Calculators for Statistical Table Entries

 
 		z to P
 
 		chi-square to P
 
 		t to P
 
 		r to P
 
 		F to P
 
 		Fisher r-to-z transformation
 
 		.05 and .01 critical values of the
Studentized range statistic Q
 
 		Odds Ratio & Log Odds Ratio
 
z to P Calculator
For any given value of z, this section will calculate
º
 		the respective one-tailed probabilities of —z and +z;
º
 		the two-tailed probability of±z;
º
 		and the proportion of the normal distribution falling between —z and +z.

To proceed, enter the value of z in the designated cell and click «Calculate». Note that the programming for this section is able to perform meaningful probability calculations only for cases where |z|<5.
Click here to see the details
of the sampling distribution
to which any particular value
of z belongs.
         
  z =

Probabilities P

Text will appear in this box only if
the value of |z| is greater than 3.75.
one-tailed for —z
one-tailed for +z
two-tailed for ±z
area between ±z

 
Chi-Square to P Calculator
For values of df between 1 and 20, inclusive, this section will calculate the proportion of the relevant sampling distribution that falls to the right of a particular value of chi-square. To proceed, enter the values of chi-square and df in the designated cells and click «Calculate».
Chi-Square
 		df
 		P



   
Click here to see the details of the sampling
distribution to which any particular value of
chi-square belongs. At the prompt, enter the
appropriate value of df.
 
t to P Calculator
This section will calculate the one-tail and two-tail probabilities of t for any given value of df. To proceed, enter the values of t and df in the designated cells and click «Calculate».
t df
  P   one-tailed
two-tailed
   
Click here to see the details of the sampling
distribution to which any particular value of t
belongs. At the prompt, enter the appropriate
value of df.
 
r to P Calculator
If the true correlation between X and Y within the general population is rho=0, and if the size of the sample, N, on which an observed value of r is based is equal to or greater than 6, then the quantity

t =
 		r
sqrt[(1—r2)/(N—2)]

is distributed approximately as t with df=N—2. Application of this formula to any particular observed sample value of r will accordingly test the null hypothesis that the observed value comes from a population in which rho=0.

To assess the significance of any particular instance of r, enter the values of N[>6] and r into the designated cells below, then click the 'Calculate' button.
N =
r =
   
t
 		df
  P  
 		one-tailed
two-tailed

 
Fisher r-to-z Transformation

For any particular value of r, the Pearson product-moment correlation coefficient, this section will perform the Fisher r-to-z transformation according to the formula
     zr = (1/2)[loge(1+r) - loge(1-r)]
If a value of n is entered (optional), it will also calculate the standard error of zr as
     SEzr = 1/sqrt[n-3]

r =
n =
            
zr =
SEzr =


 
F to P Calculator

This section will calculate the proportion of the relevant sampling distribution that falls to the right of a particular value of F, as defined by the degrees of freedom for the numerator and denominator of the F-ratio. To proceed, enter the values of F and df in the designated cells and click «Calculate».

F 
Click here to see the details of the
sampling distribution to which any
particular value of F belongs. At
the prompt, enter the df values
for numerator and denominator.
 df 
 		numerator 

denominator 

P 

   


 
Critical Values of Q
This section will calculate the .05 and .01 critical values for the Studentized range statistic Q. To proceed, enter the number of groups in the analysis (k) and the number of degrees of freedom, and then click «Calculate». Note that the value of k must be between 3 and 10, inclusive.

k
 		df
 		Q.05
 		Q.01




   




 
Odds Ratio & Log Odds Ratio
Given p, an observed proportion or probability:
Odds Ratio = p/(1-p)
Log Odds Ratio = loge[p/(1-p)]
Given the Log Odds Ratio [Log(OR)]:
Odds Ratio = exp[Log(OR)]
Given the Odds Ratio (OR):
p = OR/(1+OR)

Enter any one of these items—p, Odds Ratio, or Log Odds Ratio—into the designated cell, then click the «Calculate» button to fetch the corresponding values of the other two. If entering p, the entry can be either a decimal fraction or a common fraction.

p
 		Odds Ratio
 		Log
Odds Ratio