Normality tests by groups

Perform a test of normality for each group separately. The available tests: Shapiro-Wilk (default), Lilliefors (Kolmogorov-Smirnov), Anderson-Darling and other.

test_normality(
  y,
  data = NULL,
  test = "Shapiro-Wilk",
  p_adjust_method = NULL,
  ...,
  groups = NULL,
  ss = signif_syms,
  hide_error_msg = FALSE
)

# S3 method for test_normality
print(
  x,
  ...,
  digits_p = 3,
  signif_stars = !is.null(ss),
  digits_stat = 3,
  format_stat = c("auto", "f", "g"),
  rm_zero = FALSE,
  legend = TRUE,
  show_col_method = FALSE,
  hide_error_msg = attr(x, "hide_error_msg"),
  ss = attr(x, "ss")
)

# S3 method for test_normality
pander(
  x,
  caption = NA,
  ...,
  digits_p = 3,
  signif_stars = !is.null(ss),
  digits_stat = 3,
  format_stat = c("auto", "f", "g"),
  rm_zero = FALSE,
  legend = TRUE,
  show_col_method = FALSE,
  hide_error_msg = attr(x, "hide_error_msg"),
  ss = attr(x, "ss")
)

Arguments

y	(formula|numeric|character) Either a formula, a numeric vector or a name of a column in data. If y is a formula (e.g. variable ~ factor), left-hand side provides the name of a variable to be tested. In the right-hand side there are names of factor variables to be used to create subsets. If the left-hand side is empty (e.g. ~ factor), right-hand side is treated as variable name to test.
data	(data frame|NULL) Either a data frame that contains the variables mentioned in y or NULL (if the variables are in the function's environment).
test	(string | function) Either a function that carries out a normality test or a string (case insensitive, maybe unambiguously abbreviated) with a name of a normality test. Possible names of tests: "SW", "Shapiro-Wilk" — for Shapiro-Wilk test; "Lilliefors" — for Kolmogorov-Smirnov test with Lilliefor's correction; "AD", "Anderson-Darling" — for Anderson-Darling test; "CVM", "CM", "Cramer-von Mises" — for Cramer-von Mises test; "SF", "Shapiro-Francia" — for Shapiro-Francia test; "Chi-squared","Pearsons" — for Pearson's chi-squared test of normality.
p_adjust_method	(NULL|string) A name of p value adjustment method for multiple comparisons. For available methods check stats::p.adjust.methods(). If NULL, no adjusted p value is calculated (default). If string (e.g., "holm"), an additional column p.adjust is calculated.
...	Further parameters to the function of normatity test.
groups	(NULL|factor|character) An alternative way to provide groups. If y is a numeric vector, groups must be a factor (or NULL). If y is a sting, groups must also be a string (or NULL).
ss	# FIXME: not documented
hide_error_msg	(logical) If FALSE column "error_msg" is not printed. If TRUE the column is printed if error occurs in calcultations. Default is FALSE.
x	normality_test object.
digits_p	(numeric) Number of significant digits to round a p value to. No less than 2. if digits_p = 2: values below 0.001 are printed as "<0.001"; values between 0.001 and 0.01 as "<0.01"; all other values are rounded to two decimal places. if digits_p = 3, only formatting "<0.01" is skipped.
signif_stars	(logical) If TRUE, significance stars are printed.
digits_stat	(integer) Either a number of decimal places or number of significant digits to round test statistic to.
format_stat	(character) Number format "f", "g" or "auto" (default) for test statistic. More about number formats "f" and "g" you can find in documentation of function base::formatC() section format.
rm_zero	(logical) Flag if leading zero before the point should be removed.
legend	(logical) If TRUE, legend for significance stars is printed.
show_col_method	(logical) If FALSE column "method" is not printed. Default is FALSE.
caption	(string|NULL|NA) A caption for the table with results of a normality test. If NA — a default caption is printed (default). If NULL – no caption is printed.

Value

• Function test_normality returns a data frame with normality test results for each group.

• print and pander methods format and print the results. By default, methods print.test_normality and pander.test_normality do not print column called "method".

See also

• stats::shapiro.test() in package stats;

• nortest::lillie.test() in package nortest;

• nortest::pearson.test() in package nortest;

• nortest::ad.test() in package nortest;

• nortest::cvm.test() in package nortest;

• nortest::sf.test() in package nortest.

Examples

library(biostat)
library(pander)
data(CO2)

# For whole dataset
test_normality(~uptake, data = CO2)
#> 
#>  The results of Shapiro-Wilk normality test 
#> 
#>   statistic p.value    
#> 1     0.941  <0.001 ***
#> 
#> *** - p < 0.001, ** - p < 0.01, * - p < 0.05, . - p < 0.1

# For each subgroup
test_normality(uptake ~ Treatment, data = CO2)
#> 
#>  The results of Shapiro-Wilk normality test 
#> 
#>    Treatment statistic p.value    
#> 1 nonchilled     0.945   0.043 *  
#> 2    chilled     0.898   0.001 ** 
#> 
#> *** - p < 0.001, ** - p < 0.01, * - p < 0.05, . - p < 0.1

# For each subgroup by several factor variables
rez <- test_normality(uptake ~ Type + Treatment,
                      data = CO2)
rez
#> 
#>  The results of Shapiro-Wilk normality test 
#> 
#>          Type  Treatment statistic p.value    
#> 1      Quebec nonchilled     0.825   0.002 ** 
#> 2      Quebec    chilled     0.853   0.005 ** 
#> 3 Mississippi nonchilled     0.855   0.005 ** 
#> 4 Mississippi    chilled     0.948   0.315    
#> 
#> *** - p < 0.001, ** - p < 0.01, * - p < 0.05, . - p < 0.1

# Modify printed output
print(rez, rm_zero = TRUE)
#> 
#>  The results of Shapiro-Wilk normality test 
#> 
#>          Type  Treatment statistic p.value    
#> 1      Quebec nonchilled      .825    .002 ** 
#> 2      Quebec    chilled      .853    .005 ** 
#> 3 Mississippi nonchilled      .855    .005 ** 
#> 4 Mississippi    chilled      .948    .315    
#> 
#> *** - p < 0.001, ** - p < 0.01, * - p < 0.05, . - p < 0.1

print(rez, digits_p = 2)
#> 
#>  The results of Shapiro-Wilk normality test 
#> 
#>          Type  Treatment statistic p.value    
#> 1      Quebec nonchilled     0.825   <0.01 ** 
#> 2      Quebec    chilled     0.853   <0.01 ** 
#> 3 Mississippi nonchilled     0.855   <0.01 ** 
#> 4 Mississippi    chilled     0.948    0.31    
#> 
#> *** - p < 0.001, ** - p < 0.01, * - p < 0.05, . - p < 0.1


# Choose another test of normality
rez2 <- test_normality(uptake ~ Type + Treatment,
                      data = CO2,
                      test = "chi-sq")
rez2
#> 
#>  The results of Pearson chi-square normality test 
#> 
#>          Type  Treatment statistic p.value    
#> 1      Quebec nonchilled      13.3   0.010 ** 
#> 2      Quebec    chilled      13.3   0.010 ** 
#> 3 Mississippi nonchilled      10.0   0.040 *  
#> 4 Mississippi    chilled       5.3   0.255    
#> 
#> *** - p < 0.001, ** - p < 0.01, * - p < 0.05, . - p < 0.1


# Print as a 'pandoc' table (for R Markdown reports)
pander(rez)
#> 
#> -------------------------------------------------
#>     Type       Treatment    statistic   p.value  
#> ------------- ------------ ----------- ----------
#>    Quebec      nonchilled     0.825     0.002 ** 
#> 
#>    Quebec       chilled       0.853     0.005 ** 
#> 
#>  Mississippi   nonchilled     0.855     0.005 ** 
#> 
#>  Mississippi    chilled       0.948      0.315   
#> -------------------------------------------------
#> 
#> Table: The results of Shapiro-Wilk normality test.
#> 
#> *** - p < 0.001  
#> ** - p < 0.01  
#> * - p < 0.05  
#> . - p < 0.1

pander(rez, digits_stat = 2)
#> 
#> -------------------------------------------------
#>     Type       Treatment    statistic   p.value  
#> ------------- ------------ ----------- ----------
#>    Quebec      nonchilled     0.83      0.002 ** 
#> 
#>    Quebec       chilled       0.85      0.005 ** 
#> 
#>  Mississippi   nonchilled     0.86      0.005 ** 
#> 
#>  Mississippi    chilled       0.95       0.315   
#> -------------------------------------------------
#> 
#> Table: The results of Shapiro-Wilk normality test.
#> 
#> *** - p < 0.001  
#> ** - p < 0.01  
#> * - p < 0.05  
#> . - p < 0.1

pander(rez, digits_p = 2)
#> 
#> -------------------------------------------------
#>     Type       Treatment    statistic   p.value  
#> ------------- ------------ ----------- ----------
#>    Quebec      nonchilled     0.825     <0.01 ** 
#> 
#>    Quebec       chilled       0.853     <0.01 ** 
#> 
#>  Mississippi   nonchilled     0.855     <0.01 ** 
#> 
#>  Mississippi    chilled       0.948       0.31   
#> -------------------------------------------------
#> 
#> Table: The results of Shapiro-Wilk normality test.
#> 
#> *** - p < 0.001  
#> ** - p < 0.01  
#> * - p < 0.05  
#> . - p < 0.1

pander(rez, digits_p = 4, signif_stars = FALSE)
#> 
#> ------------------------------------------------
#>     Type       Treatment    statistic   p.value 
#> ------------- ------------ ----------- ---------
#>    Quebec      nonchilled     0.825     0.0016  
#> 
#>    Quebec       chilled       0.853     0.0048  
#> 
#>  Mississippi   nonchilled     0.855     0.0052  
#> 
#>  Mississippi    chilled       0.948     0.3147  
#> ------------------------------------------------
#> 
#> Table: The results of Shapiro-Wilk normality test.
#> 


if (FALSE) {
# View unformatted results in a separate window
View(rez)
}

# Show object's class
class(rez)
#> [1] "test_normality" "data.frame"