gofsimpt {EQUIVNONINF}

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 \S 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{\pi} and \mathbf{\pi}_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{\pi} and \mathbf{\pi}_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 \sqrt{n}DSQPIH\_0

CRIT

upper critical bound to \sqrt{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, \S 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)