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Modified t test (modTtest3d)

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ruthlorenz edited this page Feb 24, 2016 · 5 revisions

Modified t-test for [lon,lat,time] data

Description

Modified student t-test for autocorrelated data using equivalent sample size. The method is based on Zwiers and von Storch, J. Clim 1995, p. 336-351.
For small sample sizes (<=30) a lookup table test is used (also described in above publication). This function only works for 3d [lon,lat,time] data.

Usage

modTtest3d(x, ...)

modTtest3d(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, paired = FALSE, var.equal = TRUE, conf.level = 0.95, timevals=NULL, ...)

modTtest3d(formula, data, subset, na.action, ...)

Arguments

  • x: a (non-empty) numeric array of data values with dimensions longitude, latitude, time where time is autocorrelated AR(1)
  • y: an optional (non-empty) numeric array of data values with dimensions longitude, latitude, time where time is autocorrelated AR(1)
  • alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
  • mu: a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
  • paired: a logical indicating whether you want a paired test.
  • var.equal: a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance, if FALSE a warning is issued because the method assumes equal variances.
  • conf.level: confidence level of the interval.
  • timevals: an optional number of time values in the x (y) timeseries. If provided the function checks for correct dimensions.
  • formula: a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs a factor with two levels giving the corresponding groups.
  • data: an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).
  • subset: an optional vector specifying a subset of observations to be used.
  • na.action: a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action"). }
  • ...: further arguments to be passed to or from methods, not used at the moment.

Details

Performs a modified t-test using the equivalent sample size in case of autocorrelation in the data (Zwiers and von Storch, 1995). When the sample size is too small (<= 30) to obtain robust results a look-up table test is performed.

Either one sample or two sample tests can be performed, the function needs timeseries of at least 12, otherwise the lookup table test fails. The lookup table test also is not suited for negative correlations <=-0.3. For negative autocorrelations and sample sizes larger than 30 a standard student t-test is performed.

The formula interface is only applicable for the 2-sample tests.

alternative = "greater" is the alternative that x has a larger mean than y.

If paired is TRUE then both x and y must be specified and they must be the same length. Missing values are silently removed (in pairs if paired is TRUE).

If the input data are effectively constant (compared to the larger of the two means) an error is generated.

Value

A list with class htest containing the following components:

  • statistic: the value of the t-statistic.
  • parameter: the degrees of freedom for the t-statistic. Is NA for the lookup table test
  • p.value: the p-value for the test. Is NA for the lookup table test
  • conf.int: a confidence interval for the mean appropriate to the specified alternative hypothesis
  • estimate: the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test.
  • null.value: the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test
  • alternative: a character string describing the alternative hypothesis
  • method: a character string indicating what type of t-test was performed
  • data.name: a character string giving the name(s) of the data

References

Zwiers and von Storch, 1995, Taking serial correlation into account in tests of the mean, J. Clim,8, p. 336--351.

Author

Ruth Lorenz

See also

t.test

Examples:

x<-array(NA,dim=c(20,50,31))
y<-array(NA,dim=c(20,50,31))

for (lon in 1:20){
        for (lat in 1:50){
                #create timeseries with AR(1) correlation
                x[lon,lat,]<-arima.sim(list(ar = 0.3),n=31,rand.gen=rnorm,sd=0.1,mean=0)
                y[lon,lat,]<-arima.sim(list(ar = 0.3),n=31,rand.gen=rnorm,sd=0.1,mean=0)
        }
}

test3d<-modTtest3d(x,y,alternative = c("two.sided"),conf.level=0.95)
print(test3d)
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