normalityAssessment: normalityAssessment and samplingDistribution

Description

normalityAssessment can be used to assess whether a variable and the sampling distribution of its mean have an approximately normal distribution.

samplingDistribution is a convenient wrapper for normalityAssessment that makes it easy to quickly generate a sample and sampling distribution from frequencies (or proportions).

dataShape computes the skewness and kurtosis.

Usage

normalityAssessment(sampleVector, samples = 10000, digits=2,
                    samplingDistColor = "#2222CC",
                    normalColor = "#00CC00",
                    samplingDistLineSize = 2,
                    normalLineSize = 1,
                    xLabel.sampleDist = NULL,
                    yLabel.sampleDist = NULL,
                    xLabel.samplingDist = NULL,
                    yLabel.samplingDist = NULL,
                    sampleSizeOverride = TRUE)
samplingDistribution(popValues = c(0, 1),
                     popFrequencies = c(50, 50),
                     sampleSize = NULL,
                     sampleFromPop = FALSE, ...)
dataShape(sampleVector, na.rm = TRUE, type = 2,
          digits = 2, conf.level = 0.95,
          plots = TRUE, xLabs = NA,
          yLabs = NA, qqCI = TRUE,
          labelOutliers = TRUE,
          sampleSizeOverride = NULL)

Arguments

sampleVector

Numeric vector containing the sample data.

samples

Number of samples to use when constructing sampling distribution.

digits

Number of digits to use when printing results.

samplingDistColor

Color to use when drawing the sampling distribution.

normalColor

Color to use when drawing the standard normal curve.

samplingDistLineSize

Size of the line used to draw the sampling distribution.

normalLineSize

Size of the line used to draw the standard normal distribution.

xLabel.sampleDist

Label of x axis of the distribution of the sample.

yLabel.sampleDist

Label of y axis of the distribution of the sample.

xLabel.samplingDist

Label of x axis of the sampling distribution.

yLabel.samplingDist

Label of y axis of the sampling distribution.

xLabs, yLabs

The axis labels for the three plots (should be vectors of three elements; the first specifies the X or Y axis label for the rightmost plot (the histogram), the second for the middle plot (the QQ plot), and the third for the rightmost plot (the box plot).

popValues

The possible values (levels) of the relevant variable. For example, for a dichotomous variable, this can be "c(1:2)" (or "c(1, 2)"). Note that samplingDistribution is for manually specifying the frequency distribution (or proportions); if you have a vector with 'raw' data, just call normalityAssessment directly.

popFrequencies

The frequencies corresponding to each value in popValues; must be in the same order! See the examples.

sampleSize

Size of the sample; the sum of the frequencies if not specified.

na.rm

Whether to remove missing data first.

type

Type of skewness and kurtosis to compute; either 1 (g1 and g2), 2 (G1 and G2), or 3 (b1 and b2). See Joanes & Gill (1998) for more information.

conf.level

Confidence of confidence intervals.

plots

Whether to display plots.

qqCI

Whether to show the confidence interval for the QQ plot.

labelOutliers

Whether to label outliers with their row number in the box plot.

sampleFromPop

If true, the sample vector is created by sampling from the population information specified; if false, rep() is used to generate the sample vector. Note that is proportions are supplied in popFrequencies, sampling from the population is necessary!

sampleSizeOverride

Whether to use the sample size of the sample as sample size for the sampling distribution, instead of the sampling distribution size. This makes sense, because otherwise, the sample size and thus sensitivity of the null hypothesis significance tests is a function of the number of samples used to generate the sampling distribution.

...

Anything else is passed on my sampingDistribution to normalityAssessment.

Value

An object with several results, the most notably of which are:

plot.sampleDist

Histogram of sample distribution

sw.sampleDist

Shapiro-Wilk normality test of sample distribution

ad.sampleDist

Anderson-Darling normality test of sample distribution

ks.sampleDist

Kolmogorov-Smirnof normality test of sample distribution

kurtosis.sampleDist

Kurtosis for sample distribution

skewness.sampleDist

Skewness for sample distribution

plot.samplingDist

Histogram of sampling distribution

sw.samplingDist

Shapiro-Wilk normality test of sampling distribution

ad.samplingDist

Anderson-Darling normality test of sampling distribution

ks.samplingDist

Kolmogorov-Smirnof normality test of sampling distribution

dataShape.samplingDist

Skewness and kurtosis for sampling distribution

Details

normalityAssessment provides a number of normality tests and draws histograms of the sample data and the sampling distribution of the mean (most statistical tests assume the latter is normal, rather than the first; normality of the sample data guarantees normality of the sampling distribution of the mean, but if the sample size is sufficiently large, the sampling distribution of the mean is approximately normal even when the sample data are not normally distributed). Note that for the sampling distribution, the degrees of freedom are usually so huge that the normality tests, negligible deviations from normality will already result in very small p-values.

samplingDistribution makes it easy to quickly assess the distribution of a variables based on frequencies or proportions, and dataShape computes skewness and kurtosis.

Examples

Run this code

# NOT RUN {
### Note: the 'not run' is simply because running takes a lot of time,
###       but these examples are all safe to run!
# }
# NOT RUN {
normalityAssessment(rnorm(35));

### Create a distribution of three possible values and
### show the sampling distribution for the mean
popValues <- c(1, 2, 3);
popFrequencies <- c(20, 50, 30);
sampleSize <- 100;
samplingDistribution(popValues = popValues,
                     popFrequencies = popFrequencies,
                     sampleSize = sampleSize);

### Create a very skewed distribution of ten possible values
popValues <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10);
popFrequencies <- c(2, 4, 8, 6, 10, 15, 12, 200, 350, 400);
samplingDistribution(popValues = popValues,
                     popFrequencies = popFrequencies,
                     sampleSize = sampleSize, digits=5);
# }

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