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| From | Erasmo Giambona <e.giambona@gmail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: Average of Sample vesus Sub-Samples |
| Date | Fri, 19 Mar 2010 17:11:45 +0100 |
Thank you all very much! Erasmo On Fri, Mar 19, 2010 at 5:05 PM, Tim Scharks <tim.scharks@gmail.com> wrote: > Ah, I see That's what I get for faulty inference and reading too fast...thanks! > > On Fri, Mar 19, 2010 at 8:59 AM, Jeph Herrin <junk@spandrel.net> wrote: >> The original question was not whether these two >> numbers could differ, but whether the average of the >> larger group could be greater than the mean of the >> two sub averages. In your case they differ, but the >> average of the larger group is smaller. >> >> I think you have to have negative numbers to reverse >> the inequality. >> >> cheers, >> Jeph >> >> >> Tim Scharks wrote: >>> >>> but what about >>> >>> A = 1, 1, 1 >>> B = 3 >>> m(A) = 1 >>> m(B) = 3 >>> (m(A)+m(B))/2=2 >>> mean (A+B) =1.5 >>> >>> uh oh... >>> >>> The problem is not negative numbers--it is your failure to weight the >>> subsample means according to their relative size: >>> >>> (m(A)*3+m(B)*1)/4 =1.5 >>> m(A+B) = 1.5 >>> >>> >>> On Fri, Mar 19, 2010 at 6:49 AM, Jeph Herrin <junk@spandrel.net> wrote: >>>> >>>> Yes, if they are negative. >>>> >>>> >>>> A = -1,-1,-1 >>>> B = -3 >>>> then >>>> mean(A) = -1 >>>> mean(B) = -3 >>>> (mean(A)+mean(B))/2 = -2 >>>> mean(A+B)= -6/4 = -1.5 >>>> >>>> -1.5 > -2 >>>> >>>> So the average of all 4 numbers is larger than >>>> the average of the means of the two subsamples. >>>> >>>> >>>> hth, >>>> Jeph >>>> >>>> >>>> >>>> >>>> >>>> Erasmo Giambona wrote: >>>>> >>>>> Dear Statalisters, >>>>> >>>>> Is it possible that the arithmetic average of a sample is larger than >>>>> the averages of two sub-samples containing overall all the >>>>> observations of the full samples? >>>>> >>>>> Any thoughts would be appreciated, >>>>> >>>>> Erasmo >>>>> * >>>>> * For searches and help try: >>>>> * http://www.stata.com/help.cgi?search >>>>> * http://www.stata.com/support/statalist/faq >>>>> * http://www.ats.ucla.edu/stat/stata/ >>>>> >>>> * >>>> * For searches and help try: >>>> * http://www.stata.com/help.cgi?search >>>> * http://www.stata.com/support/statalist/faq >>>> * http://www.ats.ucla.edu/stat/stata/ >>>> >>> >>> * >>> * For searches and help try: >>> * http://www.stata.com/help.cgi?search >>> * http://www.stata.com/support/statalist/faq >>> * http://www.ats.ucla.edu/stat/stata/ >>> >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/statalist/faq >> * http://www.ats.ucla.edu/stat/stata/ >> > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/