Spearman Rank Correlation Example
A researcher wishes to determine if a significant relationship exists between ratings on job satisfaction and ratings on following safety procedures.
Question 1 asks “How satisfied are you with your job”
12345678910
Very dissatisfiedNeutralVery satisfied
Question 2 asks “How often do you follow safety procedures?”
12345678910
NeverSometimesAlways
The data was as follows:
Case / Question 1 / Question 21 / 1 / 2
2 / 6 / 7
3 / 7 / 5
4 / 5 / 6
5 / 3 / 1
6 / 8 / 10
7 / 2 / 4
8 / 9 / 9
9 / 4 / 3
10 / 10 / 8
Step 1: Null and Alternative Hypotheses
Ho: There is no relationship between ratings on job satisfaction and ratings on following safety procedures.
H1: There is a relationship between ratings on job satisfaction and ratings on following safety procedures.
Step 1A: Determine dependent and independent variables and their formats.
Both ratings are ordinal
Step 2: Choose test statistic
Spearman Rank Order Correlation Coefficient
Step 3: Choose Alpha Level
Use Alpha level = .05
Interpreted as “There is a 5% chance that a significant relationship really does not exist although the results indicate one does (5% chance of committing a Type I error or stated as 5% chance of rejecting the Null hypothesis when in reality it is false).
Step 4: Determine the Critical Score
For the Spearman Rank Order Correlation Coefficient, there is a two step process. Step one is to determine the correlation coefficient and step 2 is to determine significance using the T-Test. The critical score is determined using a T-table Table. The first column is the Degrees of Freedom and the other columns are the Alpha levels.
The degrees of freedom for the T-test is equal to the (number of cases - 2). For example, if there are 10 cases, then the DF is (10-2) = 8
Step 5A: Run the Spearman Rank Order Correlation Coefficient Test
The Spearman Rank Order Correlation should be set up as follows:
The manner in which each respondent answered questions #1 and #2 were ranked from 1 to 10. Ties were adjusted for.
Case / Question 1. Rank / Question 2, Rank / Difference / Difference21 / 1 / 2 / 1 / 1
2 / 6 / 7 / 1 / 1
3 / 7 / 5 / 2 / 4
4 / 5 / 6 / 1 / 1
5 / 3 / 1 / 2 / 4
6 / 8 / 10 / 2 / 4
7 / 2 / 4 / 2 / 4
8 / 9 / 9 / 0 / 0
9 / 4 / 3 / 1 / 1
10 / 10 / 8 / 2 / 4
Total / 24
The following formula is used when there are no ties in the rankings. If ties are present, there is an alternative formula used.
The value .85 is interpreted as a very strong correlation. The next step is to determine if it is significant.
Step 5B: Run the T-test
Step 6: Compare your score to the critical score
To interpret the .85, compare the 4.47 to the critical score. If the obtained score is greater than the critical score, reject the Null and accept the alternative. The critical score from the t-table at .05 and DF = 8 is 2.31. (NOTE: On a T-table, use the .025 column since .025 at one end and .025 at the other end gives you .05).
Since 4.47 is greater than 2.31, Reject the Null Hypothesis and conclude there is a significant relationship between the rankings on the 2 scales.
Step 7: Conclusions
There is a significant relationship between the ratings on job satisfaction and ratings on following safety procedures. The more satisfied, the more likely they will follow procedures.