BSDA (version 0.1)

sign.test: Sign Test

Description

This function will test a hypothesis based on the sign test and reports linearly interpolated confidence intervals for one sample problems.

Usage

sign.test(x, y = NULL, md = 0, alternative = "two.sided", conf.level = 0.95)

Arguments

x

numeric vector. NAs and Infs are allowed but will be removed.

y

optional numeric vector. NAs and Infs are allowed but will be removed.

md

a single number representing the value of the population median specified by the null hypothesis.

alternative

character string, one of "greater", "less" or "two.sided", or just the initial letter of each, indicating the specification of the alternative hypothesis. For one-sample tests, alternative refers to the true

conf.level

confidence level for the returned confidence interval, restricted to lie between zero and one.

Value

• A list of class "htest", containing the following components:
• statistic
  the S-statistic (the number of positive differences between the data and the hypothesized median), with names attribute "S" .
• p.value
  the p-value for the test.
• conf.int
  a confidence interval (vector of length 2) for the true median based on linear interpolation. The confidence level is recorded in the attribute conf.level. When alternative is not "two.sided", the confidence interval will be half-infinite, to reflect the interpretation of a confidence interval as the set of all values k for which one would not reject the null hypothesis that the true mean or difference in means is k. Here infinity will be represented by Inf.
• estimate
  vector of length 1, giving the sample median; this estimates the corresponding population parameter. Component estimate has a names attribute describing its elements.
• null.value
  the value of the median specified by the null hypothesis. This equals the input argument md. Component null.value has a names attribute describing its elements.
• alternative
  records the value of the input argument alternative: "greater", "less" or "two.sided".
• data.name
  a character string (vector of length 1) containing the actual name of the input vector x.

Null Hypothesis

For the one-sample sign-test, the null hypothesis is that the median of the population from which x is drawn is md. For the two-sample dependent case, the null hypothesis is that the median for the differences of the populations from which x and y are drawn is md. The alternative hypothesis indicates the direction of divergence of the population median for x from md (i.e., "greater", "less", "two.sided".

Assumptions

The median test assumes the parent population is continuous.

Confidence Interval

A linear interpolation is returned for the related confidence interval (returned component conf.int) which can be obtained by interpolating between the possible achieved confidence levels closest to the desired level. Note however that, as explained under the description of conf.int, the confidence interval will be half-infinite when alternative is not "two.sided"; infinity will be represented by Inf.

Details

Computes a "Dependent-samples Sign-Test" if both x and y are provided. If only x is provided, computes the "Sign-Test".

References

Gibbons, J.D. and Chakraborti, S. (1992). Nonparametric Statistical Inference. Marcel Dekker Inc., New York. Kitchens, L.J.(2003). Basic Statistics and Data Analysis. Duxbury. Conover, W. J. (1980). Practical Nonparametric Statistics, 2nd ed. Wiley, New York. Lehmann, E. L. (1975). Nonparametrics: Statistical Methods Based on Ranks. Holden and Day, San Francisco.

See Also

z.test, zsum.test, tsum.test

Examples

x <- c(7.8, 6.6, 6.5, 7.4, 7.3, 7., 6.4, 7.1, 6.7, 7.6, 6.8)
sign.test(x,md=6.5)
        # Computes two-sided sign-test for the null hypothesis 
        # that the population median for 'x' is 6.5. The alternative 
        # hypothesis is that the median is not 6.5. An interpolated 95% 
        # confidence interval for the population median will be computed.
        
reaction <- c(14.3, 13.7, 15.4, 14.7, 12.4, 13.1, 9.2, 14.2, 
              14.4, 15.8, 11.3, 15.0)
sign.test(reaction, md=15, alternative="less")
        # Data from Example 6.11 page 330 of Kitchens BSDA.  
        # Computes one-sided sign-test for the null hypothesis 
        # that the population median is 15.  The alternative 
        # hypothesis is that the median is less than 15.  
        # An interpolated upper 95% upper bound for the population 
        # median will be computed.