Statistical and Visual Normality Assessment

Tests normality using sample size-appropriate methods: Shapiro-Wilk test (n less than or equal to 50) or Kolmogorov-Smirnov test with Lilliefors' correction (n greater than 50) with Q-Q plots and histograms. Evaluates skewness and kurtosis using z-score criteria based on sample size. Automatically detects outliers and provides comprehensive visual and statistical assessment.

Usage

normality(data, x, all = FALSE, color = "#79E1BE")

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

Arguments

data: Dataframe containing the variables to be summarized.
x: An object of class "normality"
all: Logical parameter that displays all row indices of values outside 95% CI. Default: FALSE.
color: Character string indicating color for plots. Default: "#79E1BE".
...: Additional arguments (not used)

Value

Returns an object of class "normality" with normality statistics and ggplot objects.

Methods (by generic)

print(normality): Print method for objects of class "normality".

References

Mishra P., Pandey C.M., Singh U., Gupta A., Sahu C., and Keshri A. Descriptive statistics and normality tests for statistical data. Ann Card Anaesth. 2019 Jan-Mar;22(1):67-72. doi: 10.4103/aca.ACA_157_18. PMID: 30648682; PMCID: PMC6350423.

Lilliefors, H.W. (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62(318), 399-402. doi: 10.1080/01621459.1967.10482916

Dallal, G.E. and Wilkinson, L. (1986). An analytic approximation to the distribution of Lilliefors' test for normality. The American Statistician, 40(4), 294-296. doi: 10.1080/00031305.1986.10475419

Examples

# Simulated clinical data
clinical_df <- clinical_data()

# Normally assesment of numerical variable
normality(clinical_df, "biomarker")
#> 
#> Normality Test for 'biomarker' 
#> 
#> n = 300 
#> mean (SD) = 48.79 (10.7) 
#> median (IQR) = 48.82 (14.8) 
#> 
#> Kolmogorov-Smirnov (Lilliefors): D = 0.030, p = 0.750 
#> Shapiro-Wilk: W = 0.997, p = 0.922 
#> Skewness: -0.06 (z = -0.40) 
#> Kurtosis: -0.06 (z = -0.22) 
#> 
#> Data appears normally distributed.
#>  


# Normally assesment of numerical variable with points outside 95% CI displayed
normality(clinical_df, "weight", all = TRUE)
#> 
#> Normality Test for 'weight' 
#> 
#> n = 300 
#> mean (SD) = 68.29 (12.6) 
#> median (IQR) = 68.90 (16.4) 
#> 
#> Kolmogorov-Smirnov (Lilliefors): D = 0.051, p = 0.056 
#> Shapiro-Wilk: W = 0.979, p < 0.001 
#> Skewness: -0.10 (z = -0.69) 
#> Kurtosis: -0.52 (z = -1.84) 
#> 
#> Data appears normally distributed.
#>  
#> VALUES OUTSIDE 95% CI (row indices): 7, 8, 9, 49, 221, 222, 247, 248, 249, 292, 293, 294, 45, 220, 44, 217, 219, 150, 43, 133 
#>