Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the Correlation data analysis tool. This tool calculates the Pearson’s, Spearman’s (rho) and Kendall’s (tau) correlation coefficients, as well as conducts various versions of a one-sample correlation test.
Example 1: Repeat Example 1 of Correlation Testing via the t Test (regarding Pearson’s correlation) using the Correlation data analysis tool.
To use this tool, press Ctrl-m and select Correlation from the menu of choices that appears. Fill in the dialog box that appears as shown in Figure 1 and press the OK button.
Figure 1 – Correlation data analysis tool dialog box
The output for the two-tailed test is shown on the right side of Figure 2 (starting at cell J3). The output contains the Pearson’s, Spearman’s and Kendall’s correlation coefficients (cells K5, K6 and K7). In addition, both the two-tailed t-test and normal test using the Fisher transformation are displayed where the hypothetical population Pearson’s correlation ρ = 0.
If you want to conduct a one-sample correlation test where ρ is equal to some value that is not zero, you would simply perform that same steps as described above and then change the value in cell N11 to this value. In this case you would need to ignore the results of the t test since they would not be accurate.
You can also change the value for alpha and/or the number of tails, and the output values will change automatically.
Figure 2 – Output from Correlation data analysis tool (Pearson’s)
Example 2: Repeat Example 3 of Spearman’s Correlation using the Correlation data analysis tool.
Press Ctrl-m and select Correlation as before, but when the dialog as in Figure 1 appears, select the Spearman’s option. The result is shown in Figure 3.
Figure 3 – Output from Correlation data analysis tool (Spearman’s)
We see from the figure that Spearman’s rho is -.67442 (cell N14). Since p-value = .005821 < .05 = α, we are pretty confident that rho is not zero. If you change the values in cells N11 and/or N12 the other values of rho, t-stat and p-value will change automatically.
Example 3: Repeat Example 1 of Kendall’s Tau using the Correlation data analysis tool.
Press Ctrl-m and select Correlation as before, but when the dialog as in Figure 1 appears, select the Kendall’s option. The result is shown in Figure 4.
Figure 4 – Output from Correlation data analysis tool (Kendall’s)
We see from the figure that Kendall’s tau is -.52381 (cell Y13) and that we are 95% confident that the actual value is in the interval (-.901, -.147). Since p-value = .006493, we are pretty confident that tau is not zero.
If you change the values in cells Y10 and/or Y11 the values of tau, s.e., etc. will change automatically.
Observation: The ties correction factor is used for the Kendall’s Tau option of the Correlation data analysis tool.