Tuesday, May 12, 2015

p value and significance


This should be easy. 

But students are prone to make mistakes in relating the p value and the test statistic. For example, one student wrote in her take home test

"Nurses attitude also do not significantly correlate with teamwork scores, r(28)=.430, p = 0.018.


The student's conclusion is wrong. When the p value that was found from the data is LOWER than the alpha value, then the test statistic (e.g. r) IS significant. In other words, as can be inferred from the diagram, the r value is significantly different from zero. It had crossed the critical boundary i.e. moving from 'not significant' zone to the 'significant' zone. 

Perhaps the mistake stems from the confusion with small numbers. Is 0.018 bigger or smaller than 0.05? If that is the case, students can use the diagram above to mark the their p value is relative to the 0.05 mark. 

The diagram should be modified when using other test statistics. If we are using z statistic, then the critical value is 1.96 when the alpha is 0.05 (i.e not dependent on df value). When we use the F test, then the minimum value is 1 instead of 0 (because F is a ratio).  

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