Re: T test

RAMS said:

***I did a t test to compare whether there is any significant difference between two treatments or not? The SPSS output says that there is a difference between the two treatments. But when i go for the 95% confidence interval for the two treatments individually was concluded that there is no significant difference. Because the two confidence intervals are overlapping. How it works? Below that i have attached my SPSS outputs. Any one please help me. Group Statistics
Treatment N Mean Std. Deviation Std. Error Mean
A 5 -2.1642 1.13053 0.50559
B 5 -0.5384 0.96450 0.43134
the variance of the two treatments are tested by Levenes test and that gives there is no significant difference between the variance of the two treatments. the t value =-2.446
p value=0.040
mean difference=-1.6258
standard error of difference=0.66458 ***

My response

The critical t is +-2.306 therefore the means ARE significantly different.
__Simulation experiment with normal samples______
I made 20´000 (3 times) simulations of:
___X=N(-2.1642, 1.13053):5
___Y=N(-0.5384, 0.95450):5
And counted the frequency of overlapping
I found 7.9%, 8.3% and 8.1%.......mean= 8.1%
The answer to the question:
__Can, for the posted data, a significant difference on the two means and overlapping individual intervals coexist? Is YES, but is unlike for normal data.______

Note
When we perform a t test we suppose normality (or at least that this condition is not strongly violated).
But if this is not the case what happens?
Simply the distribution of each individual mean does not FOLLOW the Student´s t Distribution and *overlapping* could be more frequent than 8.1%.

RAMS
Wish you to post the sample data ( 5 values of X , 5 of Y) in order that I could perform a more accurate treatment?

__________licas (Luis A. Afonso)
.

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