Theory says that correlation between -0.2 and 0.2 is barely existing (if existing at all) and SPSS says that 0.162 Spearman is a significant correlation at the 0.01 level (2-tailed). What am I missing?
My n is 400.
Very possible.
Play with the sample size and standard deviations on this applet, and see what r-squared and p-values you get.
https://econometricsbysimulation.shinyapps.io/OLS-App/
The meaning of p-value is changed by case number. You do not trust the "Theory says that correlation between -0.2 and 0.2 is barely existing (if existing at all) ". The author does not understand an introductory of inferential statistics. If you test 10 cases, the p-value is changed.
Yes, it is useful to re-visit the definition of p-value. A p-value tells you nothing about the size of the effect (r, in this case).
The p-value says only: You have a null hypothesis, "There is no correlation" or "r is equal to zero.". It then asks the question: Do you have enough evidence to reject this null hypothesis?
If the sample size is large, even a relatively small effect can garner a small (significant) p-value.
So, if your result is statistically significant, the next issue is determining the ecological or practical importance (strength) of the association identified between the variables: this is the point of the "rules of thumb" given for interpreting r (e.g., "barely exists").
When p
Reporting the confidence interval is often also useful. As far as relate the size of r to its importance, it depends on the context. Importance, effect size, and achieved significance level are all very different things. The attached plot I published (I think with clearer fonts) on interpreting an effect from the statistical output. Importance requires more context so it is not part of this scale.
Statistical significance is an empirical issue, about which theory has nothing to say.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software
- SPSS