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# Reverse Significance

### Input.

P-value for the Z-test, give the p-value in the p-value box. Leave the df boxes both zero.

P-value for the T-test, give the p-value in the p-value box and the degrees of freedom for the t-value in the first degrees of freedom box. Take care to keep the value in the second df box zero ('0').

P-value for the F-test, give the p-value in the p-value box. Give the degrees of freedom for the numerator in the first degrees of freedom box and the degrees of freedom for the denominator in the second df box.

P-value for the Correlation, give the p-value for a correlation in the parametergive the p-value in the p-value box. Give the degrees of freedom in the second df box.

P-value for the Chi-square, give the p-value in the p-value box. Give the degrees of freedom in the second df box.

Degrees of freedom is mostly the number of cases minus 1. Major exception is the Chi-square where the number of rows-1, columns-1 and layers-1..etc is taken (Thus, df(C2)=(r-1)*(c-1)*(l-1)). Also, if the t-value is the result of the t-test for a difference between two independent groups it works different, please read the discussion on the t-test helppage.

### Explanation.

Reverse significance is to replace the tables you often find at the back of statistics books. This time you can look up the parameter value on the basis of the p-value. The procedure significance allows you to look up the p-value on the basis of the parameter value. The procedures here are only relevant for continuous distribution, for discrete distributions use the relevant discrete SISA procedure.

It all works simple, fill in the p-value, the degrees of freedoms as appropriate, push the"calculate" button, and you get the parameter value.

### Technical Discussion.

The Chi-square distribution is at the basis of calculating the significance of the Correlation co-efficient also. The algorithm comes from Poole et al, the algorithm is also mentioned in the 'Epi-Info' manual (1994). The procedure provides a very good approximation (similar precision as the usual tables) of the Chi-square distribution, only in extreme cases will you have to do further validation.

The procedure to approximate the significance of the t-value and the z-value is based on algorithm '03' from Applied Statistics (1968). After making slight additional improvements the results are very satisfactory (similar precision as the usual tables), only in extreme cases will you have to do further validation. The procedure is unfortunately not very efficient as it a contains a loop. We put the cut-off point for the loop at df=3000 change this to a higher number if you want more precise results, you will find however that the improvement will be small.

The z-value calculation is based on algorithm 209 from the CACM by D.Ibbetson. The procedure is very efficient and gives good precision. The procedure is not very good for estimating large z-values. In that case the t-value is given for 3000 degrees of freedom.

The p-value for the correlation coefficient is converted via the single sided t-test, following Cohen.