plotLinearTrendTestDesign: Plots for a Sampling Design Based on a t-Test for Linear...

Description

Create plots involving sample size, power, scaled difference, and significance level for a t-test for linear trend.

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ``` plotLinearTrendTestDesign(x.var = "n", y.var = "power", range.x.var = NULL, n = 12, slope.over.sigma = switch(alternative, greater = 0.1, less = -0.1, two.sided = ifelse(two.sided.direction == "greater", 0.1, -0.1)), alpha = 0.05, power = 0.95, alternative = "two.sided", two.sided.direction = "greater", approx = FALSE, round.up = FALSE, n.max = 5000, tol = 1e-07, maxiter = 1000, plot.it = TRUE, add = FALSE, n.points = ifelse(x.var == "n", diff(range.x.var) + 1, 50), plot.col = "black", plot.lwd = 3 * par("cex"), plot.lty = 1, digits = .Options\$digits, ..., main = NULL, xlab = NULL, ylab = NULL, type = "l") ```

Arguments

 `x.var` character string indicating what variable to use for the x-axis. Possible values are `"n"` (sample size; the default), `"slope.over.sigma"` (scaled minimal detectable slope), `"power"` (power of the test), and `"alpha"` (significance level of the test). `y.var` character string indicating what variable to use for the y-axis. Possible values are `"power"` (power of the test; the default), `"slope.over.sigma"` (scaled minimal detectable slope), and `"n"` (sample size). `range.x.var` numeric vector of length 2 indicating the range of the x-variable to use for the plot. The default value depends on the value of `x.var`. When `x.var="n"` the default value is `c(3,25)`. When `x.var="slope.over.sigma"` and `alternative="greater"` or `alternative="two.sided"` and `two.sided.direction="greater"`, the default value is `c(0.1, 1)`. When `x.var="slope.over.sigma"` and `alternative="less"` or `alternative="two.sided"` and `two.sided.direction="less"`, the default value is `-c(1, 0.1)`. When `x.var="power"` the default value is `c(alpha + .Machine\$double.eps, 0.95)`. When `x.var="alpha"`, the default value is `c(0.01, 0.2)`. `n` numeric scalar indicating the sample size. The default value is `n=12`. Missing (`NA`), undefined (`NaN`), and infinite (`Inf`, `-Inf`) values are not allowed. This argument is ignored if either `x.var="n"` or `y.var="n"`. `slope.over.sigma` numeric scalar specifying the ratio of the true slope (β_1) to the population standard deviation of the error terms (σ). This is also called the "scaled slope". When `alternative="greater"` or `alternative="two.sided"` and `two.sided.direction="greater"`, the default value is `slope.over.sigma=0.1`. When `alternative="less"` or `alternative="two.sided"` and `two.sided.direction="less"`, the default value is `delta.over.sigma=-0.1`. This argument is ignored when `x.var="slope.over.sigma"` or `y.var="slope.over.sigma"`. `alpha` numeric scalar between 0 and 1 indicating the Type I error level associated with the hypothesis test. The default value is `alpha=0.05`. This argument is ignored when `x.var="alpha"`. `power` numeric scalar between 0 and 1 indicating the power associated with the hypothesis test. The default value is `power=0.95`. This argument is ignored when `x.var="power"` or `y.var="power"`. `alternative` character string indicating the kind of alternative hypothesis. The possible values are `"two.sided"` (the default), `"greater"`, and `"less"`. `two.sided.direction` character string indicating the direction (positive or negative) for the scaled minimal detectable slope when `alternative="two.sided"`. When `two.sided.direction="greater"` (the default), the scaled minimal detectable slope is positive. When `two.sided.direction="less"`, the scaled minimal detectable slope is negative. This argument is ignored if `alternative="less"` or `alternative="greater"`. `approx` logical scalar indicating whether to compute the power based on an approximation to the non-central t-distribution. The default value is `approx=FALSE`. `round.up` logical scalar indicating whether to round up the values of the computed sample size(s) to the next smallest integer. The default value is `FALSE`. `n.max` for the case when `y.var="n"`, a positive integer greater than 2 indicating the maximum sample size. The default value is `n.max=5000`. `tol` numeric scalar indicating the toloerance to use in the `uniroot` search algorithm. The default value is `tol=1e-7`. `maxiter` positive integer indicating the maximum number of iterations argument to pass to the `uniroot` function. The default value is `maxiter=1000`. `plot.it` a logical scalar indicating whether to create a new plot or add to the existing plot (see `add`) on the current graphics device. If `plot.it=FALSE`, no plot is produced, but a list of (x,y) values is returned (see VALUE). The default value is `plot.it=TRUE`. `add` a logical scalar indicating whether to add the design plot to the existing plot (`add=TRUE`), or to create a plot from scratch (`add=FALSE`). The default value is `add=FALSE`. This argument is ignored if `plot.it=FALSE`. `n.points` a numeric scalar specifying how many (x,y) pairs to use to produce the plot. There are `n.points` x-values evenly spaced between `range.x.var[1]` and `range.x.var[2]`. The default value is `n.points=50` unless `x.var="n"`, in which case `n.points=diff(range.x.var)+1`. `plot.col` a numeric scalar or character string determining the color of the plotted line or points. The default value is `plot.col="black"`. See the entry for `col` in the help file for `par` for more information. `plot.lwd` a numeric scalar determining the width of the plotted line. The default value is `3*par("cex")`. See the entry for `lwd` in the help file for `par` for more information. `plot.lty` a numeric scalar determining the line type of the plotted line. The default value is `plot.lty=1`. See the entry for `lty` in the help file for `par` for more information. `digits` a scalar indicating how many significant digits to print out on the plot. The default value is the current setting of `options("digits")`. `main, xlab, ylab, type, ...` additional graphical parameters (see `par`).

Details

See the help files for `linearTrendTestPower`, `linearTrendTestN`, and `linearTrendTestScaledMds` for information on how to compute the power, sample size, or scaled minimal detectable slope for a t-test for linear trend.

Value

`plotlinearTrendTestDesign` invisibly returns a list with components `x.var` and `y.var`, giving coordinates of the points that have been or would have been plotted.

Note

See the help files for `linearTrendTestPower`.

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

See the help file for `linearTrendTestPower`.

`linearTrendTestPower`, `linearTrendTestN`, `linearTrendTestScaledMds`.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ``` # Look at the relationship between power and sample size for the t-test for # liner trend, assuming a scaled slope of 0.1 and a 5% significance level: dev.new() plotLinearTrendTestDesign() #========== # Plot sample size vs. the scaled minimal detectable slope for various # levels of power, using a 5% significance level: dev.new() plotLinearTrendTestDesign(x.var = "slope.over.sigma", y.var = "n", ylim = c(0, 30), main = "") plotLinearTrendTestDesign(x.var = "slope.over.sigma", y.var = "n", power = 0.9, add = TRUE, plot.col = "red") plotLinearTrendTestDesign(x.var = "slope.over.sigma", y.var = "n", power = 0.8, add = TRUE, plot.col = "blue") legend("topright", c("95%", "90%", "80%"), lty = 1, bty = "n", lwd = 3 * par("cex"), col = c("black", "red", "blue")) title(main = paste("Sample Size vs. Scaled Slope for t-Test for Linear Trend", "with Alpha=0.05 and Various Powers", sep="\n")) #========== # Clean up #--------- graphics.off() ```

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