OVERVIEW

Overview of what VIT modules cover

Modules

• Randomisation Variation
• Randomisation Tests
• Sampling variation
• Bootstrap Confidence Intervals
• Confidence Interval Coverage
• A further module covering Bootstrap Significance Tests is at the design stage

The above follows the order of: "motivation"; "implementation"; "investigating how well it works" for first randomised experiments and then random sampling. The range of measures and techniques covered is circumscribed by their lending themselves to a cohesive suite of visualisations built around features you can see on primary plots of data. [Breaking: While VIT is desktop software packaged with iNZight, VITonline, an online version of VIT that plays in your browser, is under development. The sampling variation and bootstrap confidence interval modules are working for basic situations.]

Randomisation Variation

This module caters for the effects of (artificial) random allocation to groups on:

• (if a single categorical variable is supplied) proportions
• (if a single numeric variable is supplied) means and medians

This module facilitates visual exploration of the nature and extent of variation in features of a numeric variable or a binary variable from user-supplied data, due solely to an artificial random labelling of individuals as belonging to different "groups".

• For experimental data, an appreciation that randomisation into groups alone can lead to quite large observed group differences in the variable of interest is a central foundation for motivating significance tests in general and randomisation tests in particular.
• Some Lessons:
• Randomisation acting alone leads to apparent differences between groups
• These differences can be surprisingly large
• This variation can be experienced in terms of how it manifest itself:
1. in plots of data
2. as a randomisation distribution
Understandings in terms of what happens to data plots should be established first. The animations also connect the two forms of representation

Randomisation Tests (randomisation-based significance tests)

This module caters for randomisation tests on user-supplied data for: (Note: Two variables must be supplied.)

• (if a numeric variable and a categorical variable is supplied)
  group differences in means, medians, quartiles (includes 1-way anova using average deviations or F as discrepancy measures), or a ratio of interquartile ranges
• (if two categorical variables are supplied)
  group differences in proportions (includes 1-way anova equivalent for proportions using average deviations or chi-sq as discrepancy measures)
• (if 2 numeric variables are supplied)
  regression slopes or paired comparisons. [Correlations will be added at some future date.]

Sampling variation (sampling distributions)

This module caters for the variation incurred by sampling from user-supplied population data on:

• (if a single categorical variable is supplied) proportions
• (if a single numeric variable is supplied) means, medians, quartiles, interquartile ranges (IQRs)
• (if a numeric variable and a categorical is supplied) group differences in such measures (a ratio in the case of IQRs)
• (if 2 numeric variables are supplied) regression slopes. [Correlations will be added at some future date.]

This module facilitates visual exploration of the nature and extent of variation in features of binary or numeric variables when samples are repeatedly taken from user-supplied population data.

An appreciation of the variation produced by random sampling is a central foundation for motivating statistical inferences based upon sampling theory in general and upon bootstrap resampling in particular.

• Sampling variation can be experienced in terms of how it manifest itself:
1. in plots of data
2. as a sampling distribution
Understandings in terms of what happens to data plots should be established first. The animations also connect the two forms of representation

Bootstrap Confidence intervals

This module caters for bootstrap confidence interval construction from user-supplied data for:

• (if a single categorical variable is supplied) proportions
• (if a single numeric variable is supplied) means, medians, quartiles, interquartile ranges (IQRs)
• (if a numeric variable and a categorical is supplied) group differences in such measures (a ratio in the case of IQRs)
• (if 2 numeric variables are supplied) regression slopes or paired-comparison differences. [Correlations will be added at some future date.]

Confidence Interval Coverage

This module facilitates visual investigation of coverage frequencies of confidence intervals calculated from samples taken from user-supplied population data using both the boostrap and normal-theory.

This module caters for:

• (if a single categorical variable is supplied) proportions
• (if a single numeric variable is supplied) means, medians
• [We aim to eventually have coverage-investigation facilities for every feature covered in Bootstrap CIs]

Bootstrap Significance Tests

Currently at the design stage.