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

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.

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.

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)
#>   study  n1       m1       sd1          lo1      hi1  n2       m2       sd2
#> 1     1 199 1.297501 0.8203794 0.0061563102 3.611959 199 1.572915 0.9002734
#> 2     2  77 1.325658 0.7750929 0.0231261133 2.889290  77 1.597681 0.8782761
#> 3     3 166 1.212825 0.7460359 0.0158618581 3.607032 166 1.612654 0.8441273
#> 4     4 120 1.230577 0.7888702 0.0030294235 3.443851 120 1.598539 0.8776627
#> 5     5 175 1.279821 0.7477283 0.0002848415 3.409888 175 1.612636 0.8426223
#> 6     6  47 1.310062 0.8904328 0.0088877511 3.729032  47 1.613387 0.8375352
#>          lo2      hi2     skew1       skew2  g1_pmean    g1_psd    g1_tm
#> 1 0.02056929 3.654732 0.4925754  0.31062433 0.9265047 1.0938781 1.297501
#> 2 0.01601133 3.591504 0.3189877  0.31978670 1.1151683 0.9467633 1.325658
#> 3 0.02598881 3.944059 0.8236975  0.41657818 0.9398112 0.9473430 1.212825
#> 4 0.05609411 3.563257 0.5632971  0.17020660 0.8502200 1.0561320 1.230577
#> 5 0.01150730 3.784293 0.4826745  0.20444248 1.0794292 0.9082416 1.279821
#> 6 0.04276128 3.137731 0.7678702 -0.02343749 0.5917055 1.3736190 1.310062
#>      g1_tsd g1_skewness g1_kurtosis g2_pmean    g2_psd    g2_tm    g2_tsd
#> 1 0.8203794   0.5716438  -0.2242368 1.344779 1.1457492 1.572915 0.9002734
#> 2 0.7750929   0.4748739  -0.2575908 1.430489 1.0697115 1.597681 0.8782761
#> 3 0.7460359   0.5641674  -0.1261384 1.497772 0.9813048 1.612654 0.8441272
#> 4 0.7888702   0.6126086  -0.1219403 1.432897 1.0677119 1.598539 0.8776627
#> 5 0.7477283   0.4849605  -0.2135704 1.499307 0.9779920 1.612636 0.8426223
#> 6 0.8904328   0.6407774  -0.2669263 1.505538 0.9667249 1.613387 0.8375352
#>   g2_skewness g2_kurtosis
#> 1   0.3522515  -0.5744184
#> 2   0.3139299  -0.5529135
#> 3   0.2767216  -0.5033002
#> 4   0.3127301  -0.5523355
#> 5   0.2756432  -0.5008223
#> 6   0.2713042  -0.4927465
#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)
#>   study  n1        m1       sd1       lo1      hi1  n2       m2       sd2
#> 1     1 160 1.0259203 0.8995642 0.2083603 5.578894 160 1.430021 1.0598447
#> 2     2  34 1.1528144 1.1367622 0.2123795 4.932592  34 1.408080 0.9296092
#> 3     3  57 0.9959042 0.8760782 0.2089018 3.443021  57 1.508927 1.0423997
#> 4     4 155 0.9480018 0.8828343 0.2082652 3.934242 155 1.443682 0.9198336
#> 5     5 149 1.1162247 1.0968963 0.2081850 5.613920 149 1.444312 1.0826183
#> 6     6 132 1.0418582 0.8946956 0.2082168 4.301961 132 1.554712 0.7932896
#>         lo2      hi2    skew1     skew2  g1_alpha  g1_beta   g1_mean     g1_sd
#> 1 -3.177617 2.274204 1.788613 -2.230054 0.5480186 3.051904 0.1522307 0.1674999
#> 2 -1.296619 2.271800 1.655752 -1.232207 0.3488177 1.401962 0.1992357 0.2408286
#> 3 -2.287307 2.274883 1.292354 -1.627030 0.3672680 1.141989 0.2433436 0.2708861
#> 4 -2.072880 2.274900 1.530104 -1.560090 0.3641696 1.470115 0.1985349 0.2369403
#> 5 -4.294234 2.274901 1.541182 -2.244364 0.4022054 1.992201 0.1679771 0.2029134
#> 6 -2.987192 2.273312 1.508507 -2.096631 0.4877450 1.907413 0.2036379 0.2185519
#>   g1_skewness g1_kurtosis g2_alpha   g2_beta   g2_mean     g2_sd g2_skewness
#> 1    1.483046   1.8901609 2.081468 0.3813533 0.8451559 0.1944020   -1.591348
#> 2    1.331854   0.8377363 1.291009 0.4122712 0.7579545 0.2605101   -1.069528
#> 3    1.079966   0.0309162 1.394623 0.2813890 0.8321080 0.2284867   -1.581618
#> 4    1.327314   0.8548620 1.985434 0.4693019 0.8088177 0.2115640   -1.310686
#> 5    1.489420   1.5984400 2.678914 0.3877426 0.8735618 0.1648038   -1.789508
#> 6    1.234109   0.7489875 3.614481 0.5718672 0.8633971 0.1508011   -1.558126
#>   g2_kurtosis
#> 1  2.00489688
#> 2  0.07531228
#> 3  1.66667585
#> 4  1.00447883
#> 5  3.02270945
#> 6  2.29997673
mean(ex2$skew1)#sample skewness calculated from the sample
#> [1] 1.687593
mean(ex2$g1_skewness) #estimated using beta
#> [1] 1.384237