# [R] Assumptions for ANOVA: the right way to check the normality

Robert Baer rbaer at atsu.edu
Wed Jan 5 20:56:50 CET 2011

```> Someone suggested me that I don´t have to check the normality of the
> data, but
> the normality of the residuals I get after the fitting of the  linear
> model.
> I really ask you to help me to understand this point as I don´t find
> enough
> material online where to solve it.

Try the following:
fit1<- lm(response ~ stimulus + condition + stimulus:condition, data=scrd)
fit2<- lm(response ~ stimulus + condition, data=scrd)
fit3<- lm(response ~ condition, data=scrd)

# Set up for 6 plots on 1 panel
op = par(mfrow=c(2,3))

# residuals function extracts residuals
# Visual inspection is a good start for checking normality
# You get a much better feel than from some "magic number" statistic
hist(residuals(fit1))
hist(residuals(fit2))
hist(residuals(fit3))

# especially qqnorm() plots which are linear for normal data
qqnorm(residuals(fit1))
qqnorm(residuals(fit2))
qqnorm(residuals(fit3))

# Restore plot parameters
par(op)

>
> If the data are not normally distributed I have to use the kruskal wallys
> test
> me to understand.

Indeed - Kruskal-Wallis is a good test to use for one factor data that is
ordinal so it is a good alternative to your fit3.
Your "response" seems to be a discrete variable rather than a continuous
variable.
You must decide if it is reasonable to approximate it with a normal
distribution which is by definition continuous.

>
> I make a numerical example, could you please tell me if the data in this
> table
> are normally distributed or not?
>
> Help!
>
>
> number                  stimulus condition response
> 1             flat_550_W_realism         A        3
> 2             flat_550_W_realism         A        3
> 3             flat_550_W_realism         A        5
> 4             flat_550_W_realism         A        3
> 5             flat_550_W_realism         A        3
> 6             flat_550_W_realism         A        3
> 7             flat_550_W_realism         A        3
> 8             flat_550_W_realism         A        5
> 9             flat_550_W_realism         A        3
> 10            flat_550_W_realism         A        3
> 11            flat_550_W_realism         A        5
> 12            flat_550_W_realism         A        7
> 13            flat_550_W_realism         A        5
> 14            flat_550_W_realism         A        2
> 15            flat_550_W_realism         A        3
> 16            flat_550_W_realism        AH        7
> 17            flat_550_W_realism        AH        4
> 18            flat_550_W_realism        AH        5
> 19            flat_550_W_realism        AH        3
> 20            flat_550_W_realism        AH        6
> 21            flat_550_W_realism        AH        5
> 22            flat_550_W_realism        AH        3
> 23            flat_550_W_realism        AH        5
> 24            flat_550_W_realism        AH        5
> 25            flat_550_W_realism        AH        7
> 26            flat_550_W_realism        AH        2
> 27            flat_550_W_realism        AH        7
> 28            flat_550_W_realism        AH        5
> 29            flat_550_W_realism        AH        5
> 30         bump_2_step_W_realism         A        1
> 31         bump_2_step_W_realism         A        3
> 32         bump_2_step_W_realism         A        5
> 33         bump_2_step_W_realism         A        1
> 34         bump_2_step_W_realism         A        3
> 35         bump_2_step_W_realism         A        2
> 36         bump_2_step_W_realism         A        5
> 37         bump_2_step_W_realism         A        4
> 38         bump_2_step_W_realism         A        4
> 39         bump_2_step_W_realism         A        4
> 40         bump_2_step_W_realism         A        4
> 41         bump_2_step_W_realism        AH        3
> 42         bump_2_step_W_realism        AH        5
> 43         bump_2_step_W_realism        AH        1
> 44         bump_2_step_W_realism        AH        5
> 45         bump_2_step_W_realism        AH        4
> 46         bump_2_step_W_realism        AH        4
> 47         bump_2_step_W_realism        AH        5
> 48         bump_2_step_W_realism        AH        4
> 49         bump_2_step_W_realism        AH        3
> 50         bump_2_step_W_realism        AH        4
> 51         bump_2_step_W_realism        AH        5
> 52         bump_2_step_W_realism        AH        4
> 53         hole_2_step_W_realism         A        3
> 54         hole_2_step_W_realism         A        3
> 55         hole_2_step_W_realism         A        4
> 56         hole_2_step_W_realism         A        1
> 57         hole_2_step_W_realism         A        4
> 58         hole_2_step_W_realism         A        3
> 59         hole_2_step_W_realism         A        5
> 60         hole_2_step_W_realism         A        4
> 61         hole_2_step_W_realism         A        3
> 62         hole_2_step_W_realism         A        4
> 63         hole_2_step_W_realism         A        7
> 64         hole_2_step_W_realism         A        5
> 65         hole_2_step_W_realism         A        1
> 66         hole_2_step_W_realism         A        4
> 67         hole_2_step_W_realism        AH        7
> 68         hole_2_step_W_realism        AH        5
> 69         hole_2_step_W_realism        AH        5
> 70         hole_2_step_W_realism        AH        1
> 71         hole_2_step_W_realism        AH        5
> 72         hole_2_step_W_realism        AH        5
> 73         hole_2_step_W_realism        AH        5
> 74         hole_2_step_W_realism        AH        2
> 75         hole_2_step_W_realism        AH        6
> 76         hole_2_step_W_realism        AH        5
> 77         hole_2_step_W_realism        AH        5
> 78         hole_2_step_W_realism        AH        6
> 79     bump_2_heel_toe_W_realism         A        3
> 80     bump_2_heel_toe_W_realism         A        3
> 81     bump_2_heel_toe_W_realism         A        3
> 82     bump_2_heel_toe_W_realism         A        2
> 83     bump_2_heel_toe_W_realism         A        3
> 84     bump_2_heel_toe_W_realism         A        3
> 85     bump_2_heel_toe_W_realism         A        4
> 86     bump_2_heel_toe_W_realism         A        3
> 87     bump_2_heel_toe_W_realism         A        4
> 88     bump_2_heel_toe_W_realism         A        4
> 89     bump_2_heel_toe_W_realism         A        6
> 90     bump_2_heel_toe_W_realism         A        5
> 91     bump_2_heel_toe_W_realism         A        4
> 92     bump_2_heel_toe_W_realism        AH        7
> 93     bump_2_heel_toe_W_realism        AH        3
> 94     bump_2_heel_toe_W_realism        AH        4
> 95     bump_2_heel_toe_W_realism        AH        2
> 96     bump_2_heel_toe_W_realism        AH        5
> 97     bump_2_heel_toe_W_realism        AH        6
> 98     bump_2_heel_toe_W_realism        AH        4
> 99     bump_2_heel_toe_W_realism        AH        4
> 100    bump_2_heel_toe_W_realism        AH        4
> 101    bump_2_heel_toe_W_realism        AH        5
> 102    bump_2_heel_toe_W_realism        AH        2
> 103    bump_2_heel_toe_W_realism        AH        6
> 104    bump_2_heel_toe_W_realism        AH        5
> 105    hole_2_heel_toe_W_realism         A        3
> 106    hole_2_heel_toe_W_realism         A        3
> 107    hole_2_heel_toe_W_realism         A        1
> 108    hole_2_heel_toe_W_realism         A        3
> 109    hole_2_heel_toe_W_realism         A        3
> 110    hole_2_heel_toe_W_realism         A        5
> 111    hole_2_heel_toe_W_realism         A        2
> 112    hole_2_heel_toe_W_realism        AH        5
> 113    hole_2_heel_toe_W_realism        AH        1
> 114    hole_2_heel_toe_W_realism        AH        3
> 115    hole_2_heel_toe_W_realism        AH        6
> 116    hole_2_heel_toe_W_realism        AH        5
> 117    hole_2_heel_toe_W_realism        AH        4
> 118    hole_2_heel_toe_W_realism        AH        4
> 119    hole_2_heel_toe_W_realism        AH        3
> 120    hole_2_heel_toe_W_realism        AH        3
> 121    hole_2_heel_toe_W_realism        AH        1
> 122    hole_2_heel_toe_W_realism        AH        5
> 123 bump_2_combination_W_realism         A        4
> 124 bump_2_combination_W_realism         A        2
> 125 bump_2_combination_W_realism         A        4
> 126 bump_2_combination_W_realism         A        1
> 127 bump_2_combination_W_realism         A        4
> 128 bump_2_combination_W_realism         A        4
> 129 bump_2_combination_W_realism         A        2
> 130 bump_2_combination_W_realism         A        4
> 131 bump_2_combination_W_realism         A        2
> 132 bump_2_combination_W_realism         A        4
> 133 bump_2_combination_W_realism         A        2
> 134 bump_2_combination_W_realism         A        6
> 135 bump_2_combination_W_realism        AH        7
> 136 bump_2_combination_W_realism        AH        3
> 137 bump_2_combination_W_realism        AH        4
> 138 bump_2_combination_W_realism        AH        1
> 139 bump_2_combination_W_realism        AH        6
> 140 bump_2_combination_W_realism        AH        5
> 141 bump_2_combination_W_realism        AH        5
> 142 bump_2_combination_W_realism        AH        6
> 143 bump_2_combination_W_realism        AH        5
> 144 bump_2_combination_W_realism        AH        4
> 145 bump_2_combination_W_realism        AH        2
> 146 bump_2_combination_W_realism        AH        4
> 147 bump_2_combination_W_realism        AH        2
> 148 bump_2_combination_W_realism        AH        5
> 149 hole_2_combination_W_realism         A        5
> 150 hole_2_combination_W_realism         A        2
> 151 hole_2_combination_W_realism         A        4
> 152 hole_2_combination_W_realism         A        1
> 153 hole_2_combination_W_realism         A        5
> 154 hole_2_combination_W_realism         A        4
> 155 hole_2_combination_W_realism         A        3
> 156 hole_2_combination_W_realism         A        5
> 157 hole_2_combination_W_realism         A        2
> 158 hole_2_combination_W_realism         A        5
> 159 hole_2_combination_W_realism         A        5
> 160 hole_2_combination_W_realism         A        1
> 161 hole_2_combination_W_realism        AH        7
> 162 hole_2_combination_W_realism        AH        5
> 163 hole_2_combination_W_realism        AH        3
> 164 hole_2_combination_W_realism        AH        1
> 165 hole_2_combination_W_realism        AH        6
> 166 hole_2_combination_W_realism        AH        4
> 167 hole_2_combination_W_realism        AH        7
> 168 hole_2_combination_W_realism        AH        5
> 169 hole_2_combination_W_realism        AH        5
> 170 hole_2_combination_W_realism        AH        2
> 171 hole_2_combination_W_realism        AH        6
> 172 hole_2_combination_W_realism        AH        2
> 173 hole_2_combination_W_realism        AH        4
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