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Re: Why multiply t by sample std dev?
Posted:
Oct 2, 2012 6:42 PM


On 02/10/2012 2:02 PM, Paul wrote: > On Oct 2, 9:39 am, Bruce Weaver <bwea...@lakeheadu.ca> wrote: >> On 01/10/2012 9:54 PM, Rich Ulrich wrote: >> >> >> >> >> >>> On Mon, 1 Oct 2012 12:45:45 0700 (PDT), Paul >>> <paul.domas...@gmail.com> wrote: >> >>>> On Sun, 30 Sep 2012 12:55:11 0700 (PDT), Paul >>>> <paul.domas...@gmail.com> wrote: >> >>> ... snip a bunch >> >>>> Thanks, Dave, Rich, >> >>>> I think I pinpointed the source of my confusion. I didn't really >>>> know what t was. It was just a curve and a table that we blindly used >>>> according to a recipe. Well, Wikipedia >>> (http://en.wikipedia.org/wiki/Student%27s_tdistribution) defined the >>> tvalue in a manner similar to >>>> Rich: >> >>>> [ (sample mean)  (population mean) ] / (sample standard deviation) >> >>> No! >>> It does not say that. It uses the sample standard ERROR. >>> You are going to confuse yourself on into the future if you do >>> not grasp the distinction and keep it clear. >> >>> The Standard Error is the name used for the SD of a statistic. >>> Yes, it is also a standard deviation. But the "SD of a sample" >>> is distinct and larger than the "SD of a sample mean." >> >> And to complete the thought, the (estimated) standard error (SE) of the >> MEAN = the sample SD divided by the square root of the sample size. > > Thanks for the clarification of terminology. I also found > http://en.wikipedia.org/wiki/Standard_error to be helpful. There > should be square root of the sample size in the denominator: > > t = [ (sample mean)  (population mean) ] / [ (sample SD) (square root > of sample size) ] > > where the denominator estimates the standard deviation of the > estimated mean of the population. >
The denominator for your singlesample ttest should be:
[ (sample SD) / (square root of sample size) ]
 Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/Home "When all else fails, RTFM."



