[R] Problem with 2-ways ANOVA interactions
frodo.jedi at yahoo.com
Thu Jan 6 00:10:24 CET 2011
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:
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)
Analysis of Variance Table
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_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:
mean of x mean of y
#Now we have a significative difference between these two stimuli (p-value =
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?
Thanks in advance
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