Dear all,
I need an help because I don´t know how to perform the analysis in the right
way, as I get different beheaviors using t-test and two ways ANOVA.
In what follow I post the table, my goal and the strange results I got.
I kindly ask you an help because I really don´t know how to solve this problem.
So the table is this:
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
My goal is to understand if condition AH is better than condition A (i.e. if
there is statistical significance between the evaluation of stimuli presented
in condition A and AH).
The same stimuli have been presented to subjects in two conditions: A and AH,
where AH is the condition A plus something elese (let´s call it "H"). I want
to know if adding "H" bring to better results in the participants evaluations
of the stimuli rather than the stimulus presented only with condition "A".
(Data in column "response" are evaluation on realism of the stimulus from a 7
point scale.)
Here my analysis:
I did a t-test between the same stimulus in condition A and in condition AH,
and the result is that there is significant difference.
Instead in the 2 ways anova we see that there is no significant difference in
the interaction stimulus:condition.
Why this happen? Where is the error?
I report the data and the analysis so you can see:
1) t-test:
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)
#First I check homeschedaicity:
> var.test(flat_550_W_realism,flat_550_W_realism_AH)
F test to compare two variances
data: flat_550_W_realism and flat_550_W_realism_AH
F = 0.7486, num df = 14, denom df = 13, p-value = 0.597
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.2428979 2.2546308
sample estimates:
ratio of variances
0.7485758
p-value greather than 0.05 so in the t-test I put the option var.equal=TRUE:
> 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)
2) Now I put the results of the ANOVA (2 ways):
fit1<- lm(response ~ stimulus + condition + stimulus:condition, data=scrd)
#model with interaction
> summary(fit1)
Call:
lm(formula = response ~ stimulus + condition + stimulus:condition,
data = scrd)
Residuals:
Min 1Q Median 3Q Max
-3.7500 -0.7333 0.1429 1.0714 3.3571
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.25000 0.43598 7.455 5.47e-12 ***
stimulusbump_2_heel_toe_W_realism 0.36538 0.60459 0.604 0.546
stimulusbump_2_step_W_realism 0.02273 0.63042 0.036 0.971
stimulusflat_550_W_realism 0.48333 0.58492 0.826 0.410
stimulushole_2_combination_W_realism 0.25000 0.61656 0.405 0.686
stimulushole_2_heel_toe_W_realism -0.39286 0.71828 -0.547 0.585
stimulushole_2_step_W_realism 0.39286 0.59414 0.661 0.509
conditionAH 0.96429 0.59414 1.623 0.107
stimulusbump_2_heel_toe_W_realism:conditionAH -0.19505 0.83899 -0.232 0.816
stimulusbump_2_step_W_realism:conditionAH -0.32035 0.86627 -0.370 0.712
stimulusflat_550_W_realism:conditionAH 0.23095 0.81730 0.283 0.778
stimulushole_2_combination_W_realism:conditionAH -0.07967 0.84766 -0.094 0.925
stimulushole_2_heel_toe_W_realism:conditionAH -0.18506 0.94138 -0.197 0.844
stimulushole_2_step_W_realism:conditionAH 0.14286 0.84024 0.170 0.865
---
Signif. codes: 0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â
1
Residual standard error: 1.51 on 159 degrees of freedom
Multiple R-squared: 0.1276, Adjusted R-squared: 0.05625
F-statistic: 1.789 on 13 and 159 DF, p-value: 0.04895
> anova(fit1, test='Chisq') #show factors with significance tests
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 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â
1
Here you can notice that the pvalue for stimulus:condition (and therefore
also for the stimulus flat_550_W_realism in the 2 conditions A and AH) is
0.9955,
so this time the difference is not significative.
Now, could someone explain me this beheaviour? I really do not understand. Do I
have to believe to
ANOVA or to t-test? Help!!!
Which kind of analysis can I do?..and how can I interpret the results in the
right way?
Is there anyone that can show me how to conduct the analysis with R?
Thanks in advance
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