[Correlation Coefficient]

Critical Values for r (Correlation Coefficient) Table

See example below the table!

 

Table One: Levels of Significance of Correlation Coefficient

N

  

Levels

of

Significance

    

Number of pairs

0.20 (80%)

0.10 (90%)

0.05 (95%)

0.02 (98%)

0.01 (99%)

  

4
-
1.00
-
-
-
  

5
0.80
0.90
-
1.00
-
  

6
0.66
0.83
0.89
0.94
1.00
  

7
0.57
0.71
0.79
0.89
0.93
  

8
0.52
0.64
0.74
0.83
0.88
  

9
0.48
0.60
0.68
0.78
0.83
  

10
0.45
0.56
0.65
0.73
0.79
  

11
0.41
0.52
0.61
0.71
0.77
  

12
0.39
0.50
0.59
0.68
0.75
  

13
0.37
0.47
0.56
0.65
0.71
  

14
0.36
0.46
0.54
0.63
0.69
  

15
0.34
0.44
0.52
0.60
0.66
  

16
0.33
0.42
0.51
0.58
0.64
  

17
0.32
0.41
0.49
0.57
0.62
  

18
0.31
0.40
0.48
0.55
0.61
  

19
0.30
0.39
0.46
0.54
0.60
  

20
0.29
0.38
0.45
0.53
0.58
  

21
0.29
0.37
0.44
0.51
0.56
  

22
0.28
0.36
0.43
0.50
0.55
  

23
0.27
0.35
0.42
0.49
0.54
  

24
0.27
0.34
0.41
0.48
0.53
  

25
0.26
0.34
0.40
0.48
0.52
  

26
0.26
0.33
0.39
0.46
0.51
  

27
0.25
0.32
0.38
0.45
0.50
  

28
0.25
0.32
0.38
0.44
0.49
  

29
0.24
0.31
0.37
0.44
0.48
  

30
0.24
0.31
0.36
0.43
0.47
  
             
             

Example:

Suppose a student is studying the relationship between turbidity and dissolved oxygen. The student compares the data for both water parameters and calculates a correlation coefficient where r = -0.896.

Since the absolute value is beteen 0.50 and 1.00, we can assume that there is a correlationg between the two variables.

Since the value is negative, there is a negative correlation between turbidity and dissolved oxygen. In other words, when turbidity is high, dissolved oxygen is low, and viceaversa.

To figure out the significance level of our correlation between temperature and dissolved oxygen, we use the table above. If 7 pairs of data were used, we would look down along the column N (number of pairs) to 7. We would scan across that row until we find a number exactly at 0.89 or as close as possible. It happens that 0.89 is under the levels of significance column of 0.02. This means our correlation of coeefficient is significant at the level of 98%.

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