Copyright: Distribution Help Copyright® 1993 Mark Von Tress


Distribution Function Help

This program calculates probabilities for some of the more important continuous distribution functions. It also calculates the power function and sample sizes for  the normal and t-tests on means.

The Go buttons start the calculation, and the Q buttons closes the window.

The main menu functions are:

Normal Probs

t distribution

Chi square distribution

F and beta distribution

Power functions and Sample Sizes

If you like this program and use it regularly, please send $10 US to

Mark Von Tress
PO Box 171173
Arlington TX 76003


Normal Probs
Normal Probabilities

•	Probs: Enter a standard normal variable, z, and get the probabablity less than or equal to z.

•	Mean Std Probs: Enter a normal random variable, X=x, having mean, mean, and standard deviation, std. Prob is the probability that X<=x.

Percentiles

•	Quantile: Enter the probability, q. z is the value of a standard normal random variable having probability q less than or equal to it. It is the 100*q'th percentile.

•	Inv Nm std: Enter the probability, prob, mean and standard deviation,std. x is the value of a normal random variable with mean and std dev. having probability prob less than or equal to it.


t distribution

•	Prob: enter t, and the degrees of freedom, df. Returns prob=P(T(df) <= t )

•	inverse t: enter prob, and the degrees of freedom, df. Returns t such that
prob = P(T(df) <= t ).

Non central t distribution

•	Non central t: enter t, the degrees of freedom, df, and the non-centrality parameter, nc(>0). Returns prob=P(T(df,nc) <= t ). Non centrality parameter matches SAS usage.

•	nct quantiles: enter prob, the degrees of freedom, df, and the non-centrality parmeter, nc(>0). Returns t such that prob = P(T(df,nc) <= t ).


Chi Square Probs
Chi-Square Probs

•	Chi-square: Input chi-square, chi, and degrees of freedom, df. Returns prob=P(X(df)<chi )

•	Inv ChiSquare: Input prob, and degrees of freedom. Returns x such that prob=P(X(df)<x)

Non-Central Chi Square

•	NC ChiSquare: input non-central chi square variate, chi,  the degrees of freedom, df, and the non-centrality parameter.  Returns prob = P( X(df,nc) < chi). Note, noncentrality parameter is 2*lambda in Abramowitz and Stegun equation 26.4.25. Handbook of Mathematical Functions. Also the noncentrality parameter matches the use in SAS.

•	Inv NCChiSqr: Inverse non-central Chi-square, input prob, df, and nc. Returns x such that prob=P( X(df,nc)<x)

Gamma Distribution

•	Gamma: Input gamma variate, g, alpha, a, and beta, b. Returns prob=P(G(a,b)<g).

•	InvGamma: Input prob, alpha, a, and beta b. Returns g such that prob=P(G(a,b)<g)


F and beta probs
F distribution

•	Fdist: input F variate, f, degrees of freedom df1,df2. Return prob=P(F(df1,df2)<f).

•	Invf: input prob, degrees of freedom df1,df2. Return f such that prob=P(F(df1,df2)<f).

NonCentral F

•	NonCentralF: input F variate, f, degrees of freedom df1,df2, and noncentrality parameter. Return prob=P(F(df1,df2,nc)<f). The non-centrality parameter matches SAS.

•	Ncf inverse: input prob, degrees of freedom df1,df2, and noncentrality parameter. Return f such that prob=P(F(df1,df2,nc)<f). The non-centrality parameter matches SAS.

Beta

•	Beta: input beta variate, x, alpha, a, and beta, b. Returns prob=P(B(a,b)<x).


Power Functions and Sample Size

The power functions and sample size menus calculate the power of hypothesis tests and sample sizes for several well known statistical tests.  The 1 sample tests compare means to a constant. The 2 sample tests compare two means. The last test compares two proportions.

The menus are fairly similar. You select the parameter to solve for by using a radio button. Then you input the other information needed to describe the test. Then press the go button.

Normal Tests

T-tests

Compare Percentages


Normal Tests

These calculate power and sample size for the 1 and 2 sample tests on normal means.

Z test 1 sample:

Select a left, right, or 2-sided alternative using the Sides radio button.  Select the parameter to solve for using the 'Solve for' radio button. Enter the type 1 error, alpha, the standard deviation, and the size of the difference to detect. Enter the sample size if solving for the power, and enter power if solving for the sample size. Select the go button to calculate the selected parameter.

Z test 2 sample:

Select a left, right, or 2-sided alternative using the Sides radio button.  Select the parameter to solve for using the 'Solve for' radio button. Enter the type 1 error, alpha, the standard deviation, and the size of the difference to detect. Enter the sample size if solving for the power, and enter power if solving for the sample size. Select the go button to calculate the selected parameter.


t Tests

TTest 1 Sample

Select a left, right, or 2-sided alternative using the Sides radio button.  Select the parameter to solve for using the 'Solve for' radio button. Enter the type 1 error, alpha, the standard deviation, and the size of the difference to detect. Enter the sample size if solving for the power, and enter power if solving for the sample size. Select the go button to calculate the selected parameter.

TTest 2 Sample

Select a left, right, or 2-sided alternative using the Sides radio button.  Select the parameter to solve for using the 'Solve for' radio button. Enter the type 1 error, alpha, the standard deviation, and the size of the difference to detect. Enter the sample size if solving for the power, and enter power if solving for the sample size. Select the go button to calculate the selected parameter.


Compare Proportions
Compare Proportions: p1-p2

Select the parameter to solve for using the 'Solve for' radio button. Enter the type 1 error, alpha, the proportions, p1 and p2. Enter the sample size if solving for the power, and enter power if solving for the sample size. Select the go button to calculate the selected parameter.