{ "cells": [ { "cell_type": "markdown", "id": "f06a5ae3-44b9-4c22-a35e-8b235ec6db0c", "metadata": {}, "source": [ "# ANOVA Assumptions - R" ] }, { "cell_type": "markdown", "id": "1b113b1f-7a2c-459f-be84-71c90c33563d", "metadata": { "tags": [] }, "source": [ "## Shapiro-Wilk Test (on responses)\n", "\n", "* **Assumption:** Normality\n", "* **Context of Use:** t-test, ANOVA, LM, LMM\n", "* **Reporting:** \"To test the assumption of conditional normality, a Shapiro-Wilk test was run on the response Y for each combination of levels of factors X1 and X2. All combinations were found to be statistically non-significant except condition (b,b), which showed a statistically significant deviation from normality (W = .794, p < .01).\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "db6e0233-e067-41c4-a20b-1167d10b18d2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
1 1aa11.867340
2 2ab15.453745
3 3ba15.782415
4 4bb13.626554
5 5aa11.608195
6 6ab19.540674
7 7ba15.878829
8 8bb16.654611
9 9aa17.370245
1010ab17.547025
1111ba19.423109
1212bb16.369147
1313aa22.896627
1414ab14.037504
1515ba15.564130
1616bb16.109281
1717aa 7.028036
1818ab21.508059
1919ba17.644257
2020bb16.054999
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 11.867340\\\\\n", "\t2 & 2 & a & b & 15.453745\\\\\n", "\t3 & 3 & b & a & 15.782415\\\\\n", "\t4 & 4 & b & b & 13.626554\\\\\n", "\t5 & 5 & a & a & 11.608195\\\\\n", "\t6 & 6 & a & b & 19.540674\\\\\n", "\t7 & 7 & b & a & 15.878829\\\\\n", "\t8 & 8 & b & b & 16.654611\\\\\n", "\t9 & 9 & a & a & 17.370245\\\\\n", "\t10 & 10 & a & b & 17.547025\\\\\n", "\t11 & 11 & b & a & 19.423109\\\\\n", "\t12 & 12 & b & b & 16.369147\\\\\n", "\t13 & 13 & a & a & 22.896627\\\\\n", "\t14 & 14 & a & b & 14.037504\\\\\n", "\t15 & 15 & b & a & 15.564130\\\\\n", "\t16 & 16 & b & b & 16.109281\\\\\n", "\t17 & 17 & a & a & 7.028036\\\\\n", "\t18 & 18 & a & b & 21.508059\\\\\n", "\t19 & 19 & b & a & 17.644257\\\\\n", "\t20 & 20 & b & b & 16.054999\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 11.867340 |\n", "| 2 | 2 | a | b | 15.453745 |\n", "| 3 | 3 | b | a | 15.782415 |\n", "| 4 | 4 | b | b | 13.626554 |\n", "| 5 | 5 | a | a | 11.608195 |\n", "| 6 | 6 | a | b | 19.540674 |\n", "| 7 | 7 | b | a | 15.878829 |\n", "| 8 | 8 | b | b | 16.654611 |\n", "| 9 | 9 | a | a | 17.370245 |\n", "| 10 | 10 | a | b | 17.547025 |\n", "| 11 | 11 | b | a | 19.423109 |\n", "| 12 | 12 | b | b | 16.369147 |\n", "| 13 | 13 | a | a | 22.896627 |\n", "| 14 | 14 | a | b | 14.037504 |\n", "| 15 | 15 | b | a | 15.564130 |\n", "| 16 | 16 | b | b | 16.109281 |\n", "| 17 | 17 | a | a | 7.028036 |\n", "| 18 | 18 | a | b | 21.508059 |\n", "| 19 | 19 | b | a | 17.644257 |\n", "| 20 | 20 | b | b | 16.054999 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 11.867340\n", "2 2 a b 15.453745\n", "3 3 b a 15.782415\n", "4 4 b b 13.626554\n", "5 5 a a 11.608195\n", "6 6 a b 19.540674\n", "7 7 b a 15.878829\n", "8 8 b b 16.654611\n", "9 9 a a 17.370245\n", "10 10 a b 17.547025\n", "11 11 b a 19.423109\n", "12 12 b b 16.369147\n", "13 13 a a 22.896627\n", "14 14 a b 14.037504\n", "15 15 b a 15.564130\n", "16 16 b b 16.109281\n", "17 17 a a 7.028036\n", "18 18 a b 21.508059\n", "19 19 b a 17.644257\n", "20 20 b b 16.054999" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has two factors (X1,X2) each w/two levels (a,b) and continuous response Y\n", "df <- read.csv(\"data/2F2LBs_normal.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 2, "id": "444d31ef-210f-4c18-8b50-e456a0cfff9f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: df[df$X1 == \"a\" & df$X2 == \"a\", ]$Y\n", "W = 0.97554, p-value = 0.93\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: df[df$X1 == \"a\" & df$X2 == \"b\", ]$Y\n", "W = 0.93417, p-value = 0.3147\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: df[df$X1 == \"b\" & df$X2 == \"a\", ]$Y\n", "W = 0.98454, p-value = 0.9914\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: df[df$X1 == \"b\" & df$X2 == \"b\", ]$Y\n", "W = 0.7938, p-value = 0.003064\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Shapiro-Wilk conditional normality test\n", "# (on the response within each condition)\n", "shapiro.test(df[df$X1 == \"a\" & df$X2 == \"a\",]$Y) # condition a,a\n", "shapiro.test(df[df$X1 == \"a\" & df$X2 == \"b\",]$Y) # condition a,b\n", "shapiro.test(df[df$X1 == \"b\" & df$X2 == \"a\",]$Y) # condition b,a\n", "shapiro.test(df[df$X1 == \"b\" & df$X2 == \"b\",]$Y) # condition b,b" ] }, { "cell_type": "markdown", "id": "992c4259-8eb6-4de4-8af0-cba968489c97", "metadata": { "tags": [] }, "source": [ "## Shapiro-Wilk Test (on residuals)\n", "\n", "* **Assumption:** Normality\n", "* **Context of Use:** t-test, ANOVA, LM, LMM\n", "* **Reporting:** \"To test the normality assumption, a Shapiro-Wilk test was run on the residuals of a between-subjects full-factorial ANOVA model. The test was statistically non-significant (W = .988, p = .798), indicating compliance with the normality assumption. A Q-Q plot of residuals visually confirms the same (Figure 1).\"" ] }, { "cell_type": "code", "execution_count": 3, "id": "eb5a37f5-4e5d-4a0b-8329-0a4ef8ec88f3", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
1 1aa11.867340
2 2ab15.453745
3 3ba15.782415
4 4bb13.626554
5 5aa11.608195
6 6ab19.540674
7 7ba15.878829
8 8bb16.654611
9 9aa17.370245
1010ab17.547025
1111ba19.423109
1212bb16.369147
1313aa22.896627
1414ab14.037504
1515ba15.564130
1616bb16.109281
1717aa 7.028036
1818ab21.508059
1919ba17.644257
2020bb16.054999
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 11.867340\\\\\n", "\t2 & 2 & a & b & 15.453745\\\\\n", "\t3 & 3 & b & a & 15.782415\\\\\n", "\t4 & 4 & b & b & 13.626554\\\\\n", "\t5 & 5 & a & a & 11.608195\\\\\n", "\t6 & 6 & a & b & 19.540674\\\\\n", "\t7 & 7 & b & a & 15.878829\\\\\n", "\t8 & 8 & b & b & 16.654611\\\\\n", "\t9 & 9 & a & a & 17.370245\\\\\n", "\t10 & 10 & a & b & 17.547025\\\\\n", "\t11 & 11 & b & a & 19.423109\\\\\n", "\t12 & 12 & b & b & 16.369147\\\\\n", "\t13 & 13 & a & a & 22.896627\\\\\n", "\t14 & 14 & a & b & 14.037504\\\\\n", "\t15 & 15 & b & a & 15.564130\\\\\n", "\t16 & 16 & b & b & 16.109281\\\\\n", "\t17 & 17 & a & a & 7.028036\\\\\n", "\t18 & 18 & a & b & 21.508059\\\\\n", "\t19 & 19 & b & a & 17.644257\\\\\n", "\t20 & 20 & b & b & 16.054999\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 11.867340 |\n", "| 2 | 2 | a | b | 15.453745 |\n", "| 3 | 3 | b | a | 15.782415 |\n", "| 4 | 4 | b | b | 13.626554 |\n", "| 5 | 5 | a | a | 11.608195 |\n", "| 6 | 6 | a | b | 19.540674 |\n", "| 7 | 7 | b | a | 15.878829 |\n", "| 8 | 8 | b | b | 16.654611 |\n", "| 9 | 9 | a | a | 17.370245 |\n", "| 10 | 10 | a | b | 17.547025 |\n", "| 11 | 11 | b | a | 19.423109 |\n", "| 12 | 12 | b | b | 16.369147 |\n", "| 13 | 13 | a | a | 22.896627 |\n", "| 14 | 14 | a | b | 14.037504 |\n", "| 15 | 15 | b | a | 15.564130 |\n", "| 16 | 16 | b | b | 16.109281 |\n", "| 17 | 17 | a | a | 7.028036 |\n", "| 18 | 18 | a | b | 21.508059 |\n", "| 19 | 19 | b | a | 17.644257 |\n", "| 20 | 20 | b | b | 16.054999 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 11.867340\n", "2 2 a b 15.453745\n", "3 3 b a 15.782415\n", "4 4 b b 13.626554\n", "5 5 a a 11.608195\n", "6 6 a b 19.540674\n", "7 7 b a 15.878829\n", "8 8 b b 16.654611\n", "9 9 a a 17.370245\n", "10 10 a b 17.547025\n", "11 11 b a 19.423109\n", "12 12 b b 16.369147\n", "13 13 a a 22.896627\n", "14 14 a b 14.037504\n", "15 15 b a 15.564130\n", "16 16 b b 16.109281\n", "17 17 a a 7.028036\n", "18 18 a b 21.508059\n", "19 19 b a 17.644257\n", "20 20 b b 16.054999" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has two factors (X1,X2) each w/two levels (a,b) and continuous response Y\n", "df <- read.csv(\"data/2F2LBs_normal.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 4, "id": "5876585b-9f87-40a6-a2ee-a17024729768", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: residuals(m)\n", "W = 0.98751, p-value = 0.7979\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = aov(Y ~ X1*X2, data=df) # make anova model\n", "shapiro.test(residuals(m))" ] }, { "cell_type": "code", "execution_count": 5, "id": "f8081020-c716-4bd5-b68b-4418556d46e0", "metadata": {}, "outputs": [ { "data": { "image/png": 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et2bVtaVzM0sR68/sZrpRUIAEB+ePr0qbGxcY6ZqWLFik+fPs11BjMzs/Dw8Bw3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\nHQAAgEZQ7AAAADSCYgcAAKAR/w8qBp0tMScwdAAAAABJRU5ErkJggg==", "text/plain": [ "Plot with title “Normal Q-Q Plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "par(mfrow=c(1,1))\n", "qqnorm(residuals(m)); qqline(residuals(m)) # Q-Q plot" ] }, { "cell_type": "markdown", "id": "f8947f04-9a46-4f61-9140-6c414ac4453d", "metadata": { "tags": [] }, "source": [ "## Anderson-Darling Test (on responses)\n", "\n", "* **Assumption:** Normality\n", "* **Context of Use:** t-test, ANOVA, LM, LMM\n", "* **Reporting:** \"To test the assumption of conditional normality, an Anderson-Darling test was run on the response Y for each combination of levels of factors X1 and X2. All combinations were found to be statistically non-significant except condition (b,b), which showed a statistically significant deviation from normality (A = 1.417, p < .001).\"" ] }, { "cell_type": "code", "execution_count": 6, "id": "c047138a-2e14-4abb-a726-2c3463621c02", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
1 1aa11.867340
2 2ab15.453745
3 3ba15.782415
4 4bb13.626554
5 5aa11.608195
6 6ab19.540674
7 7ba15.878829
8 8bb16.654611
9 9aa17.370245
1010ab17.547025
1111ba19.423109
1212bb16.369147
1313aa22.896627
1414ab14.037504
1515ba15.564130
1616bb16.109281
1717aa 7.028036
1818ab21.508059
1919ba17.644257
2020bb16.054999
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 11.867340\\\\\n", "\t2 & 2 & a & b & 15.453745\\\\\n", "\t3 & 3 & b & a & 15.782415\\\\\n", "\t4 & 4 & b & b & 13.626554\\\\\n", "\t5 & 5 & a & a & 11.608195\\\\\n", "\t6 & 6 & a & b & 19.540674\\\\\n", "\t7 & 7 & b & a & 15.878829\\\\\n", "\t8 & 8 & b & b & 16.654611\\\\\n", "\t9 & 9 & a & a & 17.370245\\\\\n", "\t10 & 10 & a & b & 17.547025\\\\\n", "\t11 & 11 & b & a & 19.423109\\\\\n", "\t12 & 12 & b & b & 16.369147\\\\\n", "\t13 & 13 & a & a & 22.896627\\\\\n", "\t14 & 14 & a & b & 14.037504\\\\\n", "\t15 & 15 & b & a & 15.564130\\\\\n", "\t16 & 16 & b & b & 16.109281\\\\\n", "\t17 & 17 & a & a & 7.028036\\\\\n", "\t18 & 18 & a & b & 21.508059\\\\\n", "\t19 & 19 & b & a & 17.644257\\\\\n", "\t20 & 20 & b & b & 16.054999\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 11.867340 |\n", "| 2 | 2 | a | b | 15.453745 |\n", "| 3 | 3 | b | a | 15.782415 |\n", "| 4 | 4 | b | b | 13.626554 |\n", "| 5 | 5 | a | a | 11.608195 |\n", "| 6 | 6 | a | b | 19.540674 |\n", "| 7 | 7 | b | a | 15.878829 |\n", "| 8 | 8 | b | b | 16.654611 |\n", "| 9 | 9 | a | a | 17.370245 |\n", "| 10 | 10 | a | b | 17.547025 |\n", "| 11 | 11 | b | a | 19.423109 |\n", "| 12 | 12 | b | b | 16.369147 |\n", "| 13 | 13 | a | a | 22.896627 |\n", "| 14 | 14 | a | b | 14.037504 |\n", "| 15 | 15 | b | a | 15.564130 |\n", "| 16 | 16 | b | b | 16.109281 |\n", "| 17 | 17 | a | a | 7.028036 |\n", "| 18 | 18 | a | b | 21.508059 |\n", "| 19 | 19 | b | a | 17.644257 |\n", "| 20 | 20 | b | b | 16.054999 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 11.867340\n", "2 2 a b 15.453745\n", "3 3 b a 15.782415\n", "4 4 b b 13.626554\n", "5 5 a a 11.608195\n", "6 6 a b 19.540674\n", "7 7 b a 15.878829\n", "8 8 b b 16.654611\n", "9 9 a a 17.370245\n", "10 10 a b 17.547025\n", "11 11 b a 19.423109\n", "12 12 b b 16.369147\n", "13 13 a a 22.896627\n", "14 14 a b 14.037504\n", "15 15 b a 15.564130\n", "16 16 b b 16.109281\n", "17 17 a a 7.028036\n", "18 18 a b 21.508059\n", "19 19 b a 17.644257\n", "20 20 b b 16.054999" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has two factors (X1,X2) each w/two levels (a,b) and continuous response Y\n", "df <- read.csv(\"data/2F2LBs_normal.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 9, "id": "236ede63-265a-4e12-94e8-2cd4a0279c98", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "\n", "\tAnderson-Darling normality test\n", "\n", "data: df[df$X1 == \"a\" & df$X2 == \"a\", ]$Y\n", "A = 0.23266, p-value = 0.7557\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tAnderson-Darling normality test\n", "\n", "data: df[df$X1 == \"a\" & df$X2 == \"b\", ]$Y\n", "A = 0.35901, p-value = 0.4023\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tAnderson-Darling normality test\n", "\n", "data: df[df$X1 == \"b\" & df$X2 == \"a\", ]$Y\n", "A = 0.16003, p-value = 0.934\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tAnderson-Darling normality test\n", "\n", "data: df[df$X1 == \"b\" & df$X2 == \"b\", ]$Y\n", "A = 1.4167, p-value = 0.0007191\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(nortest)\n", "ad.test(df[df$X1 == \"a\" & df$X2 == \"a\",]$Y) # condition a,a\n", "ad.test(df[df$X1 == \"a\" & df$X2 == \"b\",]$Y) # condition a,b\n", "ad.test(df[df$X1 == \"b\" & df$X2 == \"a\",]$Y) # condition b,a\n", "ad.test(df[df$X1 == \"b\" & df$X2 == \"b\",]$Y) # condition b,b" ] }, { "cell_type": "markdown", "id": "074c66d8-1472-47cc-b5c6-f5560544a344", "metadata": { "tags": [] }, "source": [ "## Anderson-Darling Test (on residuals)\n", "\n", "* **Assumption:** Normality\n", "* **Context of Use:** t-test, ANOVA, LM, LMM\n", "* **Reporting:** \"To test the normality assumption, an Anderson-Darling test was run on the residuals of a between-subjects full-factorial ANOVA model. The test was statistically non-significant (A = 0.329, p = .510), indicating compliance with the normality assumption. A Q-Q plot of residuals visually confirms the same (Figure 1).\"" ] }, { "cell_type": "code", "execution_count": 10, "id": "1009101b-af2e-4712-92d6-2a49fef88d68", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
1 1aa11.867340
2 2ab15.453745
3 3ba15.782415
4 4bb13.626554
5 5aa11.608195
6 6ab19.540674
7 7ba15.878829
8 8bb16.654611
9 9aa17.370245
1010ab17.547025
1111ba19.423109
1212bb16.369147
1313aa22.896627
1414ab14.037504
1515ba15.564130
1616bb16.109281
1717aa 7.028036
1818ab21.508059
1919ba17.644257
2020bb16.054999
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 11.867340\\\\\n", "\t2 & 2 & a & b & 15.453745\\\\\n", "\t3 & 3 & b & a & 15.782415\\\\\n", "\t4 & 4 & b & b & 13.626554\\\\\n", "\t5 & 5 & a & a & 11.608195\\\\\n", "\t6 & 6 & a & b & 19.540674\\\\\n", "\t7 & 7 & b & a & 15.878829\\\\\n", "\t8 & 8 & b & b & 16.654611\\\\\n", "\t9 & 9 & a & a & 17.370245\\\\\n", "\t10 & 10 & a & b & 17.547025\\\\\n", "\t11 & 11 & b & a & 19.423109\\\\\n", "\t12 & 12 & b & b & 16.369147\\\\\n", "\t13 & 13 & a & a & 22.896627\\\\\n", "\t14 & 14 & a & b & 14.037504\\\\\n", "\t15 & 15 & b & a & 15.564130\\\\\n", "\t16 & 16 & b & b & 16.109281\\\\\n", "\t17 & 17 & a & a & 7.028036\\\\\n", "\t18 & 18 & a & b & 21.508059\\\\\n", "\t19 & 19 & b & a & 17.644257\\\\\n", "\t20 & 20 & b & b & 16.054999\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 11.867340 |\n", "| 2 | 2 | a | b | 15.453745 |\n", "| 3 | 3 | b | a | 15.782415 |\n", "| 4 | 4 | b | b | 13.626554 |\n", "| 5 | 5 | a | a | 11.608195 |\n", "| 6 | 6 | a | b | 19.540674 |\n", "| 7 | 7 | b | a | 15.878829 |\n", "| 8 | 8 | b | b | 16.654611 |\n", "| 9 | 9 | a | a | 17.370245 |\n", "| 10 | 10 | a | b | 17.547025 |\n", "| 11 | 11 | b | a | 19.423109 |\n", "| 12 | 12 | b | b | 16.369147 |\n", "| 13 | 13 | a | a | 22.896627 |\n", "| 14 | 14 | a | b | 14.037504 |\n", "| 15 | 15 | b | a | 15.564130 |\n", "| 16 | 16 | b | b | 16.109281 |\n", "| 17 | 17 | a | a | 7.028036 |\n", "| 18 | 18 | a | b | 21.508059 |\n", "| 19 | 19 | b | a | 17.644257 |\n", "| 20 | 20 | b | b | 16.054999 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 11.867340\n", "2 2 a b 15.453745\n", "3 3 b a 15.782415\n", "4 4 b b 13.626554\n", "5 5 a a 11.608195\n", "6 6 a b 19.540674\n", "7 7 b a 15.878829\n", "8 8 b b 16.654611\n", "9 9 a a 17.370245\n", "10 10 a b 17.547025\n", "11 11 b a 19.423109\n", "12 12 b b 16.369147\n", "13 13 a a 22.896627\n", "14 14 a b 14.037504\n", "15 15 b a 15.564130\n", "16 16 b b 16.109281\n", "17 17 a a 7.028036\n", "18 18 a b 21.508059\n", "19 19 b a 17.644257\n", "20 20 b b 16.054999" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has two factors (X1,X2) each w/two levels (a,b) and continuous response Y\n", "df <- read.csv(\"data/2F2LBs_normal.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 11, "id": "b4f2658b-96b6-4ac4-b033-1689c9eb4b3c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tAnderson-Darling normality test\n", "\n", "data: residuals(m)\n", "A = 0.32859, p-value = 0.5102\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(nortest)\n", "m = aov(Y ~ X1*X2, data=df) # make anova model\n", "ad.test(residuals(m))" ] }, { "cell_type": "code", "execution_count": 12, "id": "02e7e704-2868-42c9-8cda-1603555e0dfb", "metadata": {}, "outputs": [ { "data": { "image/png": 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et2bVtaVzM0sR68/sZrpRUIAEB+ePr0qbGxcY6ZqWLFik+fPs11BjMzs/Dw8Bw3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\nqZPa6QAAgEZwxK6QhIaGHjt2zN/fPzY2NjY21t/f/9ixY6Gho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"text/plain": [ "Plot with title “Normal Q-Q Plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "par(mfrow=c(1,1))\n", "qqnorm(residuals(m)); qqline(residuals(m)) # Q-Q plot" ] }, { "cell_type": "markdown", "id": "9277a9d4-32e8-4bd9-a7e7-54f9011191ec", "metadata": { "tags": [] }, "source": [ "## Levene's Test\n", "\n", "* **Assumption:** Homoscedasticity (Homogeneity of Variance)\n", "* **Context of Use:** t-test, ANOVA, LM, LMM\n", "* **Reporting:** \"To test the homoscedasticity assumption, Levene’s test was run on a between-subjects full-factorial ANOVA model. The test was statistically significant (F(3, 56) = 3.97, p < .05), indicating a departure from homoscedasticity.\"" ] }, { "cell_type": "code", "execution_count": 13, "id": "c40b584c-acab-48a9-a4a2-5a57bb39e46f", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
1 1aa11.867340
2 2ab15.453745
3 3ba15.782415
4 4bb13.626554
5 5aa11.608195
6 6ab19.540674
7 7ba15.878829
8 8bb16.654611
9 9aa17.370245
1010ab17.547025
1111ba19.423109
1212bb16.369147
1313aa22.896627
1414ab14.037504
1515ba15.564130
1616bb16.109281
1717aa 7.028036
1818ab21.508059
1919ba17.644257
2020bb16.054999
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 11.867340\\\\\n", "\t2 & 2 & a & b & 15.453745\\\\\n", "\t3 & 3 & b & a & 15.782415\\\\\n", "\t4 & 4 & b & b & 13.626554\\\\\n", "\t5 & 5 & a & a & 11.608195\\\\\n", "\t6 & 6 & a & b & 19.540674\\\\\n", "\t7 & 7 & b & a & 15.878829\\\\\n", "\t8 & 8 & b & b & 16.654611\\\\\n", "\t9 & 9 & a & a & 17.370245\\\\\n", "\t10 & 10 & a & b & 17.547025\\\\\n", "\t11 & 11 & b & a & 19.423109\\\\\n", "\t12 & 12 & b & b & 16.369147\\\\\n", "\t13 & 13 & a & a & 22.896627\\\\\n", "\t14 & 14 & a & b & 14.037504\\\\\n", "\t15 & 15 & b & a & 15.564130\\\\\n", "\t16 & 16 & b & b & 16.109281\\\\\n", "\t17 & 17 & a & a & 7.028036\\\\\n", "\t18 & 18 & a & b & 21.508059\\\\\n", "\t19 & 19 & b & a & 17.644257\\\\\n", "\t20 & 20 & b & b & 16.054999\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 11.867340 |\n", "| 2 | 2 | a | b | 15.453745 |\n", "| 3 | 3 | b | a | 15.782415 |\n", "| 4 | 4 | b | b | 13.626554 |\n", "| 5 | 5 | a | a | 11.608195 |\n", "| 6 | 6 | a | b | 19.540674 |\n", "| 7 | 7 | b | a | 15.878829 |\n", "| 8 | 8 | b | b | 16.654611 |\n", "| 9 | 9 | a | a | 17.370245 |\n", "| 10 | 10 | a | b | 17.547025 |\n", "| 11 | 11 | b | a | 19.423109 |\n", "| 12 | 12 | b | b | 16.369147 |\n", "| 13 | 13 | a | a | 22.896627 |\n", "| 14 | 14 | a | b | 14.037504 |\n", "| 15 | 15 | b | a | 15.564130 |\n", "| 16 | 16 | b | b | 16.109281 |\n", "| 17 | 17 | a | a | 7.028036 |\n", "| 18 | 18 | a | b | 21.508059 |\n", "| 19 | 19 | b | a | 17.644257 |\n", "| 20 | 20 | b | b | 16.054999 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 11.867340\n", "2 2 a b 15.453745\n", "3 3 b a 15.782415\n", "4 4 b b 13.626554\n", "5 5 a a 11.608195\n", "6 6 a b 19.540674\n", "7 7 b a 15.878829\n", "8 8 b b 16.654611\n", "9 9 a a 17.370245\n", "10 10 a b 17.547025\n", "11 11 b a 19.423109\n", "12 12 b b 16.369147\n", "13 13 a a 22.896627\n", "14 14 a b 14.037504\n", "15 15 b a 15.564130\n", "16 16 b b 16.109281\n", "17 17 a a 7.028036\n", "18 18 a b 21.508059\n", "19 19 b a 17.644257\n", "20 20 b b 16.054999" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has two factors (X1,X2) each w/two levels (a,b) and continuous response Y\n", "df <- read.csv(\"data/2F2LBs_normal.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 14, "id": "01dd3f44-3fd1-4517-9b58-4d699851b5b5", "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Loading required package: carData\n", "\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A anova: 2 × 3
DfF valuePr(>F)
<int><dbl><dbl>
group 33.9651240.01238959
56 NA NA
\n" ], "text/latex": [ "A anova: 2 × 3\n", "\\begin{tabular}{r|lll}\n", " & Df & F value & Pr(>F)\\\\\n", " & & & \\\\\n", "\\hline\n", "\tgroup & 3 & 3.965124 & 0.01238959\\\\\n", "\t & 56 & NA & NA\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A anova: 2 × 3\n", "\n", "| | Df <int> | F value <dbl> | Pr(>F) <dbl> |\n", "|---|---|---|---|\n", "| group | 3 | 3.965124 | 0.01238959 |\n", "| | 56 | NA | NA |\n", "\n" ], "text/plain": [ " Df F value Pr(>F) \n", "group 3 3.965124 0.01238959\n", " 56 NA NA" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tWelch Two Sample t-test\n", "\n", "data: Y by X1\n", "t = 0.80702, df = 43.125, p-value = 0.4241\n", "alternative hypothesis: true difference in means between group a and group b is not equal to 0\n", "95 percent confidence interval:\n", " -1.188936 2.775540\n", "sample estimates:\n", "mean in group a mean in group b \n", " 15.56348 14.77018 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Coefficient covariances computed by hccm()\n", "\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A anova: 5 × 3
DfFPr(>F)
<dbl><dbl><dbl>
(Intercept) 1103.03498562.652463e-14
X1 1 0.41298625.230802e-01
X2 1 8.05918516.296776e-03
X1:X2 1 3.64413536.139637e-02
Residuals56 NA NA
\n" ], "text/latex": [ "A anova: 5 × 3\n", "\\begin{tabular}{r|lll}\n", " & Df & F & Pr(>F)\\\\\n", " & & & \\\\\n", "\\hline\n", "\t(Intercept) & 1 & 103.0349856 & 2.652463e-14\\\\\n", "\tX1 & 1 & 0.4129862 & 5.230802e-01\\\\\n", "\tX2 & 1 & 8.0591851 & 6.296776e-03\\\\\n", "\tX1:X2 & 1 & 3.6441353 & 6.139637e-02\\\\\n", "\tResiduals & 56 & NA & NA\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A anova: 5 × 3\n", "\n", "| | Df <dbl> | F <dbl> | Pr(>F) <dbl> |\n", "|---|---|---|---|\n", "| (Intercept) | 1 | 103.0349856 | 2.652463e-14 |\n", "| X1 | 1 | 0.4129862 | 5.230802e-01 |\n", "| X2 | 1 | 8.0591851 | 6.296776e-03 |\n", "| X1:X2 | 1 | 3.6441353 | 6.139637e-02 |\n", "| Residuals | 56 | NA | NA |\n", "\n" ], "text/plain": [ " Df F Pr(>F) \n", "(Intercept) 1 103.0349856 2.652463e-14\n", "X1 1 0.4129862 5.230802e-01\n", "X2 1 8.0591851 6.296776e-03\n", "X1:X2 1 3.6441353 6.139637e-02\n", "Residuals 56 NA NA" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(car) # for leveneTest and Anova\n", "leveneTest(Y ~ X1*X2, data=df, center=mean)\n", "# if a violation occurs and only a t-test is needed, use a Welch t-test\n", "t.test(Y ~ X1, data=df, var.equal=FALSE) # Welch t-test\n", "# if a violation occurs and an ANOVA is needed, use a White-adjusted ANOVA\n", "m = aov(Y ~ X1*X2, data=df)\n", "Anova(m, type=3, white.adjust=TRUE)" ] }, { "cell_type": "markdown", "id": "c2d8522a-6a1e-455e-bd34-1c840b35ae04", "metadata": { "tags": [] }, "source": [ "## Brown-Forsythe Test\n", "\n", "* **Assumption:** Homoscedasticity (Homogeneity of Variance)\n", "* **Context of Use:** t-test, ANOVA, LM, LMM\n", "* **Reporting:** \"To test the homoscedasticity assumption, the Brown-Forsythe test was run on a between-subjects full-factorial ANOVA model. The test was statistically significant (F(3, 56) = 3.75, p < .05), indicating a departure from homoscedasticity.\"" ] }, { "cell_type": "code", "execution_count": 15, "id": "70d3af27-f903-4ded-9c83-4ac05ed7a980", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
1 1aa11.867340
2 2ab15.453745
3 3ba15.782415
4 4bb13.626554
5 5aa11.608195
6 6ab19.540674
7 7ba15.878829
8 8bb16.654611
9 9aa17.370245
1010ab17.547025
1111ba19.423109
1212bb16.369147
1313aa22.896627
1414ab14.037504
1515ba15.564130
1616bb16.109281
1717aa 7.028036
1818ab21.508059
1919ba17.644257
2020bb16.054999
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 11.867340\\\\\n", "\t2 & 2 & a & b & 15.453745\\\\\n", "\t3 & 3 & b & a & 15.782415\\\\\n", "\t4 & 4 & b & b & 13.626554\\\\\n", "\t5 & 5 & a & a & 11.608195\\\\\n", "\t6 & 6 & a & b & 19.540674\\\\\n", "\t7 & 7 & b & a & 15.878829\\\\\n", "\t8 & 8 & b & b & 16.654611\\\\\n", "\t9 & 9 & a & a & 17.370245\\\\\n", "\t10 & 10 & a & b & 17.547025\\\\\n", "\t11 & 11 & b & a & 19.423109\\\\\n", "\t12 & 12 & b & b & 16.369147\\\\\n", "\t13 & 13 & a & a & 22.896627\\\\\n", "\t14 & 14 & a & b & 14.037504\\\\\n", "\t15 & 15 & b & a & 15.564130\\\\\n", "\t16 & 16 & b & b & 16.109281\\\\\n", "\t17 & 17 & a & a & 7.028036\\\\\n", "\t18 & 18 & a & b & 21.508059\\\\\n", "\t19 & 19 & b & a & 17.644257\\\\\n", "\t20 & 20 & b & b & 16.054999\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 11.867340 |\n", "| 2 | 2 | a | b | 15.453745 |\n", "| 3 | 3 | b | a | 15.782415 |\n", "| 4 | 4 | b | b | 13.626554 |\n", "| 5 | 5 | a | a | 11.608195 |\n", "| 6 | 6 | a | b | 19.540674 |\n", "| 7 | 7 | b | a | 15.878829 |\n", "| 8 | 8 | b | b | 16.654611 |\n", "| 9 | 9 | a | a | 17.370245 |\n", "| 10 | 10 | a | b | 17.547025 |\n", "| 11 | 11 | b | a | 19.423109 |\n", "| 12 | 12 | b | b | 16.369147 |\n", "| 13 | 13 | a | a | 22.896627 |\n", "| 14 | 14 | a | b | 14.037504 |\n", "| 15 | 15 | b | a | 15.564130 |\n", "| 16 | 16 | b | b | 16.109281 |\n", "| 17 | 17 | a | a | 7.028036 |\n", "| 18 | 18 | a | b | 21.508059 |\n", "| 19 | 19 | b | a | 17.644257 |\n", "| 20 | 20 | b | b | 16.054999 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 11.867340\n", "2 2 a b 15.453745\n", "3 3 b a 15.782415\n", "4 4 b b 13.626554\n", "5 5 a a 11.608195\n", "6 6 a b 19.540674\n", "7 7 b a 15.878829\n", "8 8 b b 16.654611\n", "9 9 a a 17.370245\n", "10 10 a b 17.547025\n", "11 11 b a 19.423109\n", "12 12 b b 16.369147\n", "13 13 a a 22.896627\n", "14 14 a b 14.037504\n", "15 15 b a 15.564130\n", "16 16 b b 16.109281\n", "17 17 a a 7.028036\n", "18 18 a b 21.508059\n", "19 19 b a 17.644257\n", "20 20 b b 16.054999" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has two factors (X1,X2) each w/two levels (a,b) and continuous response Y\n", "df <- read.csv(\"data/2F2LBs_normal.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 16, "id": "23adc841-c99a-41bb-bcea-131e7323e035", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A anova: 2 × 3
DfF valuePr(>F)
<int><dbl><dbl>
group 33.7502520.01587369
56 NA NA
\n" ], "text/latex": [ "A anova: 2 × 3\n", "\\begin{tabular}{r|lll}\n", " & Df & F value & Pr(>F)\\\\\n", " & & & \\\\\n", "\\hline\n", "\tgroup & 3 & 3.750252 & 0.01587369\\\\\n", "\t & 56 & NA & NA\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A anova: 2 × 3\n", "\n", "| | Df <int> | F value <dbl> | Pr(>F) <dbl> |\n", "|---|---|---|---|\n", "| group | 3 | 3.750252 | 0.01587369 |\n", "| | 56 | NA | NA |\n", "\n" ], "text/plain": [ " Df F value Pr(>F) \n", "group 3 3.750252 0.01587369\n", " 56 NA NA" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tWelch Two Sample t-test\n", "\n", "data: Y by X1\n", "t = 0.80702, df = 43.125, p-value = 0.4241\n", "alternative hypothesis: true difference in means between group a and group b is not equal to 0\n", "95 percent confidence interval:\n", " -1.188936 2.775540\n", "sample estimates:\n", "mean in group a mean in group b \n", " 15.56348 14.77018 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Coefficient covariances computed by hccm()\n", "\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A anova: 5 × 3
DfFPr(>F)
<dbl><dbl><dbl>
(Intercept) 1103.03498562.652463e-14
X1 1 0.41298625.230802e-01
X2 1 8.05918516.296776e-03
X1:X2 1 3.64413536.139637e-02
Residuals56 NA NA
\n" ], "text/latex": [ "A anova: 5 × 3\n", "\\begin{tabular}{r|lll}\n", " & Df & F & Pr(>F)\\\\\n", " & & & \\\\\n", "\\hline\n", "\t(Intercept) & 1 & 103.0349856 & 2.652463e-14\\\\\n", "\tX1 & 1 & 0.4129862 & 5.230802e-01\\\\\n", "\tX2 & 1 & 8.0591851 & 6.296776e-03\\\\\n", "\tX1:X2 & 1 & 3.6441353 & 6.139637e-02\\\\\n", "\tResiduals & 56 & NA & NA\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A anova: 5 × 3\n", "\n", "| | Df <dbl> | F <dbl> | Pr(>F) <dbl> |\n", "|---|---|---|---|\n", "| (Intercept) | 1 | 103.0349856 | 2.652463e-14 |\n", "| X1 | 1 | 0.4129862 | 5.230802e-01 |\n", "| X2 | 1 | 8.0591851 | 6.296776e-03 |\n", "| X1:X2 | 1 | 3.6441353 | 6.139637e-02 |\n", "| Residuals | 56 | NA | NA |\n", "\n" ], "text/plain": [ " Df F Pr(>F) \n", "(Intercept) 1 103.0349856 2.652463e-14\n", "X1 1 0.4129862 5.230802e-01\n", "X2 1 8.0591851 6.296776e-03\n", "X1:X2 1 3.6441353 6.139637e-02\n", "Residuals 56 NA NA" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(car) # for leveneTest, Anova\n", "leveneTest(Y ~ X1*X2, data=df, center=median)\n", "# if a violation occurs and only a t-test is needed, use a Welch t-test\n", "t.test(Y ~ X1, data=df, var.equal=FALSE) # Welch t-test\n", "# if a violation occurs and an ANOVA is needed, use a White-adjusted ANOVA\n", "m = aov(Y ~ X1*X2, data=df)\n", "Anova(m, type=3, white.adjust=TRUE)" ] }, { "cell_type": "markdown", "id": "5c007c1f-7299-47a1-8ca1-a7108fd64c01", "metadata": { "tags": [] }, "source": [ "## Mauchly's Test of Sphericity\n", "\n", "* **Assumption:** Sphericity\n", "* **Context of Use:** repeated measures ANOVA\n", "* **Reporting:** \"To test the sphericity assumption for repeated measures ANOVA, Mauchly’s test of sphericity was run on a mixed factorial ANOVA model with a between-subjects factor X1 and a within-subjects factor X2. The test was statistically significant for both X2 (W = .637, p < .01) and X1×X2 (W = .637, p < .01), indicating sphericity violations. Accordingly, the Greenhouse-Geisser correction was used when reporting these ANOVA results.\"" ] }, { "cell_type": "code", "execution_count": 17, "id": "14ce354c-76c9-4478-8ea3-9029293290ea", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 20 × 4
SX1X2Y
<int><chr><chr><dbl>
11aa20.2145
21ab23.7485
31ac20.7960
42aa20.8805
52ab23.2595
62ac19.1305
73aa21.2635
83ab23.4945
93ac20.8545
104aa20.7080
114ab23.9220
124ac18.2575
135aa21.0075
145ab23.4700
155ac17.7105
166aa19.9115
176ab24.2975
186ac19.8550
197aa22.1050
207ab25.3800
\n" ], "text/latex": [ "A data.frame: 20 × 4\n", "\\begin{tabular}{r|llll}\n", " & S & X1 & X2 & Y\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & a & a & 20.2145\\\\\n", "\t2 & 1 & a & b & 23.7485\\\\\n", "\t3 & 1 & a & c & 20.7960\\\\\n", "\t4 & 2 & a & a & 20.8805\\\\\n", "\t5 & 2 & a & b & 23.2595\\\\\n", "\t6 & 2 & a & c & 19.1305\\\\\n", "\t7 & 3 & a & a & 21.2635\\\\\n", "\t8 & 3 & a & b & 23.4945\\\\\n", "\t9 & 3 & a & c & 20.8545\\\\\n", "\t10 & 4 & a & a & 20.7080\\\\\n", "\t11 & 4 & a & b & 23.9220\\\\\n", "\t12 & 4 & a & c & 18.2575\\\\\n", "\t13 & 5 & a & a & 21.0075\\\\\n", "\t14 & 5 & a & b & 23.4700\\\\\n", "\t15 & 5 & a & c & 17.7105\\\\\n", "\t16 & 6 & a & a & 19.9115\\\\\n", "\t17 & 6 & a & b & 24.2975\\\\\n", "\t18 & 6 & a & c & 19.8550\\\\\n", "\t19 & 7 & a & a & 22.1050\\\\\n", "\t20 & 7 & a & b & 25.3800\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 20 × 4\n", "\n", "| | S <int> | X1 <chr> | X2 <chr> | Y <dbl> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | a | a | 20.2145 |\n", "| 2 | 1 | a | b | 23.7485 |\n", "| 3 | 1 | a | c | 20.7960 |\n", "| 4 | 2 | a | a | 20.8805 |\n", "| 5 | 2 | a | b | 23.2595 |\n", "| 6 | 2 | a | c | 19.1305 |\n", "| 7 | 3 | a | a | 21.2635 |\n", "| 8 | 3 | a | b | 23.4945 |\n", "| 9 | 3 | a | c | 20.8545 |\n", "| 10 | 4 | a | a | 20.7080 |\n", "| 11 | 4 | a | b | 23.9220 |\n", "| 12 | 4 | a | c | 18.2575 |\n", "| 13 | 5 | a | a | 21.0075 |\n", "| 14 | 5 | a | b | 23.4700 |\n", "| 15 | 5 | a | c | 17.7105 |\n", "| 16 | 6 | a | a | 19.9115 |\n", "| 17 | 6 | a | b | 24.2975 |\n", "| 18 | 6 | a | c | 19.8550 |\n", "| 19 | 7 | a | a | 22.1050 |\n", "| 20 | 7 | a | b | 25.3800 |\n", "\n" ], "text/plain": [ " S X1 X2 Y \n", "1 1 a a 20.2145\n", "2 1 a b 23.7485\n", "3 1 a c 20.7960\n", "4 2 a a 20.8805\n", "5 2 a b 23.2595\n", "6 2 a c 19.1305\n", "7 3 a a 21.2635\n", "8 3 a b 23.4945\n", "9 3 a c 20.8545\n", "10 4 a a 20.7080\n", "11 4 a b 23.9220\n", "12 4 a c 18.2575\n", "13 5 a a 21.0075\n", "14 5 a b 23.4700\n", "15 5 a c 17.7105\n", "16 6 a a 19.9115\n", "17 6 a b 24.2975\n", "18 6 a c 19.8550\n", "19 7 a a 22.1050\n", "20 7 a b 25.3800" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Example data\n", "# df has subjects (S), one between-Ss factor (X1), and one within-Ss factor (X2)\n", "df <- read.csv(\"data/2F23LMs_mauchly.csv\")\n", "head(df, 20)" ] }, { "cell_type": "code", "execution_count": 21, "id": "a35b810c-a8ba-469e-aea2-62a04f5de213", "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Converting \"X2\" to factor for ANOVA.”\n", "Warning message:\n", "“Converting \"X1\" to factor for ANOVA.”\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A data.frame: 2 × 4
EffectWpp<.05
<chr><dbl><dbl><chr>
3X2 0.63702360.008782794*
4X1:X20.63702360.008782794*
\n" ], "text/latex": [ "A data.frame: 2 × 4\n", "\\begin{tabular}{r|llll}\n", " & Effect & W & p & p<.05\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t3 & X2 & 0.6370236 & 0.008782794 & *\\\\\n", "\t4 & X1:X2 & 0.6370236 & 0.008782794 & *\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 2 × 4\n", "\n", "| | Effect <chr> | W <dbl> | p <dbl> | p<.05 <chr> |\n", "|---|---|---|---|---|\n", "| 3 | X2 | 0.6370236 | 0.008782794 | * |\n", "| 4 | X1:X2 | 0.6370236 | 0.008782794 | * |\n", "\n" ], "text/plain": [ " Effect W p p<.05\n", "3 X2 0.6370236 0.008782794 * \n", "4 X1:X2 0.6370236 0.008782794 * " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(ez) # for ezANOVA\n", "df <- read.csv(\"data/2F23LMs_mauchly.csv\")\n", "df$S = factor(df$S) # Subject id is nominal\n", "m = ezANOVA(dv=Y, between=c(X1), within=c(X2), wid=S, type=3, data=df) # use c() for >1 factors\n", "m$Mauchly # p<.05 indicates a sphericity violation for within-Ss effects" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.2.2" } }, "nbformat": 4, "nbformat_minor": 5 }