Package 'vartest'

Ansari Bradley Test

Description

ansari.test performs Ansari Bradley variance homogeneity test.

Usage

ansari.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Ansari Bradley Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

See Also

ansari_test

Examples

library(vartest)

ansari.test(Sepal.Length ~ Species, data = iris)

out <- ansari.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Bartlett's Test

Description

bartletts.test performs Bartlett variance homogeneity test.

Usage

bartletts.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Bartlett's Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Lee, H.B., Katz, G.S., Restori, A.F. (2010). A Monte Carlo Study of Seven Homogeneity of Variance Tests. Journal of Mathematics and Statistics, 6:3, 359-366.

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

See Also

bartlett.test

Examples

library(vartest)

bartletts.test(Sepal.Length ~ Species, data = iris)

out <- bartletts.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---

Capon Test

Description

capon.test performs Capon variance homogeneity test.

Usage

capon.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Capon Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Capon, J. (1961). Asymptotic Efficiency of Certain Locally Most Powerful Rank Tests. The Annals of Mathematical Statistics, 32:1, 88-100.

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Examples

library(vartest)

capon.test(Sepal.Length ~ Species, data = iris)

out <- capon.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Cochran's C Test

Description

cochrans.test performs Cochran's C variance homogeneity test.

Usage

cochrans.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Cochran's C Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Wang, Y., Gil, P.R., Chen, Y.H., Kromrey, J.D., Kim, E.S., Pham, T., Nguyen, D., Romano, J.L. (2017). Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor Anova Models. Educational and Psychological Measurement, 77:2, 305-329.

Cochran, W.G. (1941). The Distribution of The Largest of a set of Estimated Variances as a Fraction of Their Total. Annals of Eugenics, 11:1, 47-52.

See Also

cochran.test

Examples

library(vartest)

cochrans.test(Sepal.Length ~ Species, data = iris)

out <- cochrans.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---

David Barton Test

Description

david.barton.test performs David Barton variance homogeneity test.

Usage

david.barton.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "David Barton Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Barton, D.E., David, F.N. (1958). A Test For Birth Order Effect. Annals of Human Genetics, 22:3, 250-257.

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Gibbons, J.D., Chakraborti, S. (2010). Nonparametric Statistical Inference. CRC Press, 5th Ed., 316-320.

Examples

library(vartest)

david.barton.test(Sepal.Length ~ Species, data = iris)

out <- david.barton.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Duran Test

Description

duran.test performs Duran variance homogeneity test.

Usage

duran.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters. This median-centered variant of the test is also referred to as the Conover-Iman test in literature (Conover and Iman, 1978).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Duran Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Iman, R.L.(1978). Some Exact Tables For The Squared Ranks Test. Communications in Statistics - Simulation and Computation, B7(5), 491-513.

Examples

library(vartest)

duran.test(Sepal.Length ~ Species, data = iris)

out <- duran.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Fisher's Test

Description

f.test performs Fisher's variance homogeneity test.

Usage

f.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Fisher's Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Gorbunova, A.A., Lemeshko, B.Y. (2012). Application of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption. 2nd Stochastic Modeling Techniques and Data Analysis International Conference, 5:8, 253-260.

Examples

library(vartest)

f.test(Sepal.Length ~ Species, data = iris)

out <- f.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Fligner-Killeen Test

Description

fk.test performs Fligner-Killeen variance homogeneity test.

Usage

fk.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Fligner-Killeen Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Fligner, M.A., Killeen, T.J.(1976). Distribution-Free Two-Sample Tests for Scale. Journal of the American Statistical Association, 71:353, 210-213.

See Also

fligner_test

Examples

library(vartest)

fk.test(Sepal.Length ~ Species, data = iris)

out <- fk.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

G Test

Description

g.test performs G variance homogeneity test.

Usage

g.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "G Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

UE't Lam, R. (2010). Scrutiny of Variance Results for Outliers: Cochran's Test Optimized. Analytica Chimica Acta, 659(1-2), 68-84.

Wang, Y., Gil, P.R., Chen, Y.H., Kromrey, J.D., Kim, E.S., Pham, T., Nguyen, D., Romano, J.L. (2017). Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor Anova Models. Educational and Psychological Measurement, 77:2, 305-329.

Examples

library(vartest)

g.test(Sepal.Length ~ Species, data = iris)

out <- g.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---

Hartley's Maximum F-Ratio Test

Description

hartley.test performs Hartley's Maximum F-Ratio variance homogeneity test.

Usage

hartley.test(formula, data, size = "mean", alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
size	a character string to define how to number of group observation. "mean": mean, "harmonic": harmonic mean, "maxn": maximum n, and "minvar": minimum variance.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components::

statistic	the corresponding test statistic.
parameter	the parameter(s) of the maximum F-ratio distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Hartley's Maximum F-Ratio Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Gorbunova, A.A., Lemeshko, B.Y. (2012). Application of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption. 2nd Stochastic Modeling Techniques and Data Analysis International Conference, 5:8, 253-260.

Bhandary, M., Dai, H. (2008). An Alternative Test for the Equality of Variances for Several Populations When the Underlying Distributions are Normal. Communications in Statistics-Simulation and Computation, 38:1, 109-117.

See Also

hartleyTest

Examples

library(vartest)

hartley.test(Sepal.Length ~ Species, data = iris, size = "mean")

out <- hartley.test(Sepal.Length ~ Species, data = iris, size = "mean")
summary(out)

---

Klotz Test

Description

klotz.test performs Klotz variance homogeneity test.

Usage

klotz.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Klotz Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Klotz, J. (1962). Nonparametric Tests for Scale. The Annals of Mathematical Statistics, 33:2, 498-512.

See Also

klotz_test

Examples

library(vartest)

klotz.test(Sepal.Length ~ Species, data = iris)

out <- klotz.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Levene's Test

Description

levene.test performs Levene variance homogeneity test.

Usage

levene.test(formula, data, center = "mean", deviation = "absolute", 
  trim.rate = 0.25, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
center	a character string to define how to center. "mean": mean, "median": median, and "trim.mean": trimmed mean.
deviation	a character string to define how to specify the deviation. "absolute": absolute deviation and "squared": squared deviation.
trim.rate	the rate of observations trimmed from each tail of the distribution. Default is set to 0.25.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Levene's Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Wang, Y., Gil, P.R., Chen, Y.H., Kromrey, J.D., Kim, E.S., Pham, T., Nguyen, D., Romano, J.L. (2017). Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor Anova Models. Educational and Psychological Measurement, 77:2, 305-329.

Brown, M.B., Forsythe, A.B. (1974). Robust Tests for the Equality of Variances. Journal of the American Statistical Association, 69:346, 364-367.

See Also

leveneTest

Examples

library(vartest)

levene.test(Sepal.Length ~ Species, data = iris, center="median", deviation="absolute")
levene.test(Sepal.Length ~ Species, data = iris, center="median", deviation="squared")
levene.test(Sepal.Length ~ Species, data = iris, center="mean", deviation="absolute")
levene.test(Sepal.Length ~ Species, data = iris, center="mean", deviation="squared")
levene.test(Sepal.Length ~ Species, data = iris, center="trim.mean", deviation="absolute")
levene.test(Sepal.Length ~ Species, data = iris, center="trim.mean", deviation="squared")

out <- levene.test(Sepal.Length~Species, data=iris, center="median", deviation="absolute")
summary(out)

---

Mood Test

Description

mood.test performs Mood variance homogeneity test.

Usage

mood.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Mood Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Mood, A.M. (1954). On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests. The Annals of Mathematical Statistics, 25:3, 514-522.

See Also

mood_test

Examples

library(vartest)

mood.test(Sepal.Length ~ Species, data = iris)

out <- mood.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Modified Z Variance Test

Description

mzv.test performs Modified Z Variance variance homogeneity test.

Usage

mzv.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Modified Z Variance Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Wang, Y., Gil, P.R., Chen, Y.H., Kromrey, J.D., Kim, E.S., Pham, T., Nguyen, D., Romano, J.L. (2017). Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor Anova Models. Educational and Psychological Measurement, 77:2, 305-329.

Overall, J.E., Woodward, J.A. (1974). A Simple Test for Heterogeneity of Variance in Complex Factorial Designs. Psychometrika, 39:3, 311-318.

Examples

library(vartest)

mzv.test(Sepal.Length ~ Species, data = iris)

out <- mzv.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

O'Brien Test

Description

obrien.test performs O'Brien variance homogeneity test.

Usage

obrien.test(formula, data, center = "mean", trim.rate = 0.25, alpha = 0.05, 
  na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
center	a character string to define how to center. "mean": mean, "median": median, and "trim.mean": trimmed mean.
trim.rate	the rate of observations trimmed from each tail of the distribution. Default is set to 0.25.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "O'Brien Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

O'Brien, R.G. (1981). A Simple Test for Variance Effects in Experimental Designs. Psychological Bulletin, 89:3, 570-574.

Gorbunova, A.A., Lemeshko, B.Y. (2012). Application of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption. 2nd Stochastic Modeling Techniques and Data Analysis International Conference, 5:8, 253-260.

Examples

library(vartest)

obrien.test(Sepal.Length ~ Species, data = iris, center = "mean")

out <- obrien.test(Sepal.Length ~ Species, data = iris, center = "mean")
summary(out)

---

Print Method for Summary of Variance Homogeneity Test Results

Description

Prints the formatted summary of a vht object to the console.

Usage

## S3 method for class 'summary.vht'
print(x, ...)

Arguments

x	An object returned by summary.vht().
...	Additional arguments.

Author(s)

Merve Kasikci and Osman Dag

See Also

summary.vht

Examples

out <- bartletts.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---

Data-Driven Selection of the Optimal Variance Homogeneity Test

Description

select_vartest performs an automated, simulation-based evaluation to identify the optimal variance homogeneity test for a dataset.

Usage

select_vartest(formula, data, nrep = 1000, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
nrep	an integer specifying the number of Monte Carlo replications to perform for the simulation. The default is 1000.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

The function calculates the empirical moments of the input data and uses the Pearson distribution system to generate random datasets. By evaluating 28 distinct methodological modifications of variance homogeneity tests on these generated datasets, the function recommends the method that yields the highest adjusted power (with the lowest Type I error).

Value

A data frame presenting empirical power, Type I error rate, and adjusted power for each variance homogeneity test.

Author(s)

Muhammed Ali Yilmaz and Osman Dag

Examples

library(vartest)

out <- select_vartest(Sepal.Length ~ Species, data = iris, nrep = 1000)
out

---

Siegel Tukey Test

Description

siegel.tukey.test performs Siegel Tukey variance homogeneity test.

Usage

siegel.tukey.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Siegel Tukey Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Gibbons, J.D., Chakraborti, S. (2010). Nonparametric Statistical Inference. CRC Press, 5th Ed., 316-320.

Siegel, S., Tukey, J.W. (1960). A Nonparametric Sum of Ranks Procedure for Relative Spread in Unpaired Samples. Journal of the American Statistical Association, 55:291, 429-445.

See Also

GSTTest

Examples

library(vartest)

siegel.tukey.test(Sepal.Length ~ Species, data = iris)

out <- siegel.tukey.test(Sepal.Length ~ Species, data = iris)
summary(out)

---

Summary Method for Variance Homogeneity Test Results

Description

Provides a concise summary of the results from a variance homogeneity test in the package.

Usage

## S3 method for class 'vht'
summary(object, ...)

Arguments

object	An object of class vht, typically returned by variance homogeneity tests.
...	Additional arguments.

Details

This method is specifically designed for objects of class vht. It prints test method, dependent variable, grouping variable, test statistic, degrees of freedom, and p-value.

Value

Prints a summary to the console.

Author(s)

Merve Kasikci and Osman Dag

Examples

out <- bartletts.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---

Talwar and Gentle Test

Description

talwar.gentle.test performs Talwar and Gentle variance homogeneity test.

Usage

talwar.gentle.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Details

Prior to testing for variance homogeneity, the data within each group are centered by their corresponding group median to eliminate the confounding effects of location parameters (Conover et al., 1981).

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate chi-squared distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Talwar and Gentle Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. Technometrics, 23:4, 351-361.

Talwar, P.P., Gentle, J.E. (1976). A Robust Test for the Homogeneity of Scales. Communications in Statistics - Theory and Methods, 6:4, 363-369.

Examples

library(vartest)

talwar.gentle.test(Sepal.Length ~ Species, data = iris)

out <- talwar.gentle.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---

Z Variance Test

Description

zv.test performs Z variance homogeneity test.

Usage

zv.test(formula, data, alpha = 0.05, na.rm = TRUE, verbose = TRUE)

Arguments

formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.
data	a tibble or data frame containing the variables in formula.
alpha	the level of significance to assess variance homogeneity. Default is set to alpha = 0.05.
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
verbose	a logical for printing output to R console.

Value

A list with class "vht" containing the following components:

statistic	the corresponding test statistic.
parameter	the parameter(s) of the approximate F distribution of the test statistic.
p.value	the p-value of the test.
method	the character string "Z Variance Test".
data	a data frame containing the variables in which NA values (if exist) are removed.
formula	a formula of the form lhs ~ rhs where lhs gives the sample values and rhs the corresponding groups.

Author(s)

Gozde Cosar and Osman Dag

References

Gorbunova, A.A., Lemeshko, B.Y. (2012). Application of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption. 2nd Stochastic Modeling Techniques and Data Analysis International Conference, 5:8, 253-260.

Wang, Y., Gil, P.R., Chen, Y.H., Kromrey, J.D., Kim, E.S., Pham, T., Nguyen, D., Romano, J.L. (2017). Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor Anova Models. Educational and Psychological Measurement, 77:2, 305-329.

Overall, J.E., Woodward, J.A. (1974). A Simple Test for Heterogeneity of Variance in Complex Factorial Designs. Psychometrika, 39:3, 311-318.

Examples

library(vartest)

zv.test(Sepal.Length ~ Species, data = iris)

out <- zv.test(Sepal.Length ~ Species, data = iris, verbose = FALSE)
summary(out)

---