I am analyzing survey data for a membership organization. We have survey data from 2000, 2005, and 2010, and each year has between 400-600 respondents (the survey was sent to all members). In all years, the ratio of men to women is highly male, and there are many more people in the upper age categories. However, it seems that both of these demographic measures are moving toward a more equal balance, but the change is small. What statistical test can I use to see if the change across the years is actually significant?
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$\begingroup$ A test implies some comparison of an estimated parameter (population means for example). Are you saying the questions and answer are identical in each survey? So you have something like a vector of numbers for each period along with the characteristics of the individual who responded to the survey? $\endgroup$– Ram AhluwaliaCommented Sep 2, 2011 at 3:33
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2$\begingroup$ If organization is your population and you surveyed all or nearly all its members then you don't need any significance test since any differences then are absolutely significant. $\endgroup$– ttnphnsCommented Sep 2, 2011 at 9:06
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1$\begingroup$ @ttn Good point, but I bet there's a substantial non-response rate. Even in small dedicated professional organizations a survey response greater than 50% is rare. $\endgroup$– whuber ♦Commented Sep 2, 2011 at 11:50
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$\begingroup$ @whuber: The response rate was indeed between 30 - 50 percent for each of the surveys. $\endgroup$– Sara SullivanCommented Sep 7, 2011 at 2:05
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$\begingroup$ @Quant Guy the questions were the same in all three surveys, and the response options were also the same. Male or Female for gender, and the responses for age were by decade (21-30 yrs old, 31-40 yrs old, etc ). $\endgroup$– Sara SullivanCommented Sep 7, 2011 at 2:08
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2 Answers
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I can't think of a good way to test the entire trend, but if you're satisfied with separately testing 2000 vs. 2005 and then 2005 vs. 2010, try looking into the Chi-Square Test. It'll tell whether (or to what extent) the breakdown in one year is proportional to the breakdown in the other. Along with the Chi-Square result itself, you'll probably want to obtain a related correlation coefficient such as Phi for the gender test or Cramer's V for the age test. That'll do more to quantify the extent to which the proportions are a function of the passage of time.
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you need to see if the difference between age and sex between different years is larger than the confidence intervals for age and sex in each of the groups [group of 2000, of 2005 and of 2010, for instance].
Also, maybe run a linear regression of age versus time of measuring?
as for sex, yeah, chisquare
