Pearson correlation coefficient can be used to express the relationship between two variables when data are quantitative (interval or ratio scales) and both variables follow normal distributions. When data are qualitative ordinal scales then the relationship between two variables can be calculated by using Spearman correlation or Kendall Tau correlation, and when data are qualitative nominal scales in the form of contingency table then the relationship between two variables can be calculated by using Cramer correlation. Those qualitative data correlations will be discussed in other writing sessions. Symbol of correlation for population size is ρ (pronounced rho) and for sample size is r.
Formula for Pearson correlation is as follows:
The correlation coefficient has range value from -1 to 1
An industrial company has a monthly production data for ten months and the number of hours of work such as Table 1 below.
The linear relationship between production and the working hours of employees in these industries is 0.9978 or 99.78 percent. If this value is squared, we will get the value of variation influences between those variables. This value is commonly referred as the coefficient determination (r2). The coefficient determination has range value from 0 to 1. In the above example, variation in employees work hours has been influenced by variation of production for about 99.56 percent.
Test for correlation of Pearson.
This test is used to determine if there is a linear relationship between two variables is significant. This test includes the classification of parametric statistical tests.
The hypotheses being tested is
H0: ρ = 0 VS H1: ρ ≠ 0
Statistical test that used is the t-test formulated as follows
The rejection area is t < -t(a/2 , n-2) dan t > t(a/2 , n-2)
Using the data from Table 1, testing for the population correlation coefficient with 5 percent significance level is
t(0.025; 8) = 2.31
Decision: H0 was rejected because t > t(0.025; 8)
Conclusion: there is a linear relationship between the production and working hours with 95 percent level of confidence.
See you in other writing sessions, have enjoying statistics.
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*) The writer is a lecturer in The Institute of Statistics, Jakarta, Indonesia.