Chapter 6: Analysing the Data |

## Critical valuesFrom Pearson's table (reproduced here), the column headed "Level of significance for two-tailed test" gives the If we move to a sample of size 10 (df = 8) we find that a correlation of .632 or greater (or -.632 or less) For samples of size 20 (df = 18), the critical value is .444 for the .05 level of significance, .516 for the .02 level, and .561 for the .01 level. The value we were examining of -.65 can therefore be considered significant at the .01 level for samples of size 20. We would report this as r(18) = -.65, p < .01. For samples of size 100, a correlation of .65 is highly significant. For the example on logical reasoning and creativity a correlation of .736 was obtained. Looking at the line for df = 18 we would report that r(18) = .736, p < .01. These days we usually do not have to refer to statistical tables to determine the significance of a test-statistic, the computer will produce the significance level with the value of the test statistic itself. The SPSS printout in Figure 6.5 reports that the "Sig. (2-tailed)" value is .000 and puts two asterisks next to the r value of .736. This is just SPSS's way of reporting the p-value. Here, ".000" does not actually mean zero. This is just a rounding problem. If it was actually zero, that would mean that the probability of an r-value of this size or greater occurring is impossible. However, we were working with real numbers and obviously the result is possible because we just did it! Of course the actual p-value is probably something like .000376, but when this is rounded to nearest 3 decimal places, it comes out as .000. From the SPSS output which is more accurate than the tables, we would report r(18) = .736, p < .001
Output 6.5 SPSS output of the correlation between logical reasoning and creativity. SPSS uses one asterisk to indicate that p < .05 and two asterisks to imply that p < .01. SPSS never uses more than two asterisks, however, you will occasionally read published articles that use three and even four asterisks to indicate higher levels of significance. (Three asterisks usually indicates p < .001 and four indicates p < .0001). |

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