

Subject:
Which test should I use to show the equalitiy of means in two groups?
Category: Science > Math Asked by: jennyboga List Price: $3.00 
Posted:
07 Oct 2004 23:44 PDT
Expires: 06 Nov 2004 22:44 PST Question ID: 411908 
I want to show that the mean age of test person does NOT differ significantly in two groups, for example men and women. The tTest can show that they are NOT equal but which test shows that they ARE equal?  
 
 
 


Subject:
Re: Which test should I use to show the equalitiy of means in two groups?
Answered By: mathtalkga on 13 Oct 2004 18:47 PDT Rated: 
Hi, jennyboga: In your sampling you have two genders and a variety of ages in each group. One approach to analyzing such data when the outcome may depend both on the age and gender is through regression, which you have tried. If we could go back in time and redesign your "experiment", an alternative approach might more closely meet the intuitive idea of eliminating age as a factor from the analysis. Such an approach is called matched or paired observations. In other words, prior to measuring the outcome or dependent variable, one pairs up individuals from the two groups so that their ages are equal (or nearly so). Then the analysis of the outcomes can be done using the gender variable within each pair. The "cost" of such a paired observation study is naturally a bit higher than one which accepts observations of unmatched samples. It commits one to equal sample sizes of men and women, for example, and carries a greater risk of "losing" data over the course of a study when one or the other of a pair must drop out. So, for the sake of thinking about "next time", here are a couple of sites that explain some of the theory and the procedures involved. [Analysis of paired observations  NIST] http://www.itl.nist.gov/div898/handbook/prc/section3/prc311.htm [Testing paired observations online] http://home.clara.net/sisa/pairwhlp.htm regards, mathtalkga 
jennyboga
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Subject:
Re: Which test should I use to show the equalitiy of means in two groups?
From: mathtalkga on 08 Oct 2004 05:17 PDT 
Hi, jennyboga: In essence there is no separate test which "shows that they ARE equal". Let's back up a step and make sure we're talking about the same issue. There are two populations, and for each we have a random sample of ages (e.g. of men and of women as you suggest). If we have the _entire_ population for both groups, then of course we can calculate the two means. That would accordingly tell whether the two means are equal or not. With only a sample, however, the exact population mean is not known. Under these conditions the best we can hope for is a technique like Student's ttest that says whether the sample results are reasonably likely _if_ the population means were equal. [Here we come to a subtlety that you may or may not intend to introduce. The usual "null hypothesis" would be that the two samples are drawn from the same underlying population, or equivalently that the two populations have the same distribution. In that case both the means and the variances (and other statistics) for the two populations will agree. So it's conceivable that you are asking for tests that check equality of means under a "broader" null hypothesis, in which means might be equal but variances (or equiv. standard deviations) are unequal.] Student's ttest relies on a normal approximation to the distribution of sample means. For this approximation to be valid requires a modestly large sample size in relation to the population variance. There are other "robust" statistics which are useful in situations where a normal approximation is suspect. For example, a normal distribution is continuous but "age" is normally recorded in whole numbers, which produces a discrete distribution for means of a fixed sample size. [As sample size grows the distinction becomes less significant.] regards, mathtalkga 
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