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Describe Relationship: Categorical y vs Numeric x

Source: R/desc.qn.R
desc.qn.Rd

Computes descriptive statistics for the relationship between a categorical variable y and a numeric variable x.

Usage

.descQN(y, x, conf.level = 0.95, breaks, right)

# S3 method for class 'Desc.qn'
print(x, verbose = NULL, ...)

Arguments

x

a numeric variable

verbose

amount of printed output

...

further arguments passed to methods

y

a categorical variable (factor or coercible to factor)

conf.level

confidence level for interval estimates (default 0.95)

breaks

numeric vector defining cut points for x. If not supplied, quartiles of x are used.

right

logical; passed to cut(), defining interval closure

Value

an object of class c("Desc.qn", "Desc") with components:

grpTable

group-wise summary table

kw

result of the Kruskal-Wallis test

eta2

effect size

levene

result of Levene's test

tauB

estimate, confidence interval, and p-value for Kendall's tau-b

spearman

estimate, confidence interval, and p-value for Spearman's correlation

auc

area under the curve for a binary outcome

prevTable

prevalence table for a binary outcome with columns:

quantile

quantile group

n

number of complete cases in the group

est

point estimate of the prevalence

lci

lower confidence interval bound

uci

upper confidence interval bound

caTest

result of the Cochran-Armitage test for a binary outcome

Details

The function summarizes how a numeric variable x differs across levels of a categorical variable y.

Computed statistics

  • Group-wise descriptive statistics (median, IQR, counts)

  • Kruskal-Wallis test with effect size (\(\eta^2\))

  • Levene's test for homogeneity of variance

  • Kendall's Tau-b with confidence interval and p-value

  • Spearman correlation (reported for higher verbosity levels)

Binary outcomes If y has two levels:

  • Area under the curve (AUC)

  • Prevalence across quantile groups of x

  • Cochran-Armitage trend test

Quantile grouping The numeric variable x is optionally discretized using breaks. By default, quartiles are used.

Plots

The plot method pharos::plot.Desc.qn() is part of pharos; its help page documents which and all further arguments. It draws one of the following displays:

which = 1

Spineplot of y against x (default).

which = 2

Conditional density plot: the conditional distribution of y along x.

which = 3

Overlaid kernel density estimates of x, one per level of y.

which = 4

Boxplots of x by level of y.

which = 5

Prevalence of the second level of y with Wilson confidence intervals across the groups of x; binary y only.

See also

desc(), desc.nn(), desc.nq(), desc.qq(), kruskal.test(), lumen::leveneTest()

Plot method: pharos::plot.Desc.qn()

Other desc: desc(), desc.Date(), desc.factor(), desc.nn, desc.nq, desc.numeric(), desc.qq, desc.table(), desc.ts()

Examples

# basic usage via desc()
desc(quality ~ delivery_min, Pizza)
#> ────────────────────────────────────────────────────────────────────────────── 
#> quality ~ delivery_min (Pizza) (Desc.qn)
#> 
#> Summary:
#> pairs: 1209, valid: 1008 (83.4%), missings: 201 (16.6%), groups: 3
#> 
#>             low   medium     high
#> median   35.100   25.850   21.400
#> iqr      16.650   13.725   12.850
#> n           156      356      496
#> np        15.5%    35.3%    49.2%
#> 
#> Kruskal-Wallis rank sum test:
#>   H = 122,  df = 2,  p = <0.001
#>   η² = 0.120 (moderate)
#> 
#> Levene's test for homogeneity of variance (center = median):
#>   F = 5.3528,  df1 = 2,  df2 = 1005,  p = 0.00487
#> 
#> Kendall Tau-b:  -0.266  (-0.313, -0.220)  ***  small
#> 
#> Conditional distribution of y by x-quantile:
#>         xCut
#> yOk      [9–17) [17–24) [24–33) [33–66)
#>   low     5.3%   8.8%   13.4%   33.9%  
#>   medium 30.0%  33.1%   41.5%   36.6%  
#>   high   64.8%  58.2%   45.1%   29.6%  
#> 


# more detail
desc(quality ~ delivery_min, Pizza, verbose = 3)
#> ────────────────────────────────────────────────────────────────────────────── 
#> quality ~ delivery_min (Pizza) (Desc.qn)
#> 
#> Summary:
#> pairs: 1209, valid: 1008 (83.4%), missings: 201 (16.6%), groups: 3
#> 
#>             low   medium     high
#> mean     33.925   26.522   22.615
#> median   35.100   25.850   21.400
#> sd       11.742   10.113    9.497
#> iqr      16.650   13.725   12.850
#> n           156      356      496
#> np        15.5%    35.3%    49.2%
#> NAs           0        0        0
#> zeros         0        0        0
#> 
#> Kruskal-Wallis rank sum test:
#>   H = 122,  df = 2,  p = <0.001
#>   η² = 0.120 (moderate)
#> 
#> Levene's test for homogeneity of variance (center = median):
#>   F = 5.3528,  df1 = 2,  df2 = 1005,  p = 0.00487
#> 
#> Kendall Tau-b:  -0.266  (-0.313, -0.220)  ***  small
#> Spearman r:     -0.335  (-0.389, -0.279)  ***  moderate
#> 
#> Conditional distribution of y by x-quantile:
#>         xCut
#> yOk      [9–17) [17–24) [24–33) [33–66)
#>   low     5.3%   8.8%   13.4%   33.9%  
#>   medium 30.0%  33.1%   41.5%   36.6%  
#>   high   64.8%  58.2%   45.1%   29.6%  
#> 


# store result, print and plot separately
d <- desc(quality ~ delivery_min, Pizza, plotit = FALSE)
print(d, verbose = 1)
#> ────────────────────────────────────────────────────────────────────────────── 
#> quality ~ delivery_min (Pizza) (Desc.qn)
#> 
#> Summary:
#> pairs: 1209, valid: 1008 (83.4%), missings: 201 (16.6%), groups: 3
#> 
#>             low   medium     high
#> median   35.100   25.850   21.400
#> n           156      356      496
#> np        15.5%    35.3%    49.2%
#> 
#> Kruskal-Wallis rank sum test:
#>   H = 122,  df = 2,  p = <0.001
#>   η² = 0.120 (moderate)
#> 
#> Conditional distribution of y by x-quantile:
#>         xCut
#> yOk      [9–17) [17–24) [24–33) [33–66)
#>   low     5.3%   8.8%   13.4%   33.9%  
#>   medium 30.0%  33.1%   41.5%   36.6%  
#>   high   64.8%  58.2%   45.1%   29.6%  
#> 

# the plots, see pharos::plot.Desc.qn()
plot(d, which = 1)                     # spineplot

plot(d, which = 2)                     # conditional density

plot(d, which = 3)                     # densities by level of y

plot(d, which = 4)                     # boxplots


# binary y: AUC, prevalence by groups of x, Cochran-Armitage test
# (complaint is stored as 0/1 and would be described as numeric-numeric)
pz <- transform(Pizza, complaint = factor(complaint, levels = 0:1,
                                          labels = c("no", "yes")))
d2 <- desc(complaint ~ delivery_min, pz, plotit = FALSE)
d2
#> ────────────────────────────────────────────────────────────────────────────── 
#> complaint ~ delivery_min (pz) (Desc.qn)
#> 
#> Summary:
#> pairs: 1209, valid: 1080 (89.3%), missings: 129 (10.7%), groups: 2
#> 
#>              no      yes
#> median   23.700   29.000
#> iqr      14.750   16.200
#> n           875      205
#> np        81.0%    19.0%
#> 
#> Kruskal-Wallis rank sum test:
#>   H = 25,  df = 1,  p = <0.001
#>   η² = 0.022 (small)
#> 
#> Levene's test for homogeneity of variance (center = median):
#>   F = 3.5339,  df1 = 1,  df2 = 1078,  p = 0.0604
#> 
#> AUC = 61.2%  (no vs yes)
#> 
#> Kendall Tau-b:   0.124  ( 0.076,  0.173)  ***  small
#> 
#> Prevalence of "yes" by groups (Wilson CI):
#>                            n      est      lci      uci
#> ---------------------------------------------------- 
#>   [9–17)               271    13.3%     9.8%    17.8%
#>   [17–24)              267    13.9%    10.2%    18.5%
#>   [24–33)              271    19.6%    15.3%    24.7%
#>   [33–66)              271    29.2%    24.1%    34.8%
#> 
#> Cochran-Armitage trend test:
#>   Z = -4.998,  p = <0.001
#> 
plot(d2, which = 5)                    # prevalence with Wilson CI


# own breaks instead of quartiles
desc(complaint ~ delivery_min, pz, breaks = c(20, 30, 40))
#> ────────────────────────────────────────────────────────────────────────────── 
#> complaint ~ delivery_min (pz) (Desc.qn)
#> 
#> Summary:
#> pairs: 1209, valid: 1080 (89.3%), missings: 129 (10.7%), groups: 2
#> 
#>              no      yes
#> median   23.700   29.000
#> iqr      14.750   16.200
#> n           875      205
#> np        81.0%    19.0%
#> 
#> Kruskal-Wallis rank sum test:
#>   H = 25,  df = 1,  p = <0.001
#>   η² = 0.022 (small)
#> 
#> Levene's test for homogeneity of variance (center = median):
#>   F = 3.5339,  df1 = 1,  df2 = 1078,  p = 0.0604
#> 
#> AUC = 61.2%  (no vs yes)
#> 
#> Kendall Tau-b:   0.124  ( 0.076,  0.173)  ***  small
#> 
#> Prevalence of "yes" by groups (Wilson CI):
#>                            n      est      lci      uci
#> ---------------------------------------------------- 
#>   [9–20)               358    14.0%    10.8%    17.9%
#>   [20–30)              378    16.1%    12.8%    20.2%
#>   [30–40)              225    24.4%    19.3%    30.5%
#>   [40–66)              119    32.8%    25.0%    41.6%
#> 
#> Cochran-Armitage trend test:
#>   Z = -4.966,  p = <0.001
#> 


# pipe
desc(quality ~ delivery_min, Pizza) |> plot(which = 2)