verification (version 1.45)

pdpropper: Power Divergence Test for Equal of Given Proportions

Description

Used for testing the null that proportions (probabilities of success) in several groups are the same, or that they equal certain given values.

Usage

pdpropper(x, n, p = NULL, lambda = c(-2, -1, -1/2, 0, 2/3, 1),
    alternative = c("two.sided", "less", "greater"),
    alpha = 0.05, correct = FALSE)

Value

Returns an object of either class htest or, if lambda is a vector with length greater than 1, a list of htest components. See powerdiverger for more information.

Arguments

x

a vector of counts of successes, a one-dimensional table with two entries, or a two-dimensional table (or matrix) with two columns, giving hte counts of successes and failures, resp.

n

a vector of counts of trials, which is ignored if x is a matrix or a table.

p

a vector of probabilities of success. Must have same length as the number of groups specified by x, and its elements must be in (0,1).

lambda

vector of lambda values.

alternative

a character string specifying the alternative hypothesis.

alpha

single numeric giving the size of the test

correct

logical stating whether or not to apply the moment correction or not.

Author

Eric Gilleland

Details

See the help file for powerdiverger for more information on the power-divergence statistic. This function is specific to testing equal or given proportions. The former does not allow this type of testing, though they are very similar tests.

See the help file for prop.test for more information about the type of test. For lambda = 1, the two tests should give the same results.

References

Cressie, N., and T. R. C. Read (1984). Multinomial goodness-of-fit tests. J. Roy. Stat. Soc., 46, 440--464.

Freeman, M. F., and J. W. Tukey (1950). Transformations related to the angular and the square root. Ann. Math. Stat., 21, 607--611, doi: 10.1214/aoms/1177729756.

Gilleland, E., D. Munoz-Esparza, and D. D. Turner (2023). Competing forecast verification: Using the power-divergence statistic for testing the frequency of better.

Kullback, S., and R. A. Leibler (1951). On information and sufficiency. Ann. Math. Stat., 22, 79--86, doi: 10.1214/aoms/1177729694.

Neyman, J. (1949). Contribution to the theory of the x2 test. Proc. First Berkeley Symp. on Mathematical Statistics and Probability, Berkeley, CA, University of California, 239--273.

Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos. Mag., 50, 157--175, doi: 10.1080/14786440009463897.

Read, T. R. C., and N. A. C. Cressie (1988). Goodness-of-Fit Statistics for Discrete Multivariate Data. 1st ed. Springer-Verlag, New York, 212 pp.

See Also

prop.test, powerdiverger

Examples

# These examples are the same as those in prop.test.
heads <- rbinom(1, size = 100, prob = .5)
prop.test(heads, 100, correct = FALSE)
pdpropper( heads, 100 )

## Data from Fleiss (1981), p. 139.
## H0: The null hypothesis is that the four populations from which
##     the patients were drawn have the same true proportion of smokers.
## A:  The alternative is that this proportion is different in at
##     least one of the populations.

smokers  <- c( 83, 90, 129, 70 )
patients <- c( 86, 93, 136, 82 )
prop.test(smokers, patients)
pdpropper( smokers, patients )