标题: Test statistic - Hypothesis [打印本页] 作者: simeezee 时间: 2011-7-11 20:10 标题: Test statistic - Hypothesis
Hi guys,
I would like to ask a question about "test statistic" definition in Hypothesis reading
as stated in the reading, test statistic = (sample stat - value of the pop parameter under Ho) / (std error of the sample stat)
I was wondering why it's not the opposite. I would have defined it like this
test statistic = (value of the pop parameter under Ho - sample stat) / (std error of the sample stat)
Because in a way, the normal distribution (say if the statistic is the mean) here is the distribution of the sample mean. So its parameters are:
- sample mean
- standard error of the sample mean
if we want to calculate z , it's z = (x - sample mean)/standard error and not (sample mean - x)/ standard error
May be I'm dumb, but I find that Hypothesis reading is a list of recipes to follow, without any good explanations.
that for your help作者: dmar 时间: 2011-7-11 20:10
you want to see how far away your sample stat is from your mean... (in terms of standard deviations).
(x-mu)/sigma is giving you in terms of distance of the standard deviations how far away your sample statistic is from the mean of your population... and then you decide if that is statistically significant, or is just a passing aberration.
CP作者: MythosHF 时间: 2011-7-11 20:10
bben Wrote:
-------------------------------------------------------
> as stated in the reading, test statistic = (sample
> stat - value of the pop parameter under Ho) / (std
> error of the sample stat)
>
> I was wondering why it's not the opposite. I would
> have defined it like this
> test statistic = (value of the pop parameter under
> Ho - sample stat) / (std error of the sample
> stat)
>
> Because in a way, the normal distribution (say if
> the statistic is the mean) here is the
> distribution of the sample mean. So its parameters
> are:
> - sample mean
> - standard error of the sample mean
>
> if we want to calculate z , it's z = (x - sample
> mean)/standard error and not (sample mean - x)/
> standard error
Your sample statistic is refering to the population mean - not the sample mean.
cpk is right that you are testing how far away your sample mean is from the population mean (much like how for the Z-score you are showing how far away X is from the sample mean) in this case your sample stat is like the point estimate X and your population parameter is like the sample mean.
So these two equations are the same. You take you point estimate of the parameter and subtract the parameter of the larger group (either sample or population)作者: JPSem 时间: 2011-7-11 20:10
tks guys for your help作者: Bluetick1010 时间: 2011-7-11 20:10
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Edited 1 time(s). Last edit at Friday, December 17, 2010 at 06:25AM by bben.
