10  Visual Statistical Analysis

10.1 Learning Outcome

In this hands-on exercise, you will gain hands-on experience on using:

• ggstatsplot package to create visual graphics with rich statistical information,

• performance package to visualise model diagnostics, and

• parameters package to visualise model parameters

10.2 Visual Statistical Analysis with ggstatsplot

ggstatsplot is an extension of ggplot2 package for creating graphics with details from statistical tests included in the information-rich plots themselves.

-   To provide alternative statistical inference methods by default.
-   To follow best practices for statistical reporting. For all statistical tests reported in the plots, the default template abides by the [APA](https://my.ilstu.edu/~jhkahn/apastats.html) gold standard for statistical reporting. For example, here are results from a robust t-test:

10.3 Getting Started

10.3.1 Installing and launching R packages

In this exercise, ggstatsplot and tidyverse will be used.

pacman::p_load(ggstatsplot, tidyverse)

10.3.2 Importing data

Do-It-Yourself

Importing Exam.csv data by using appropriate tidyverse package.

# A tibble: 322 × 7
   ID         CLASS GENDER RACE    ENGLISH MATHS SCIENCE
   <chr>      <chr> <chr>  <chr>     <dbl> <dbl>   <dbl>
 1 Student321 3I    Male   Malay        21     9      15
 2 Student305 3I    Female Malay        24    22      16
 3 Student289 3H    Male   Chinese      26    16      16
 4 Student227 3F    Male   Chinese      27    77      31
 5 Student318 3I    Male   Malay        27    11      25
 6 Student306 3I    Female Malay        31    16      16
 7 Student313 3I    Male   Chinese      31    21      25
 8 Student316 3I    Male   Malay        31    18      27
 9 Student312 3I    Male   Malay        33    19      15
10 Student297 3H    Male   Indian       34    49      37
# ℹ 312 more rows

10.3.3 One-sample test: gghistostats() method

In the code chunk below, gghistostats() is used to to build an visual of one-sample test on English scores.

set.seed(1234)

gghistostats(
  data = exam,
  x = ENGLISH,
  type = "bayes",
  test.value = 60,
  xlab = "English scores"
)

Default information: - statistical details - Bayes Factor - sample sizes - distribution summary

10.3.4 Unpacking the Bayes Factor

• A Bayes factor is the ratio of the likelihood of one particular hypothesis to the likelihood of another. It can be interpreted as a measure of the strength of evidence in favor of one theory among two competing theories.

• That’s because the Bayes factor gives us a way to evaluate the data in favor of a null hypothesis, and to use external information to do so. It tells us what the weight of the evidence is in favor of a given hypothesis.

• When we are comparing two hypotheses, H1 (the alternate hypothesis) and H0 (the null hypothesis), the Bayes Factor is often written as B10. It can be defined mathematically as

• The Schwarz criterion is one of the easiest ways to calculate rough approximation of the Bayes Factor.

10.3.5 How to interpret Bayes Factor

A Bayes Factor can be any positive number. One of the most common interpretations is this one—first proposed by Harold Jeffereys (1961) and slightly modified by Lee and Wagenmakers in 2013:

10.3.6 Two-sample mean test: ggbetweenstats()

In the code chunk below, ggbetweenstats() is used to build a visual for two-sample mean test of Maths scores by gender.

ggbetweenstats(
  data = exam,
  x = GENDER, 
  y = MATHS,
  type = "np",
  messages = FALSE
)

Default information: - statistical details - Bayes Factor - sample sizes - distribution summary

10.3.7 Oneway ANOVA Test: ggbetweenstats() method

In the code chunk below, ggbetweenstats() is used to build a visual for One-way ANOVA test on English score by race.

ggbetweenstats(
  data = exam,
  x = RACE, 
  y = ENGLISH,
  type = "p",
  mean.ci = TRUE, 
  pairwise.comparisons = TRUE, 
  pairwise.display = "s",
  p.adjust.method = "fdr",
  messages = FALSE
)

• “ns” → only non-significant
• “s” → only significant
• “all” → everything

10.3.7.1 ggbetweenstats - Summary of tests

10.3.8 Significant Test of Correlation: ggscatterstats()

In the code chunk below, ggscatterstats() is used to build a visual for Significant Test of Correlation between Maths scores and English scores.

ggscatterstats(
  data = exam,
  x = MATHS,
  y = ENGLISH,
  marginal = FALSE,
  )

10.3.9 Significant Test of Association (Depedence) : ggbarstats() methods

In the code chunk below, the Maths scores is binned into a 4-class variable by using cut().

exam1 <- exam %>% 
  mutate(MATHS_bins = 
           cut(MATHS, 
               breaks = c(0,60,75,85,100))
)

In this code chunk below ggbarstats() is used to build a visual for Significant Test of Association

ggbarstats(exam1, 
           x = MATHS_bins, 
           y = GENDER)