Elementary Statistics and Computer Application

Testing the significance of r

The significance of r can be tested by Student’s t test. The test statistics is given by



This t is distributed as Student’s t distribution with (n-2) degrees of freedom.
The relationship between the variables is interpreted by the square of the correlation coefficient (r2) which is called coefficient of determination. The value 1-r2 is called as coefficient of alienation. If r2 is 0.72, it implies that on the basis of the samples 72% of the variation in one variable is caused by the variation of the other variable. The coefficient of determination is used to compare 2 correlation coefficients
Problem
Compute Pearsons coefficient of correlation between plant height (cm) and yield (Kgs) as per the data given below

Plant Height (cm)	39	65	62	90	82	75	25	98	36	78
Yield in Kgs	47	53	58	86	62	68	60	91	51	84

Solution

• Ho: The correlation coefficient r is not significant
• H1: The correlation coefficient r is significant.
• Level of significance 5%
From the data
n = 10






Correlation coefficient is positively correlated.
Test Statistic

ttab=t(10-2, 5%los)=2.306
Inference
t> ttab, we reject null hypothesis.

• .^..The correlation coefficient r is significant. (i.e) There is a relation between plant height and yield.