Dear All,
I have a problem in understanding how the interactions of 2 ways ANOVA work,
because I get conflicting results
from a t-test and an anova. For most of you my problem is very simple I am sure.
I need an help with an example, looking at one table I am analyzing. The table
is in attachment
and can be imported in R by means of this command:
scrd<-
read.table('/Users/luca/Documents/Analisi_passi/Codice_R/Statistics_results_bump_hole_Audio_Haptic/tables_for_R/table_realism_wood.txt',
header=TRUE, colClasse=c('numeric','factor','factor','numeric'))
This table is the result of a simple experiment. Subjects where exposed to some
stimuli and they where asked to evaluate the degree of realism
of the stimuli on a 7 point scale (i.e., data in column "response").
Each stimulus was presented in two conditions, "A" and "AH", where AH is the
condition A plus another thing (let´s call it "H").
Now, what means exactly in my table the interaction stimulus:condition?
I think that if I do the analysis anova(response ~ stimulus*condition) I will
get the comparison between
the same stimulus in condition A and in condition AH. Am I wrong?
For instance the comparison of stimulus flat_550_W_realism presented in
condition A with the same stimulus, flat_550_W_realism,
presented in condition AH.
The problem is that if I do a t-test between the values of this stimulus in the
A and AH condition I get significative difference,
while if I do the test with 2-ways ANOVA I don´t get any difference.
How is this possible?
Here I put the results analysis
#Here the result of ANOVA:
> fit1<- lm(response ~ stimulus + condition + stimulus:condition, data=scrd)
>#EQUIVALE A lm(response ~ stimulus*condition, data=scrd)
>
> anova(fit1)
Analysis of Variance Table
Response: response
Df Sum Sq Mean Sq F value Pr(>F)
stimulus 6 15.05 2.509 1.1000 0.3647
condition 1 36.51 36.515 16.0089 9.64e-05 ***
stimulus:condition 6 1.47 0.244 0.1071 0.9955
Residuals 159 362.67 2.281
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#As you can see the p-value for stimulus:condition is high.
#Now I do the t-test with the same values of the table concerning the stimulus
presented in A and AH conditions:
flat_550_W_realism =c(3,3,5,3,3,3,3,5,3,3,5,7,5,2,3)
flat_550_W_realism_AH =c(7,4,5,3,6,5,3,5,5,7,2,7,5, 5)
> t.test(flat_550_W_realism,flat_550_W_realism_AH, var.equal=TRUE)
Two Sample t-test
data: flat_550_W_realism and flat_550_W_realism_AH
t = -2.2361, df = 27, p-value = 0.03381
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.29198603 -0.09849016
sample estimates:
mean of x mean of y
3.733333 4.928571
#Now we have a significative difference between these two stimuli (p-value =
0.03381)
Why I get this beheaviour?
Moreover, how by means of ANOVA I could track the significative differences
between the stimuli presented in A and AH condition
whitout doing the t-test?
Please help!
Thanks in advance
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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