{
"cells": [
{
"cell_type": "markdown",
"id": "5b41ceb6-d385-4837-b5e0-5e21e643d6e6",
"metadata": {},
"source": [
"# Two-way ANOVA\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "3a91e1db-04f3-4c28-9707-e0a7c6df2d6a",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import statsmodels.formula.api as smf "
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6e1aa2b2-ce9b-420f-8813-e0d0f9ac327a",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'"
]
},
{
"cell_type": "markdown",
"id": "2030c8e7-a0d8-4a4d-b227-a0a81f11e02d",
"metadata": {},
"source": [
"$\\def\\stderr#1{\\mathbf{se}_{#1}}$\n",
"$\\def\\stderrhat#1{\\hat{\\mathbf{se}}_{#1}}$\n",
"$\\newcommand{\\Mean}{\\textbf{Mean}}$\n",
"$\\newcommand{\\Var}{\\textbf{Var}}$\n",
"$\\newcommand{\\Std}{\\textbf{Std}}$\n",
"$\\newcommand{\\Freq}{\\textbf{Freq}}$\n",
"$\\newcommand{\\RelFreq}{\\textbf{RelFreq}}$\n",
"$\\newcommand{\\DMeans}{\\textbf{DMeans}}$\n",
"$\\newcommand{\\Prop}{\\textbf{Prop}}$\n",
"$\\newcommand{\\DProps}{\\textbf{DProps}}$"
]
},
{
"cell_type": "markdown",
"id": "e41da4dc-40bc-4074-b3ca-5f2a2534fdcf",
"metadata": {},
"source": [
"## Definitions"
]
},
{
"cell_type": "markdown",
"id": "442020c3-458a-469b-a82e-c7f3beafb812",
"metadata": {},
"source": [
"## Formulas"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "28207dfa-61a8-47a3-8fe1-9168cbc2f096",
"metadata": {},
"outputs": [],
"source": [
"\n"
]
},
{
"cell_type": "markdown",
"id": "60311b0a-7c91-4df0-be4a-accc69028d8c",
"metadata": {},
"source": [
"## Example"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "55e6cea6-edd2-4d6c-bcbf-7f0e25b9b5b3",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" id | \n",
" gender | \n",
" education_level | \n",
" score | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 1 | \n",
" male | \n",
" school | \n",
" 5.51 | \n",
"
\n",
" \n",
" | 1 | \n",
" 2 | \n",
" male | \n",
" school | \n",
" 5.65 | \n",
"
\n",
" \n",
" | 2 | \n",
" 3 | \n",
" male | \n",
" school | \n",
" 5.07 | \n",
"
\n",
" \n",
" | 3 | \n",
" 4 | \n",
" male | \n",
" school | \n",
" 5.51 | \n",
"
\n",
" \n",
" | 4 | \n",
" 5 | \n",
" male | \n",
" school | \n",
" 5.94 | \n",
"
\n",
" \n",
"
\n",
"
"
]
},
"metadata": {
"image/png": {
"height": 433,
"width": 554
}
},
"output_type": "display_data"
}
],
"source": [
"from statsmodels.graphics.factorplots import interaction_plot\n",
"\n",
"js = jobsatisfaction\n",
"interaction_plot(js[\"education_level\"], js[\"gender\"], js[\"score\"]);"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "7a174cac-05da-4c30-8023-ca661360ab56",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" sum_sq | \n",
" df | \n",
" F | \n",
" PR(>F) | \n",
"
\n",
" \n",
" \n",
" \n",
" | education_level | \n",
" 113.684117 | \n",
" 2.0 | \n",
" 187.892103 | \n",
" 1.600455e-24 | \n",
"
\n",
" \n",
" | gender | \n",
" 0.225297 | \n",
" 1.0 | \n",
" 0.744721 | \n",
" 3.921154e-01 | \n",
"
\n",
" \n",
" | education_level:gender | \n",
" 4.439794 | \n",
" 2.0 | \n",
" 7.337895 | \n",
" 1.559245e-03 | \n",
"
\n",
" \n",
" | Residual | \n",
" 15.731300 | \n",
" 52.0 | \n",
" NaN | \n",
" NaN | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Source | \n",
" SS | \n",
" DF | \n",
" MS | \n",
" F | \n",
" p-unc | \n",
" np2 | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" gender | \n",
" 0.225297 | \n",
" 1.0 | \n",
" 0.225297 | \n",
" 0.744721 | \n",
" 3.921154e-01 | \n",
" 0.014119 | \n",
"
\n",
" \n",
" | 1 | \n",
" education_level | \n",
" 113.684117 | \n",
" 2.0 | \n",
" 56.842059 | \n",
" 187.892103 | \n",
" 1.600455e-24 | \n",
" 0.878443 | \n",
"
\n",
" \n",
" | 2 | \n",
" gender * education_level | \n",
" 4.439794 | \n",
" 2.0 | \n",
" 2.219897 | \n",
" 7.337895 | \n",
" 1.559245e-03 | \n",
" 0.220107 | \n",
"
\n",
" \n",
" | 3 | \n",
" Residual | \n",
" 15.731300 | \n",
" 52.0 | \n",
" 0.302525 | \n",
" NaN | \n",
" NaN | \n",
" NaN | \n",
"
\n",
" \n",
"
\n",
"