Help for package detectnorm

Type:

Package

Title:

Detect Nonnormality in Meta-Analysis without Raw Data

Version:

1.0.0

Maintainer:

Rongwei Sun <irissun_s@hotmail.com>

Description:

Non-normality could greatly distort the meta-analytic results, according to the simulation in Sun and Cheung (2020) <doi:10.3758/s13428-019-01334-x>. This package aims to detect non-normality for two independent groups with only limited descriptive statistics, including mean, standard deviation, minimum, and maximum.

License:

MIT + file LICENSE

URL:

https://github.com/irissun/detectnorm

BugReports:

https://github.com/irissun/detectnorm/issues

Encoding:

UTF-8

LazyData:

true

Depends:

R (≥ 2.10)

Imports:

nleqslv, ggplot2, truncnorm, Rdpack, psych

Suggests:

knitr, metafor (≥ 3.4-0), rmarkdown, testthat (≥ 3.0.0)

RdMacros:

Rdpack

RoxygenNote:

7.2.0

Config/testthat/edition:

VignetteBuilder:

knitr

NeedsCompilation:

Packaged:

2022-07-15 13:29:16 UTC; iris

Author:

Rongwei Sun

[aut, cre, cph], Shu Fai Cheung

[aut, ctb, cph]

Repository:

CRAN

Date/Publication:

2022-07-16 09:10:05 UTC

Example meta-analysis: Extremely Non-normal Data

Description

This dataset is generated by nonnormal data with function rnonnorm. It contains the descriptive data in individual studies in the meta-analysis.

Usage

beta_mdat

Format

A data.frame with 40 studies:

study: No of studies
n1: sample size of group 1 with equal sample size for the two studies. Generated with uniform distribution.
m1: mean of group 1. Population mean is equal to 1. The data of group 1 is generated with skewness = 4 and kurtosis = 2.
sd1: standard deviation of group 1. Population sd of group 1 is equal to 1.
lo1: minimum of the generated sample for group 1.
hi1: maximum of the generated sample for group 1.
n2: sample size of study 2; n1 = n2 for each study
m2: mean of group 2. Population mean is equal to 1.5. The data of group 2 is generated with skewness = -4 and kurtosis = 2.
sd2: standard deviation of group 2. Population sd of group 2 is equal to 1.
lo2: minimum of the generated sample for group 2.
hi2: maximum of the generated sample for group 2.
skew1: sample skewness for group 1.
skew2: sammple skewness for group 2.

Calculate skewness and kurtosis based on Beta distribution in one group

Description

This function can be used to calculate the skewness and kurtosis based on the Beta distribution. Also, this function estimate the shape parameters alpha and beta.

Usage

desbeta(
  vmean,
  vsd,
  lo,
  hi,
  method = "MM",
  rawdata = NULL,
  showFigure = FALSE,
  ...
)

Arguments

vmean

sample mean of the truncated data

vsd

sample standard deviation of the truncated data

lo

minimum possible value

hi

maximum possible value

method

when method = 'MM', the method used is the method of moments, when method = "ML', the method used to estimate the distribution is maximum likelihood

rawdata

when raw data is available, we could still use it to check it figuratively, if the data was closed to the normal distribution, or truncated normal distribution.

showFigure

when showFigure = TRUE, it will display the plots with theoretical normal curve and the truncated normal curve.

...

other arguments

Value

If 'showFigure = TRUE', the output will be a list with two objects: one is the data frame of shape parameters (alpha and beta), mean and standard deviation of standard beta distribution (mean and sd), and skewness and kurtosis; the other is the theoretical figures of beta and normal distributions. If 'showFigure = FALSE', the output will be only the data frame.

References

Johnson NL, Kotz S, Balakrishnan N (1995). “Continuous univariate distributions.” In volume 289, chapter 25 Beta Distributions. John wiley & sons.

Smithson M, Verkuilen J (2006). “A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables.” Psychological methods, 11(1), 54.

Examples

data('beta_mdat')
desbeta(vmean=beta_mdat$m2[6], vsd=beta_mdat$sd2[6],
hi = beta_mdat$hi2[6], lo = beta_mdat$lo2[6], showFigure = TRUE)

Calculate skewness and kurtosis based on truncated normal distribution in one group

Description

This function can be used to calculate the skewness and kurtosis based on the truncated normal distribution. Also, it can be used to estimate the mean and variance of the parent distribution (the distribution before truncated).

Usage

destrunc(
  vmean,
  vsd,
  lo,
  hi,
  rawdata = NULL,
  showFigure = FALSE,
  xstart,
  btol,
  ftol,
  ...
)

Arguments

vmean

sample mean of the truncated data

vsd

sample standard deviation of the truncated data

lo

minimum possible value

hi

maximum possible value

rawdata

when raw data is available, we could still use it to check it figuratively, if the data was closed to the normal distribution, or truncated normal distribution.

showFigure

when showFigure = TRUE, it will display the plots with theoretical normal curve and the truncated normal curve.

xstart

see the package nleqslv

btol

see the package nleqslv

ftol

see the package nleqslv

...

other arguments

Value

If 'showFigure = TRUE', the output will be a list with two objects: one is the data frame of parent mean and standard deviation (pmean and psd), mean and standard deviation of truncated normal distribution (mean and sd), and skewness and kurtosis; the other is the theoretical figures of beta and normal distributions. If 'showFigure = FALSE', the output will be only the data frame.

References

Shah SM, Jaiswal MC (1966). “Estimation of parameters of doubly truncated normal distribution from first four sample moments.” Annals of the Institute of Statistical Mathematics, 18(1), 107–111.

Robert CP (1995). “Simulation of truncated normal variables.” Statistics and computing, 5(2), 121–125.

Barr DR, Sherrill ET (1999). “Mean and variance of truncated normal distributions.” The American Statistician, 53(4), 357–361.

Examples

data("trun_mdat")
destrunc(vmean=trun_mdat$m2[6], vsd=trun_mdat$sd2[6],
hi = 4, lo = 0, showFigure = TRUE)
#example2
destrunc(vmean=trun_mdat$m1[17], vsd=trun_mdat$sd1[17],
hi = 4, lo = 0, showFigure = TRUE)

Calculate skewness and kurtosis based on Beta or truncated normal distribution in a meta-analysis for SMD (Two independent groups)

Description

This function can be used to calculate the skewness and kurtosis based on the Beta distribution with the dataset used to conduct meta-analysis.

Usage

detectnorm(
  m1i,
  sd1i,
  n1i,
  lo1i,
  hi1i,
  m2i,
  sd2i,
  n2i,
  lo2i,
  hi2i,
  data,
  showFigure = FALSE,
  distri = "beta",
  ...
)

Arguments

m1i

vector to the means of first group

sd1i

vector to specifiy the standard deviation of first group

n1i

vector to specify the sample size of first group

lo1i

vector to specify the possible minimum of the first group

hi1i

vector to specify the possible maximum of the first group

m2i

vector to the means of second group

sd2i

vector to specifiy the standard deviation of second group

n2i

vector to specify the sample size of second group

lo2i

vector to specify the possible minimum of the second group

hi2i

vector to specify the possible maximum of the second group

data

the opitional original data frame containing the data for the function

showFigure

when showFigure = TRUE, it will display all the plots (within the result as a list, result$fig) with theoretical normal curve and the truncated normal curve.

distri

Beta distribution is used when using 'distri = "beta"'; Truncated normal distribution is used when using 'distri = "truncnorm"'

...

other arguments

Value

The output of the data frame adding some columns of the possible skewness and kurtosis for each groups.

References

Barr DR, Sherrill ET (1999). “Mean and variance of truncated normal distributions.” The American Statistician, 53(4), 357–361.

Johnson NL, Kotz S, Balakrishnan N (1995). “Continuous univariate distributions.” In volume 289, chapter 25 Beta Distributions. John wiley & sons.

Robert CP (1995). “Simulation of truncated normal variables.” Statistics and computing, 5(2), 121–125.

Smithson M, Verkuilen J (2006). “A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables.” Psychological methods, 11(1), 54.

Sun RW, Cheung SF (2020). “The influence of nonnormality from primary studies on the standardized mean difference in meta-analysis.” Behavior Research Methods, 52(4), 1552–1567.

Examples

#truncated normal data
data("trun_mdat")
ex <- detectnorm(m1i = m1,sd1i = sd1,n1i = n1,
hi1i = 4,lo1i = 0,m2i = m2,sd2i = sd2,n2i = n2,
hi2i = 4,lo2i=0,distri = "truncnorm", data = trun_mdat)
head(ex)
#extremely non-normal data
data("beta_mdat")
ex2 <- detectnorm(m1i = m1,sd1i = sd1,n1i = n1,
hi1i = hi1,lo1i = lo1,m2i = m2,sd2i = sd2,n2i = n2,
hi2i = hi2,lo2i=lo2,distri = "beta", data = beta_mdat)
head(ex2)
mean(ex2$skew1)#sample skewness calculated from the sample
mean(ex2$g1_skewness) #estimated using beta

Non-normal Distribution

Description

Generating Non-normal data with specified skewness and kurtosis using Fleishman's Method

Usage

rnonnorm(n, mean = 0, sd = 1, skew = 0, kurt = 0)

Arguments

n

number of observations

mean

mean

sd

standard deviation

skew

skewness

kurt

kurtosis

Details

This function can be used to generate non-normal data with specified skewness and kurtosis using Fleishman's Power Method.

Value

A list of two objects: non-normal data is 'dat'; and the other is the Fleishman Coeffficients used to generate the distributions.

References

Fleishman AI (1978). “A method for simulating non-normal distributions.” Psychometrika, 43(4), 521–532.

Examples

set.seed(341031)
exdat <- rnonnorm(n = 100, mean = 1, sd = 2, skew = 3, kurt = 2)$dat
hist(exdat)

Example meta-analysis: Truncated Normal Data

Description

This dataset is generated by truncated normal data with function rtruncnorm with the scale of 0-4.

Usage

trun_mdat

Format

A data frame with 40 studies:

study: No of studies
n1: sample size of group 1 with equal sample size for the two studies. Generated with uniform distribution.
m1: mean of group 1. Population mean is equal to 1. The data of group 1 is generated with the scale 0-4.
sd1: standard deviation of group 1. Population sd of group 1 is equal to 1.
lo1: minimum of the generated sample for group 1.
hi1: maximum of the generated sample for group 1.
n2: sample size of study 2; n1 = n2 for each study
m2: mean of group 2. Population mean is equal to 1.5. The data of group 2 is generated with the scale 0-4.
sd2: standard deviation of group 2. Population sd of group 2 is equal to 1.
lo2: minimum of the generated sample for group 2.
hi2: maximum of the generated sample for group 2.
skew1: sample skewness for group 1.
skew2: sammple skewness for group 2.

Example meta-analysis: Extremely Non-normal Data

Description

Usage

Format

Calculate skewness and kurtosis based on Beta distribution in one group

Description

Usage

Arguments

Value

References

See Also

Examples

Calculate skewness and kurtosis based on truncated normal distribution in one group

Description

Usage

Arguments

Value

References

See Also

Examples

Calculate skewness and kurtosis based on Beta or truncated normal distribution in a meta-analysis for SMD (Two independent groups)

Description

Usage

Arguments

Value

References

Examples

Non-normal Distribution

Description

Usage

Arguments

Details

Value

References

Examples

Example meta-analysis: Truncated Normal Data

Description

Usage

Format