Dear Robert,
thanks so much!!! Now I understand!
So you also think that I have to check only the residuals and not the data
directly.
Now just for curiosity I did the the shapiro test on the residuals. The problem
is that on fit3 I don´t get from the test
that the data are normally distribuited. Why? Here the data:
> shapiro.test(residuals(fit1))
Shapiro-Wilk normality test
data: residuals(fit1)
W = 0.9848, p-value = 0.05693
#Here the test is ok: the test says that the data are distributed normally
(p-value greather than 0.05)
> shapiro.test(residuals(fit2))
Shapiro-Wilk normality test
data: residuals(fit2)
W = 0.9853, p-value = 0.06525
#Here the test is ok: the test says that the data are distributed normally
(p-value greather than 0.05)
> shapiro.test(residuals(fit3))
Shapiro-Wilk normality test
data: residuals(fit3)
W = 0.9621, p-value = 0.0001206
Now the test reveals p-value lower than 0.05: so the residuals for fit3 are not
distributed normally....
Why I get this beheaviour? Indeed in the histogram and Q-Q plot for fit3
residuals I get a normal distribution.
________________________________
From: Robert Baer <rb...@atsu.edu>
Sent: Wed, January 5, 2011 8:56:50 PM
Subject: Re: [R] Assumptions for ANOVA: the right way to check the normality
> 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:
# using your scrd data and your proposed models
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
> and not the ANOVA...so please help
> 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
>
>
>
>
> Thanks in advance
>
>
>
> [[alternative HTML version deleted]]
>
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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>
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