LOG TRANSFORMATION HYPOTHESIS TEST CALCULATOR HOW TO
However, it is not clear how to obtain the appropriate null hypothesis and how to conduct statistical testing against it. As a result, the statistical procedure of testing the null hypothesis – that the coefficient of correlation or the slope of regression is zero – might no longer be appropriate and the results need to be interpreted cautiously 1. Mathematical coupling occurs when one variable directly or indirectly contains the whole or part of another and the two variables are then analysed using correlation or regression 12. Testing the relation between percentage change and initial value using correlation or regression suffers the same criticism as testing the relation between change and baseline due to mathematical coupling 12, 13. Suppose x is the baseline value, y the post-treatment value and percentage change is defined as ( x − y)/ x. However, these studies tested the relation between percentage change and baseline value by correlating two mathematically coupled variables and it has been shown that this practice is questionable 12. The authors therefore concluded that because the aldosterone-renin ratio was highly associated with the plasma rennin activity, this ratio was not a renin-independent diagnostic test for screening primary aldosteronism. Nevertheless, a very strong negative correlation about −0.84 was found between the aldosterone-renin ratio and rennin activity. In the study, a weak positive correlation around 0.22 was found between plasma aldosterone and plasma rennin activity. Another example is a study on using the aldosterone-renin ratio for screening of primary Aldosteronism 11. Therefore, these results seemed to suggest that the improvement in thiamine status depends on the degree of thiamine deficiency at baseline. For example, one study found the improvement in thiamine deficiency measured as percentage change in erythrocyte transketolase activity coefficient was strongly correlated with its baseline value in patients admitted with malaria 10. However, a related problem with regard to how to test the relationship between percentage change and baseline value remains unresolved 6, 7, 8, 9.
Our previous study reviewed the proposed methods to resolve this controversy and clarified a misunderstanding regarding which methods are more appropriate 1. How to test the relation between change and initial value has been a controversial issue in the statistical literature 1, 2, 3, 4, 5. The usual approach to testing the relation between percentage change and baseline value tended to yield misleading results and should be avoided. Results suggested the type-I error rates increased with the magnitude of measurement errors, whilst the statistical power to detect a genuine relation decreased. We also undertook simulations to investigate the impact of measurement errors on the performance of the proposed test. Two examples were used to demonstrate how the usual testing gave rise to misleading results, whilst results from our simple test were in general consistent with those from simulations. We also proposed a simple procedure for testing the appropriate null hypothesis based on the assumption that when there is no relation between percentage change and baseline value, the coefficients of variation for repeated measurements of a random variable should remain unchanged. In this paper, we first explained why the usual testing of the relation between percentage change and baseline value is inappropriate and then demonstrated how the appropriate null hypothesis could be formulated. Testing the relation between percentage change and baseline value has been controversial, but it is not clear why this practice may yield spurious results.