Anderson-Darling Test

Description

This function computes the one-sample Anderson-Darling test statistic and p-value for fit to a normal distribution.

Usage

ADTest(data, alpha = 0.05, j = 1)

Arguments

Details

An adjusted statistic provided by D'agostino & Stephens (1986) is used, where the mean and variance of the population are treated as unknown. D'agostino & Stephen's (1986) text provides the equations used to obtain the function's p-values.

Value

An object including the test statistic, p-value, and a significance flag (list)

References

D'agostino, R. B., & Stephens, M. A. (1986). Goodness-of-fit-techniques (Vol. 68). CRC press.

Examples

values <- rnorm(100)
x <- ADTest(data = values)

D'agostino Pearson Omnibus Test

Description

This function computes the D'agostino Pearson omnibus test using adjusted Fisher- Pearson skewness and kurtosis estimators.

Usage

DPTest(data, alpha = 0.05, j = 1, warn = T)

Arguments

Value

An object including the test statistic, p-value, and a significance flag (list)

References

D'agostino, R. B., & Stephens, M. A. (1986). Goodness-of-fit-techniques (Vol. 68). CRC press.

D’agostino, R. B., & Belanger, A. (1990). A Suggestion for Using Powerful and Informative Tests of Normality. The American Statistician, 44(4), 316–321. https://doi.org/10.2307/2684359

Shreve, Joni N. and Donna Dea Holland . 2018. SAS® Certification Prep Guide: Statistical Business Analysis Using SAS®9. Cary, NC: SAS Institute Inc.

Examples

values <- rnorm(100)
x <- DPTest(data = values)

Jarque-Bera Test

Description

This function performs the Jarque-Bera test for normality using adjusted Fisher- Pearson skewness and kurtosis coefficients.

Usage

JBTest(data, alpha = 0.05, j = 1, N_Sample = 10000, warn = T)

Arguments

Details

Large samples (N >= 2000) use p-values obtained with reference to the chi-square distribution, whereas smaller samples output p-values obtained via bootstrapping. When N < 4, testing is terminated.

Value

An object including the test statistic, p-value, and a significance flag (list)

References

Jarque, C. M. and Bera, A. K. (1980). Efficient test for normality, homoscedasticity and serial independence of residuals. Economic Letters, 6(3), pp. 255-259.

Shreve, Joni N. and Donna Dea Holland . 2018. SAS® Certification Prep Guide: Statistical Business Analysis Using SAS®9. Cary, NC: SAS Institute Inc.

Examples

values <- rnorm(100)
x <- JBTest(data = values)

Kolmogorov-Smirnov-Lilliefors Test

Description

This function computes the Lilliefors variant of the one-sample Kolmogorov-Smirnov test.

Usage

KSLTest(data, alpha = 0.05, j = 1, warn = T)

Arguments

Details

Molin & Abdi's (1998) algorithmic approximation of p-values is used for hypothesis-testing. Note that this algorithm requires the imputation of 0.0 for negative output when p-values would otherwise be low in value (< 0.001) using other methods. A similar issue with extremely large values requires the imputation of 1.0 for values larger than 1.0 when p > .99.

Value

An object including the test statistic, p-value, and a significance flag (list)

References

Lilliefors, H.W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. Journal of the American Statistical Association, 62, 399-402.

Molin, P., & Abdi, H. (1998). New Tables and numerical approximation for the KolmogorovSmirnov/Lillierfors/Van Soest test of normality.

Examples

values <- rnorm(100)
x <- KSLTest(data = values)

Master Normality Testing Function

Description

This is a master function to call the appropriate test(s) to be used in the 'Rita' function.

Usage

MasterTest(c, data, alpha = 0.05, j = 1)

Arguments

Value

An results object specific to the test designated with the 'c' argument (list)

Examples

values <- rnorm(100)
x <- MasterTest(c = 1, data = values)

Master Transformation Function

Description

This is a master function used to perform the appropriate transformation(s) within the 'Rita' function.

Usage

MasterXform(c, data)

Arguments

Value

Output from the appropriate subfunction (list)

Examples

values <- rnorm(100)
x <- MasterXform(c = 2, data = values)

Rita

Description

R Exploratory Data Analysis (REDA; pronounced "rita") summarizes an input dataset by the M, SD + 5-number summary + third and fourth moments and visualizes the data according to an algorithm or as specified by the user. In addition, Rita will provide the results of one or several normality tests. Lastly, Rita normalizes the dataset with several methods and provides visualizations of the best performing method to the user.

Usage

Rita(
  data,
  test = 1,
  xform = 1,
  alpha = 0.05,
  j = 1,
  autoPlot = T,
  histPlot = F,
  densPlot = F,
  stripPlot = F,
  violinPlot = F,
  xformPlot = F,
  return = T,
  seed = 10
)

Arguments

Details

Any rows with missing values (NAs) are removed for calculation purposes; if desired, incomplete records should be imputed or removed with subsetting prior to calling Rita. In addition, note that any columns not numeric type or coercible to numeric are excluded from analysis, as are any numeric columns with 2 distinct values or less.

Value

An object containing the dataset of the best performing transformation for each variable and the specified plots (list)

Examples

values <- rnorm(100)
x <- Rita(data = values)

Shapiro-Wilk Test

Description

This function is a wrapper for shapiro.test() from the stats package. Options added include an ability to toggle a Bonferonni correction for significance, a corresponding significance flag, and reorganized output to facilitate integration with the Rita package.

Usage

SWTest(data, alpha = 0.05, j = 1, warn = T)

Arguments

Details

Note that when the sample-size of the input vector is > 5000, resampling with replacement is used to proceed with hypothesis-testing with a vector of 5000 elements. When N < 3, testing is terminated.

Value

An object including the test statistic, p-value, and a significance flag (list)

References

Patrick Royston (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Applied Statistics, 31, 115–124. 10.2307/2347973

Patrick Royston (1982). Algorithm AS 181: The W test for Normality. Applied Statistics, 31, 176–180. 10.2307/2347986

Patrick Royston (1995). Remark AS R94: A remark on Algorithm AS 181: The W test for normality. Applied Statistics, 44, 547–551. 10.2307/2986146

Examples

values <- rnorm(100)
x <- SWTest(data = values)

Arcsine Transformation

Description

This function transforms the scale, if needed, to values of unity. Then, the data is transformed by taking the arcsine of each value. Per the recommendations of Osborne(2002), data points are left-anchored at 0 to maximize the efficacy of the square-root transformation used enroute to the arcsine.

Usage

arcsineXform(sample)

Arguments

Value

The arcsine-transformed data (vector)

References

Osborne, J. W. (2002). Notes on the use of data transformations. Practical Assessment, Research and Evaluation, 9(1), 42-50.

Osborne, J. W. (2002). The Effects of Minimum Values on Data Transformations. Retrieved from https://files.eric.ed.gov/fulltext/ED463313.pdf

Examples

values <- rnorm(100)
x <- arcsineXform(values)

Chi-Square Test

Description

This function computes the chi-square test for normality.

Usage

chisqTest(data, alpha = 0.05, j = 1, df = 3)

Arguments

Details

Bins are created by cutting the data to ensure that values within these intervals would be equally probable if data are normal (Moore, 1986). By default, this function assumes that all relevant parameters (mu, sigma) are estimators, fixing the degrees of freedom at df = 3.

Value

An object including the test statistic, p-value, and a significance flag (list)

References

Moore, D.S., (1986) Tests of the chi-squared type. In: D'agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.

Examples

values <- rnorm(100)
x <- chisqTest(data = values)

Inverse/Reciprocal Transformation

Description

This function imputes minimum values per the recommendations of Osborne (2002) and subsequently transforms the data using the reciprocal.

Usage

inverseXform(sample)

Arguments

Value

The reciprocal-transformed data (vector)

References

Osborne, J. W. (2002). Notes on the use of data transformations. Practical Assessment, Research and Evaluation, 9(1), 42-50.

Osborne, J. W. (2002). The Effects of Minimum Values on Data Transformations. Retrieved from https://files.eric.ed.gov/fulltext/ED463313.pdf

Examples

values <- rnorm(100)
x <- inverseXform(values)

Adjusted Fisher-Pearson Excess Sample Kurtosis

Description

Adjusted Fisher-Pearson Excess Sample Kurtosis

Usage

kurtCoeff(data, sd)

Arguments

Value

The kurtosis value (scalar)

References

Shreve, Joni N. and Donna Dea Holland . 2018. SAS® Certification Prep Guide: Statistical Business Analysis Using SAS®9. Cary, NC: SAS Institute Inc.

Examples

values <- rnorm(100)
x <- kurtCoeff(data = values, sd = sd(values))

Logarithmic Transformation

Description

This function imputes minimum values per the recommendations of Osborne (2002) and subsequently transforms the data to a base-10 logarithmic scale.

Usage

logXform(sample)

Arguments

Value

The log-transformed data (vector)

References

Osborne, J. W. (2002). Notes on the use of data transformations. Practical Assessment, Research and Evaluation, 9(1), 42-50.

Osborne, J. W. (2002). The Effects of Minimum Values on Data Transformations. Retrieved from https://files.eric.ed.gov/fulltext/ED463313.pdf

Examples

values <- rnorm(100)
x <- logXform(values)

Logit/Log-Odds Transformation

Description

This function transforms data via the logit/log-odds transformation.

Usage

logitXform(sample, divisor = 2)

Arguments

Details

Initially, features of the input data are extracted and used to determine an initial transformation to perform.

All forms of data representing an underlying discrete scale are converted to proportions of the total sample size, if needed. In these cases, values should be stored such that elements are in absolute frequency, relative frequency, or percentage form.

For non-count data, variables are shifted and bounded at [0,1] in a manner analogous to the potential transformations of the scale performed by arcsineXform() prior to the arcine, although transformed values are not expected to outperform more suitable transformations.

Then, the empirical logit transformation is applied to avoid zeroes or ones, and the data are transformed by taking the log-odds/logit of each value.

Value

The logit-transformed data (vector)

References

Stevens, S., Valderas, J. M., Doran, T., Perera, R., & Kontopantelis, E. (2016). Analysing indicators of performance, satisfaction, or safety using empirical logit transformation. bmj, 352.

Osborne, J. W. (2002). Notes on the use of data transformations. Practical Assessment, Research and Evaluation, 9(1), 42-50.

Osborne, J. W. (2002). The Effects of Minimum Values on Data Transformations. Retrieved from https://files.eric.ed.gov/fulltext/ED463313.pdf

Warton, D. I., & Hui, F. K. (2011). The arcsine is asinine: the analysis of proportions in ecology. Ecology, 92(1), 3-10.

Examples

values <- rnorm(100)
x <- logitXform(values)

Converts Sample Standard Deviations into Population Equivalents

Description

This function converts a sample standard deviation (SD) input into the population equivalent. This code is vectorized to convert several sample standard deviations for univariate distributions of identical sample-sizes, if desired.

Usage

popSD(s, n)

Arguments

Value

The population SD(s) (vector)

References

Ruscio, J. (2021). Fundamentals of research design and statistical analysis. Ewing, NJ: The College of New Jersey, Psychology Department.

Examples

values <- rnorm(100)
x <- popSD(s = sd(values),n = 100)

Rankit Transformation

Description

This function transforms data via the Rankit, a member of the families of 'rank-based normalization methods' and 'empirical normal quantile transformations' employed in both the social sciences and quantitative genetics.

Usage

rankitXform(sample)

Arguments

Value

The Rankit-transformed data (vector)

References

Soloman, S. R., & Sawilowsky, S. S. (2009). Impact of rank-based normalizing transformations on the accuracy of test scores. Journal of Modern Applied Statistical Methods, 8(2), 9.

Peng, B., Robert, K. Y., DeHoff, K. L., & Amos, C. I. (2007, December). Normalizing a large number of quantitative traits using empirical normal quantile transformation. In BMC proceedings (Vol. 1, No. 1, p. S156). BioMed Central. doi: 10.1186/1753-6561-1-s1-s156

Bliss, C. I., Greenwood, M. L., & White, E. S. (1956). A rankit analysis of paired comparisons for measuring the effect of sprays on flavor. Biometrics, 12(4), 381-403.

Examples

values <- rnorm(100)
x <- rankitXform(values)

Adjusted Fisher-Pearson Skewness Coefficient with Sample-size Correction Factor

Description

Adjusted Fisher-Pearson Skewness Coefficient with Sample-size Correction Factor

Usage

skewCoeff(data, sd)

Arguments

Value

The skewness value (scalar)

References

Shreve, Joni N. and Donna Dea Holland . 2018. SAS® Certification Prep Guide: Statistical Business Analysis Using SAS®9. Cary, NC: SAS Institute Inc.

Examples

values <- rnorm(100)
x <- skewCoeff(data = values,sd = sd(values))

Square-root Transformation

Description

This function left anchors the minimum value to 0 per the recommendations of Osborne (2002) and subsequently transforms the data by taking the square-root of each value.

Usage

squareXform(sample)

Arguments

Value

The square-transformed data (vector)

References

Osborne, J. W. (2002). Notes on the use of data transformations. Practical Assessment, Research and Evaluation, 9(1), 42-50.

Osborne, J. W. (2002). The Effects of Minimum Values on Data Transformations. Retrieved from https://files.eric.ed.gov/fulltext/ED463313.pdf

Examples

values <- rnorm(100)
x <- squareXform(values)