Chapter 13Extra. Strength of relationships: Continuous data

1. Consider the following table which shows the scores twelve students received on two exams:

Exam 1 Exam 2 Exam 3 Exam 4
a 82.66 41.68 a 43.58 85.51
b 45.62 89.61 b 85.51 32.11
c 35.80 55.99 c 68.79 75.22
d 83.46 57.61 d 75.41 55.49
e 45.34 91.22 e 95.22 43.42
f 81.32 44.69 f 47.59 63.65
g 45.53 41.18 g 75.28 52.75
h 45.99 43.75 h 63.65 47.51
i 83.05 59.44 i 59.14 66.31
l 45.88 50.59 l 66.39 68.71
k 44.92 54.85 k 52.75 59.16
l 81.64 36.19 l 32.11 95.28

Make a scatterplot for the exam scores with the X-axis for Exam 1 and the Y-axis for Exam 2. Do another one for Exam 3 and Exam 4.

 

2. Calculate the variance and standard deviation for the scores of the first two exams.

   exam 1  exam 2
 variance    
 std. dev.    

3. Calculate the covariance between the scores on the first two exams shown in Question 1.

 

4. Calculate Pearson's r between the scores on the first two exams shown in Question 1.

 

5. Calculate Pearson's r between the scores of the two exams shown below.

 Exam 1  Rank 1    Exam 2  Rank 2
42.7  3    81.7  11
 93.6  12    49.5  2
 65.4  5    75.4  7
 68.5  6    77.6  8
 87.7  11    31.8  1
 41.7  2    84.6  12
 85.5  10    65.5  4
 82.4  9    53.5  3
 43.3  4    79.9  9
 75.5  7    75.4 6
 78.0  8    72.4  5
 41.5  1    81.0  10
         
 

6. Calculate Pearson's r between the ranks of the scores of the two exams shown in Question 5.

7. Discuss the difference between the correlations you obtained in your answer to Questions 5 and 6. A scatterplot of the data may be helpful. Is there a problem here? What is the best way to address this data?

8. Calculate Pearson's r between the scores on the third and fourth exams in Question 1.