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Q: Which test should I use to show the equalitiy of means in two groups? ( Answered ,   1 Comment )
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 Subject: Which test should I use to show the equalitiy of means in two groups? Category: Science > Math Asked by: jennybo-ga 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 t-Test can show that they are NOT equal but which test shows that they ARE equal?``` Clarification of Question by jennybo-ga on 09 Oct 2004 09:51 PDT ```I want to analyse the influence of gender on various dependant variables (using regression). For this I have two groups of test person, men and women. Since age also has a large influence on the dependend variables I need to show that the two groups dont't differ significantly in age. Can I use the t-Test and argue like this: The null hypothesis that the two means of age are equal can not be (does not have to be?) rejected because the level of significance is greater than 0,05 (0,30 for example). Or how else can I show that the difference in the mean age of the two groups does not influence the dependant variables?``` Request for Question Clarification by mathtalk-ga on 09 Oct 2004 22:18 PDT ```One approach would be to show by regression that age differences do not account for a large fraction of the variation between the two groups. In other words, treat age and gender as two independent variables and analyze variance in the dependent outcome in terms of these for the entire sample. regards, mathtalk-ga``` Clarification of Question by jennybo-ga on 13 Oct 2004 14:38 PDT ```Thank you for your answers! That helped. I tested the variables in a regression. I'm not so familiar with Google Answers. What do I need to do in order to pay for your answer?``` Request for Question Clarification by mathtalk-ga on 13 Oct 2004 14:45 PDT ```Hi, jennybo-ga: I just need to post an Answer in the answer box! Let me dress up what I said a bit and that's what I'll do. regards, mathtalk-ga```
 ```Hi, jennybo-ga: 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, mathtalk-ga```
 jennybo-ga rated this answer: and gave an additional tip of: \$2.00 `Very helpful!`
 ```Hi, jennybo-ga: 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 t-test 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 t-test 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, mathtalk-ga```