gofsimpt {EQUIVNONINF} R Documentation

## Establishing goodness of fit of an observed to a fully specified multinomial distribution: test statistic and critical bound

### 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 <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

### 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)


[Package EQUIVNONINF version 1.0.2 Index]