Test statistic - Hypothesis like, definition, opposite, question, Because

simeezee

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

dmar

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

MythosHF

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)

JPSem

tks guys for your help

Bluetick1010

.



Edited 1 time(s). Last edit at Friday, December 17, 2010 at 06:25AM by bben.