detectnorm {detectnorm} | R Documentation |

## 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.

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)
#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
```

*detectnorm*version 1.0.0 Index]