost hatch mark.  (If X < 10 for each day, then you don't have to go all the way up to 10 on the x-axis.  If X > 10, then make a few more hatch marks on the right end of the x-axis until you get to the largest value for X you have.  Remember to keep the hatch marks evenly spaced out on the x-axis.)  Now label your x-axis by writing "X = number of hours of sleep" under the numbers that you just wrote on the x-axis. 

4.     Make 11 evenly spaced hatch marks on the y-axis and put the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 to the left of the hatch marks, with 0 at the bottom hatch mark and 10 at the top hatch mark.  (If Y < 10 for each day, then you don't have to go all the way up to 10 on the y-axis.  If Y > 10, then add a few more hatch marks at the top of the y-axis until you get to the largest value of Y you have.  Remember to keep the hatch marks evenly spaced out on the y-axis.)  Now label your y-axis by writing "Y = number of hours you spent looking at a device" to the left of the numbers that you just wrote on the x-axis. 

5.     For each day last week, you have a value for X (i.e., number of hours of sleep) and a value for Y (number of hours looking at a device).  Plot the 5 points (X, Y) on your graph-- one point (X, Y) for each day.

Part IV: Report r

1.     Fill the summary table

Show a summary of the results of what you've done to this point by reporting them in a table like the one below.  (You should have both positive and negative values for z_X, and you should have both positive and negative values for z_Y.  If that's not the case, then check your work above.)  For each cell in the rightmost column (i.e., z_X x z_Y), just multiply the z-score of X and the z-score of Y from that row. 

(When you multiply pairs of z-scores, remember to round to 2 decimal places and remember to report the sign of the product of z-scores, i.e., if both z-scores you multiply have the same sign, then the product of the z-scores will be positive; if the z-scores you multiply have opposite signs, then the product of the z-scores will be negative.)

2.     Calculate Pearson r

The Pearson product-moment correlation coefficient is the mean of the products of z-scores.  That is, r is equal to the sum of the five (z_X x z_Y)'s that you just calculated in the table above, all divided by N=5.  Here is the formula for r:

            r = Σ(z_X x z_Y)/𝑁

                  where for each pair (X,Y) for a given day,

                               z_X is the z-score of X (hours sleep), 

                               z_Y is the z-score of Y (hours looking at a device), 

                   and N is the number of (X,Y) pairs.

If the value of r is positive, then the correlation between the variables is positive.  If the value of r is negative, then the correlation between the variables is negative.  Report the value for r that you got, and say whether it is a positive or a negative correlation. 

NOTE:  The largest possible value for r is +1.00, and the smallest possible value for r is -1.00.  If r = +1.00, there is a perfect positive correlation between the variables X and Y.  If r = -1.00, there is a perfect negative correlation between the variables X and Y.  These are both indicative of the strongest possible correlation between two variables.  (If r = 0.00, then there is a zero correlation between X and Y, which is the weakest possible correlation between the variables.)   If the value for r you computed is just outside this range (e.g., 1.01 or -1.01), that might be due to rounding.  But if the value for r you computed is far outside this range (e.g., 1.08 or -1.1), then you made an error somewhere.