# normalityAssessment

##### normalityAssessment and samplingDistribution

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.

- Keywords
- utilities

##### 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.

##### 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.

##### Value

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

Histogram of sample distribution

Shapiro-Wilk normality test of sample distribution

Anderson-Darling normality test of sample distribution

Kolmogorov-Smirnof normality test of sample distribution

Kurtosis for sample distribution

Skewness for sample distribution

Histogram of sampling distribution

Shapiro-Wilk normality test of sampling distribution

Anderson-Darling normality test of sampling distribution

Kolmogorov-Smirnof normality test of sampling distribution

Skewness and kurtosis for sampling distribution

##### Examples

```
# 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);
# }
```

*Documentation reproduced from package userfriendlyscience, version 0.7.2, License: GPL (>= 3)*