Automated Visualization of Statistical Hypothesis Testing

visstat_core() implements the decision tree used by visstat. It receives a data.frame and two column names, determines the corresponding analysis route, creates the diagnostic and result plots, and returns the selected test results as a visstat object.

Usage

visstat_core(
  dataframe,
  varsample,
  varfactor,
  conf.level = 0.95,
  correlation = FALSE,
  numbers = TRUE,
  minpercent = 0.05,
  group_test = NULL,
  graphicsoutput = NULL,
  plotName = NULL,
  plotDirectory = getwd(),
  plot_args = list()
)

Arguments

dataframe: data.frame with at least two columns.
varsample: character string matching a column name in dataframe. Interpreted as the response if the referenced column is of class numeric or integer and the column named by varfactor is of class factor.
varfactor: character string matching a column name in dataframe. Interpreted as the grouping variable if the referenced column is of class factor and the column named by varsample is of class numeric or integer.
conf.level: Confidence level
correlation: Logical. If FALSE (default), performs simple linear regression analysis with confidence and prediction bands. If TRUE, performs Spearman correlation analysis with trend line only (no regression interpretation).
numbers: a logical indicating whether to show numbers in mosaic count plots.
minpercent: number between 0 and 1 indicating minimal fraction of total count data of a category to be displayed in mosaic count plots.
group_test: Optional character. For Route 1 only, NULL keeps the default assumption gates, "welch" forces Welch-type mean tests, but still displays the assumption-diagnostic plot and warns when residual normality is rejected, whereas "rank" forces Wilcoxon/Kruskal-Wallis rank tests without assessing the assumptions.
graphicsoutput: saves plot(s) of type "png", "jpeg", "pdf", "svg", "ps" or "tiff" in directory specified in plotDirectory. If graphicsoutput=NULL, no plots are saved. Any other value is not supported by Cairo(): it triggers a warning and no file is written.
plotName: graphical output is stored following the naming convention "plotName.graphicsoutput" in plotDirectory. Without specifying this parameter, plotName is automatically generated following the convention "statisticalTestName_varsample_varfactor".
plotDirectory: specifies directory, where generated plots are stored. Default is current working directory.
plot_args: Optional named list of base graphics parameters.

Value

An object of class "visstat" containing the results of the automatically selected statistical test. The specific contents depend on which test was performed. Additionally, the returned object includes two attributes:

plot_paths: Character vector of file paths where plots were saved (if graphicsoutput was specified)
captured_plots: List of captured plot objects for programmatic access

Details

The decision logic is organised into four routes. Route 1 handles a numeric response with a categorical predictor. By default, Route 1 uses residual-based test selection: Shapiro–Wilk on model residuals gates mean-based versus rank-based analysis, and Levene gates equal-variance versus Welch-type mean tests inside the mean branch. Above 5000 observations, where shapiro.test() is undefined, the Anderson–Darling test takes over as the residual-normality gate. Alternatively, group_test = "welch" forces Welch-type mean tests, and group_test = "rank" forces Wilcoxon/Kruskal–Wallis tests.

Route 2 handles ordered responses with categorical predictors by converting the ordered response to integer level codes and applying Wilcoxon or Kruskal–Wallis tests. Route 3 handles two numeric variables by fitting lm() by default, or Spearman rank correlation when correlation = TRUE. Route 4 handles two unordered factors with Pearson's \(\chi^2\) test or Fisher's exact test, depending on expected counts. If both variables are ordered and correlation = TRUE, Kendall's \(\tau_b\) is used.

The significance level alpha is defined as 1 - conf.level. Assumption tests are interpreted relative to this threshold.

Under the default group_test = NULL, Route 1 issues a warning when the group sizes are unbalanced, the largest group standard deviations occur in the smallest groups, and the route selected is either the equal-variance test or a rank-based test. In that configuration those two routes can exceed the nominal significance level, whereas a selected Welch test does not and is therefore not flagged; see the Route 1 simulations in vignette("visStatistics").

Implemented main tests:

t.test(), wilcox.test(), aov(), oneway.test(), lm(), kruskal.test(), fisher.test(), chisq.test().

Implemented tests for assumptions:

Normality: shapiro.test() and ad.test()
Heteroscedasticity: bartlett.test() and levene.test() and bp.test()

For the general linear model the Shapiro-Wilk, Anderson-Darling, Levene and Bartlett tests are applied to the internally studentised residuals r_i = e_i / (SE_res sqrt(1 - h_i)), which remove the leverage-dependent variance of the raw residuals (Var(e_i) = sigma^2 (1 - h_i)).

Implemented post hoc tests:

TukeyHSD() for aov()
games.howell() for oneway.test()
pairwise.wilcox.test() for kruskal.test()

The Q-Q envelopes in the assumption diagnostics are simulated (see qq_lm_envelope). The number of simulated refits is taken from the option visStatistics.qq_nsim and defaults to 5000. As visstat_core() has no corresponding argument, this option is the only way to change it here; lower it to trade precision for speed, for instance options(visStatistics.qq_nsim = 1000L).

Examples

old_qq_nsim <- getOption("visStatistics.qq_nsim")
options(visStatistics.qq_nsim = 100L)

# Welch Two Sample t-test (t.test())
visstat_core(mtcars, "mpg", "am")


#> Warning: Statistical assumptions violated:
#> Homoscedasticity violated (Breusch-Pagan p = 0.0242 )
#> Analysis proceeded but interpret results cautiously.
#> RECOMMENDATION: Consider exploring alternatives outside visstat() such as data transformations,
#> generalised linear models, or robust regression. For a non-causal alternative
#> consider rerunning with correlation = TRUE.

## Wilcoxon rank sum test (wilcox.test())
grades_gender <- data.frame(
  Sex = as.factor(c(rep("Girl", 20), rep("Boy", 20))),
  Grade = c(
    19.3, 18.1, 15.2, 18.3, 7.9, 6.2, 19.4,
    20.3, 9.3, 11.3, 18.2, 17.5, 10.2, 20.1, 13.3, 17.2, 15.1, 16.2, 17.3,
    16.5, 5.1, 15.3, 17.1, 14.8, 15.4, 14.4, 7.5, 15.5, 6.0, 17.4,
    7.3, 14.3, 13.5, 8.0, 19.5, 13.4, 17.9, 17.7, 16.4, 15.6
  )
)
visstat_core(grades_gender, "Grade", "Sex")



## Welch's oneway ANOVA not assuming equal variances (oneway.test())
anova_npk <- visstat_core(npk, "yield", "block")


anova_npk # prints summary of tests
#> Object of class 'visstat'
#> 
#> Available components:
#> [1] "summary statistics of ANOVA" "post-hoc analysis "         
#> [3] "conf.level"                  "effect_size"                

## Kruskal-Wallis rank sum test (kruskal.test())
visstat_core(iris, "Petal.Width", "Species")


visstat_core(InsectSprays, "count", "spray")



## Simple linear regression  (lm())
visstat_core(trees, "Girth", "Height", conf.level = 0.99)



## Pearson's Chi-squared test (chisq.test())
### Transform array to data.frame
HairEyeColorDataFrame <- counts_to_cases(as.data.frame(HairEyeColor))
visstat_core(HairEyeColorDataFrame, "Hair", "Eye")



## Fisher's exact test (fisher.test())
HairEyeColorMaleFisher <- HairEyeColor[, , 1]
### slicing out a 2 x2 contingency table
blackBrownHazelGreen <- HairEyeColorMaleFisher[1:2, 3:4]
blackBrownHazelGreen <- counts_to_cases(as.data.frame(blackBrownHazelGreen))
fisher_stats <- visstat_core(blackBrownHazelGreen, "Hair", "Eye")


options(visStatistics.qq_nsim = old_qq_nsim)