gofsimpt: Establishing goodness of fit of an observed to a fully...

In EQUIVNONINF: Testing for Equivalence and Noninferiority

Description

The function computes all quantities required for carrying out the asymptotic test for goodness rather than lack of fit of an observed to a fully specified multinomial distribution derived in Par. 9.1 of Wellek S (2010) Testing statistical hypotheses of equivalence and noninferiority. Second edition.

Usage

gofsimpt(alpha,n,k,eps,x,pio) 

Arguments

alpha	significance level
n	sample size
k	number of categories
eps	margin to the Euclidean distance between the vectors \mathbf{π} and \mathbf{π}_0 of true and hypothesized cell probabilities
x	vector of length k with the observed cell counts as components
pio	prespecified vector of cell probabilities

Value

alpha	significance level
n	sample size
k	number of categories
eps	margin to the Euclidean distance between the vectors \mathbf{π} and \mathbf{π}_0 of true and hypothesized cell probabilities
X(1,K)	observed cell counts
PI0(1,K)	hypothecized cell probabilities
DSQPIH_0	observed value of the squared Euclidean distance
VN_N	square root of the estimated asymtotic variance of √{n}DSQPIH\_0
CRIT	upper critical bound to √{n}DSQPIH\_0
REJ	indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis

Author(s)

Stefan Wellek <[e-mail]>
Peter Ziegler <[e-mail]>

References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 9.1.

Examples

x<- c(17,16,25,9,16,17)
pio <- rep(1,6)/6
gofsimpt(0.05,100,6,0.15,x,pio)

Example output

Loading required package: BiasedUrn
  n = 100  alpha = 0.05   eps = 0.15    x(1,K) = 17 16 25 9 16 17   pio(1,K) = 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667    DSQPIH_0 = 0.01293333   VN_N = 0.009199652   CRIT = 0.007367919   REJ = 0

EQUIVNONINF documentation built on July 12, 2021, 5:08 p.m.