Simple Interactive Statistical Analysis
Reverse Significance
Input.
Z-value, give the p-value for a z in the p-value box. Push the "z-value" button for the z-value.
T-test, give the p-value for a t in the parameter box and the degrees of freedom for the t-value in the degrees of freedom box. Take care to keep the value in the number of cases box less than one ('1'). Instead of the degrees of freedom for the t-value you can also give the number of cases for group one in the degrees of freedom box and the number of cases for group two in the number of cases box.
F-test, give the p-value for an f in the parameter box. Give the degrees of freedom for the numerator in the degrees of freedom box and the degrees of freedom for the denominator in the number of cases box.
Correlation, give the p-value for a correlation in the parameter box. Give the degrees of freedom or the number of cases in the appropriate box.
Chi-square, give the p-value for a Chi-square in the parameter box. You must give the degrees of freedom in the degrees of freedom box.
Explanation.
Reverse significance is to replace the tables you often find at the back of statistics books. 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 parameter, the degrees of freedom or the number of cases, push the appropriate 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.
