For a sample of n = 20 individuals, how large a Pearson correlation is necessary to be statistically significant for a two-tailed test with a = .05?
To determine the minimum Pearson correlation necessary to be statistically significant for a two-tailed test with a significance level (a) of 0.05, you need to consult a statistical table or use a statistical software package.
The critical value of the Pearson correlation coefficient (r) will depend on the degrees of freedom (n - 2), where n is the sample size. In this case, since n = 20, the degrees of freedom would be 20 - 2 = 18.
To find the critical value, you can use a statistical table or a statistical calculator. The table provides critical values for various alpha levels based on degrees of freedom. Alternatively, you can use statistical software that automatically calculates critical values.
However, to illustrate the process, let's use an online statistical calculator to find the critical value for a two-tailed test with a significance level of 0.05 and 18 degrees of freedom:
1. Open a web browser and search for "Pearson correlation coefficient critical value calculator" or a similar term.
2. Choose a reputable statistical website or software.
3. Enter the significance level of 0.05 and the degrees of freedom (18) into the calculator.
4. The calculator will provide you with the critical value of the Pearson correlation coefficient.
For example, using a statistical calculator, the critical value for a two-tailed test with a significance level of 0.05 and 18 degrees of freedom is approximately 0.444.
Therefore, for the sample size of n = 20, a Pearson correlation coefficient larger than 0.444 (in either positive or negative direction) would be necessary to achieve statistical significance at the 0.05 level.