Question

Subject                   X                                Y

            1                      18                                22

            2                      13                                19

          3                      25                                35

            4                      16                                24

            5                      27                                56

            6                      16                                25

            7                      9                                30

With an alpha level of .05 and a two-tail test, what would be a significant correlation coefficient for the above scores (what is the critical value)?

Question options:

.729

.7545

.789

.6664

Answer 1

r Critical is the minimum value of r that would be considered significant for a given sample size and alpha level. r Critical is usually looked up on a chart but can be calculated directly with the Excel formula.

Using chart:

The critical value of the Pearson product moment correlation coefficient for the degree of freedom of n - 2 = 7 -2 = 5 and alpha = 0.05 and a two-tailed test can be looked up from the critical r table, we find the critical value to 0.7545.

Using EXCEL

I have used EXCEL Addin Real statistics to find the correlation coefficient of X and Y.

EXCEL> AddIn> Real Statistics > Data Analysis > Corr > Correlation Tests

Input Range 1: Select data of X

Input Range 2: Select data of Y

Alpha =0.05

Test Type: Pearson's

Number of Tails: 2

Ok

	Correlation Coefficients
	Pearson	0.7
	Spearman	0.5
	Kendall	0.4
	Pearson's coeff (t test)			Pearson's coeff (Fisher)
	Alpha	0.1		Rho	0
	Tails	2		Alpha	0.1
				Tails	2
	corr	0.7
	std err	0.3		corr	0.7
	t	2.3		std err	0.4
	p-value	0.1		z	1.8
	lower	-0.1		p-value	0.1
	upper	1.5		lower	-0.1
				upper	1

We get the Pearson's correlation coefficient, r of 0.72128 which is not significant at 5% level of significance as two-tailed p-value is 0.06733 which is more than 0.05 and with a t-statistic value of 2.32855. The critical t-value for df = n -2 = 7-2 and alpha = 0.05 is 2.570543. Also, the r value is less than the critical r -value.