Sign Test

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

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: is a character string, one of "greater", "less", or "two.sided", or the initial letter of each, indicating the specification of the alternative hypothesis. For one-sample tests, alternative refers to the true median of the parent population in relation to the hypothesized value of the median.
conf.level: confidence level for the returned confidence interval, restricted to lie between zero and one
...: further arguments to be passed to or from methods

Value

A list of class htest_S, 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: is 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 the 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: is avector of length 1, giving the sample median; this estimates the corresponding population parameter. Component estimate has a names attribute describing its elements.
null.value: is 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
Confidence.Intervals: a 3 by 3 matrix containing the lower achieved confidence interval, the interpolated confidence interval, and the upper achived confidence interval

Details

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

Note

The reported confidence interval is based on linear interpolation. The lower and upper confidence levels are exact.

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".)

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.

Author

Alan T. Arnholt

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)
#> 
#> 	One-sample Sign-Test
#> 
#> data:  x
#> s = 9, p-value = 0.02148
#> alternative hypothesis: true median is not equal to 6.5
#> 95 percent confidence interval:
#>  6.571273 7.457455
#> sample estimates:
#> median of x 
#>           7 
#> 
#> Achieved and Interpolated Confidence Intervals: 
#> 
#>                   Conf.Level L.E.pt U.E.pt
#> Lower Achieved CI     0.9346 6.6000 7.4000
#> Interpolated CI       0.9500 6.5713 7.4575
#> Upper Achieved CI     0.9883 6.5000 7.6000
#> 
        # 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")
#> 
#> 	One-sample Sign-Test
#> 
#> data:  reaction
#> s = 2, p-value = 0.03271
#> alternative hypothesis: true median is less than 15
#> 95 percent confidence interval:
#>      -Inf 14.82845
#> sample estimates:
#> median of x 
#>       14.25 
#> 
#> Achieved and Interpolated Confidence Intervals: 
#> 
#>                   Conf.Level L.E.pt  U.E.pt
#> Lower Achieved CI     0.9270   -Inf 14.7000
#> Interpolated CI       0.9500   -Inf 14.8285
#> Upper Achieved CI     0.9807   -Inf 15.0000
#> 
        # 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.