Exam 1

1. Metainformation

   Tag	Value
   file	Descriptive-statistics_eur-descriptive-109-en_eur-descriptive-109-en
   name	eur-descriptive-109-en
   section	Descriptive statistics/Summary Statistics/Bivariate statistics/Correlation
   type	num
   solution	0.435
   tolerance	0.01
   Type	Calculate
   Program	Calculater
   Language	English
   Level	Statistical Literacy

   Question

   Below you find the scores of six students on the course 1.1 exam (social psychology) and the course 1.3 exam (statistics). Calculate the correlation between the exam scores of course 1.1 and course 1.3.

   Students	Exam Course 1.1	Exam Course 1.3
   1	7.5	6.8
   2	6.2	5.4
   3	5.2	7.6
   4	8.2	7.6
   5	9.2	8.4
   6	6.9	4.7

   
   

   Solution

   	Students	Exam Course 1.1	Exam Course 1.3	Squared Deviation 1.1	Squared Deviation 1.3	Product deviation 1.1 – deviation 1.3
   	1	7.5	6.8	(7.5 ‐ 7.2)(7.5 ‐ 7.2)	(6.8 ‐ 6.75)(6.8 ‐ 6.75)	(7.5 ‐ 7.2)(6.8 ‐ 6.75)
   	2	6.2	5.4	(6.2 ‐ 7.2)(6.2 ‐ 7.2)	(5.4 ‐ 6.75)(5.4 ‐ 6.75)	(6.2 ‐ 7.2)(5.4 ‐ 6.75)
   	3	5.2	7.6	(5.2 ‐ 7.2)(5.2 ‐ 7.2)	(7.6 ‐ 6.75)(7.6 ‐ 6.75)	(5.2 ‐ 7.2)(7.6 ‐ 6.75)
   	4	8.2	7.6	(8.2 ‐ 7.2)(8.2 ‐ 7.2)	(7.6 ‐ 6.75)(7.6 ‐ 6.75)	(8.2 ‐ 7.2)(7.6 ‐ 6.75)
   	5	9.2	8.4	(9.2 ‐ 7.2)(9.2 ‐ 7.2)	(8.4 ‐ 6.75)(8.4 ‐ 6.75)	(9.2 ‐ 7.2)(8.4 ‐ 6.75)
   	6	6.9	4.7	(6.9 ‐ 7.2)(6.9 ‐ 7.2)	(4.7 ‐ 6.75)(4.7 ‐ 6.75)	(6.9 ‐ 7.2)(4.7 ‐ 6.75)
   Sum		43.2	40.5	10.18	10.2	4.43
   Mean		7.2	6.75	1.697	1.699	0.738

   The mean is calculated by summing the scores on the exam and dividing this sum by the number of participants:

   Mean Exam 1.1 = $\frac{43.20}{6} = 7.20$

   Mean Exam 1.3 = $\frac{40.50}{6} = 6.75$

   The covariance is calculated by summing the product of the deviation scores and divide this by N:

   Covariance Exam 1.1, Exam 1.3: $Cov_{E1.1, E1.3} \frac{4.43}{6}=0.738$

   The correlation is calculated by dividing the covariance by the product of the standard deviations.

   The standard deviation is calculated by taking the square root of the variance:

   Standard deviation $SD_{Exam 1.1} = \sqrt{1.697} = 1.303$

   Standard deviation $SD_{Exam 1.3} = \sqrt{1.699} = 1.304$

   Correlation Exam 1.1, Exam 1.3: $Cor_{E1.1, E1.3} = \frac{0.738}{1.303 \times 1.304}=.435$.