cumstu(x,df [,upper:T or lower:F]), x and df REAL, elements of df > 0 cumstu(x,df,delta [,upper:T or lower:F]), x, df > 0, delta REAL |

cumstu(Val,df) computes P(t <= Val) where t is a Student's t random variable with df degrees of freedom. Val and df can be scalars, vectors, matrices or arrays, but must have the same size and shape if neither is a scalar. When both are scalars, the result is a scalar; if there is a non-scalar argument, the result has the same size and shape as that argument. The degrees of freedom must be positive, but not necessarily integral. cumstu(Val,df,upper:T) and cumstu(Val,df,lower:F) compute upper tail probabilities P(t >= Val). The result is mathematically equivalent to 1 - cumstu(Val,df) but may be more accurate for large Val. Two tailed P values for an observed t statistic Val can be computed with the macro twotailt(Val,df) or as 2*cumstu(abs(Val),df,upper:T)). Example: Compute two-tail P-value of H_0: mu = 10 using sample mean xbar and standard deviation s from sample of size n: Cmd> 2*cumstu(abs(sqrt(n)*(xbar-10)/s), n-1, upper:T) #2-tail P-value cumstu(Val,df,delta) computes P(t <= Val) where t is a non-central Student's t random variable with df degrees of freedom and noncentrality parameter delta. All three arguments can be scalars, vectors, matrices or arrays, but any non-scalar arguments must have the same size and shape which will be the size and shape of the result. cumstu(Val,df,delta,upper:T) computes the upper tail probability P(t >= Val). When Val = (xbar - mu_0)/(s/sqrt(n)) is computed from a random sample of size n from N(mu_a, sigma^2), delta = sqrt(n)*(mu_a - mu_0)/sigma. Example: Compute the power of a one-tail 5% t-test of H_0: mu = 10 vs H_a: mu > 10 when mu = 15: Cmd> cumstu(invstu(.05,n-1,upper:T),n-1,sqrt(n)*(15-10)/sigma,upper:T) See also twotailt(), invstu(), subtopic cumF:"non_central_F", power() and power2().

Gary Oehlert 2003-01-15