Reliability ANOVA

README.md

Demonstrate consequences of a violation of the common variance assumption for ANOVA.

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Reliability ANOVA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reliability ANOVA\n",
    "\n",
    "Test what happens when the common variance assumption is violated in a one-way ANOVA-based ICC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "using Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "variance_orig = 1.0\n",
    "variance_new = 0.6\n",
    "size = 50_000;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = MersenneTwister(928381) # make reproducible\n",
    "values = zeros(size, 2)\n",
    "values[:,1] = randn(rng, Float64, size) * variance_orig\n",
    "values[:,2] = values[:,1] * (variance_new / variance_orig);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
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       "0.8749839265078074"
      ]
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     "execution_count": 59,
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   ],
   "source": [
    "# compute the ANOVA\n",
    "overall_mean = mean(values)\n",
    "individual_means = mean(values, dims=2)\n",
    "ss_between = sum((individual_means .- overall_mean).^2)\n",
    "ss_within = sum((values .- individual_means .+ overall_mean) .^ 2)\n",
    "icc = (ss_between - ss_within) / ss_between"
   ]
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