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Significant Difference Test on Attribute Importance

Hi,

I am doing a CBC study to run market simulator with two sub-groups(male vs female: 100 vs 100 in sample size).

Now I want to understand there is a significant difference between each of attribute within male and female.

I read the previous post: https://www.sawtoothsoftware.com/education/ss/ss20.shtml#ss20sig indicated that the way to ths is "Compute a t-statistic by dividing the mean difference by the standard error of the differences".

What I am not sure is how to get the standard error from SMRT, I got the below share of performance score by "Run Manager" -> "Export". Is there any where I can find the Std Error value to apply on this? Or is there way to calculate according these?

Importance    Attribute 1    Attribute 2    Attribute 3    Attribute 4    Attribute 5    Attribute 6    Attribute 7
ALL    0.27000     0.08005     0.11192     0.10073     0.08067     0.12047     0.23616
Male    0.24574     0.09314     0.11377     0.09034     0.07782     0.13307     0.24612
Female    0.27839     0.06333     0.10310     0.10542     0.10480     0.10525     0.23971
asked Feb 20, 2013 by Leen (285 points)
retagged Feb 20, 2013 by Walter Williams

1 Answer

+1 vote
My understanding is that you wish to do a between-groups t-test to test for significant difference of an attribute importance for male vs. female.

First, compute means and standard deviations for the attribute in question for Males and Females.

Mean of course is computed in Excel as =Mean(), where you put the range of the cells containing the importance scores (for a single attribute) within the parentheses.

Standard deviation is computed in Excel as =Stdev(), where you put the range of the cells containing the importance scores (for a single attribute) within the parentheses.

Now, you have:
X_bar_Male (mean of males for the attribute)
X_bar_Female (mean of females for the attribute)
Stdev_Male (standard deviation for the attribute for males)
Stdev_Female (standard deviation for the attribute for females)

Next, compute the standard error for each group:

Stderr_Male = stdev_Male / SQRT(N_Male)
Stderr_Female = stdev_Female / SQRT(N_Female)

Where N_Male is the sample size of Males and N_Female is the sample size of females
SQRT means to take the square root

Next, compute the pooled standard error (Pooled_stderr) for the attribute across the two groups:

Pooled_stderr = SQRT(Stderr_Male^2 + Stderr_Female^2)

Where "^2" means to square the value.

Next, compute the t-statistic:

t = (X_bar_Male - X_bar_Female) / Pooled_stderr

If the t-statistic has absolute magnitude of 1.96 or greater, this is 95% confidence to reject the null hypothesis that the two groups have the same importance for the attribute.
answered Feb 20, 2013 by Bryan Orme Platinum Sawtooth Software, Inc. (133,765 points)
Hi Bryan,

Thanks for your detail explaination. But I still have few points unclear that...

Yes, I want to do the between-groups t-test for the significant difference of an (one) attribute importance for male vs. female. Or say..is 24.57% on attribute 1 for male group has significant differnece with female group's 27.84% on the same attribute 1.

So to my understanding, the first step to compute the mean value is for a single attribute, fo example let's say for attribute 1, and also the same with standard deviation.

I am not understand on the X_bar_male and X_bar_female, Stdev_male, Stdev_Female, from the first step, the mean and stdev is calcuate on each of attribute by pairs(male vs. female), so how to get the mean of males for the attribute? As the attribute importance sum to 100 and both groups has same attribute, the mean of attribute importance of each of group will have the same mean value, is that right?


Thanks,
Leen
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