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Assumptions for ANOVA: the right way to check the normality

Robert Baer

Wed, Jan 5, 2011 11:56 AM

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)

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



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Thread (13 messages)

Frodo Jedi Assumptions for ANOVA: the right way to check the normality Jan 5 Robert Baer Assumptions for ANOVA: the right way to check the normality Jan 5 Frodo Jedi Assumptions for ANOVA: the right way to check the normality Jan 5 Greg Snow Assumptions for ANOVA: the right way to check the normality Jan 6 Frodo Jedi Assumptions for ANOVA: the right way to check the normality Jan 6 Greg Snow Assumptions for ANOVA: the right way to check the normality Jan 6 Frodo Jedi Assumptions for ANOVA: the right way to check the normality Jan 6 Ben Ward Assumptions for ANOVA: the right way to check the normality Jan 6 Greg Snow Assumptions for ANOVA: the right way to check the normality Jan 7 Ben Ward Assumptions for ANOVA: the right way to check the normality Jan 7 Frodo Jedi Assumptions for ANOVA: the right way to check the normality Jan 8 Greg Snow Assumptions for ANOVA: the right way to check the normality Jan 10 Mike Marchywka Assumptions for ANOVA: the right way to check the normality Jan 10