On 13 Mar 2001 21:18:38 GMT, [EMAIL PROTECTED] () wrote:
>In article <[EMAIL PROTECTED]>,
> RD <[EMAIL PROTECTED]> writes:
>>On 13 Mar 2001 07:12:33 -0800, [EMAIL PROTECTED] (dennis roberts) wrote:
>>
>>>1. some test statistics are naturally (the way they work anyway) ONE sided
>>>with respect to retain/reject decisions
>>>
>>>example: chi square test for independence ... we reject ONLY when chi
>>>square is LARGER than some CV ... to put a CV at the lower end of the
>>>relevant chi square distribution makes no sense
>>>
>>Hmm... do not want to start flame war but just can not go by such HUGE
>>misconception about chi squared test. Indeed exactly reverse is true :
>>chi squred test is always two tailed. There is nothing to prove just
>>look at the definition : Khi^2(n)=sum(Z^2).
>
>Please amplify what you mean by "just look at the definition":
>If you mean that positive and negative residuals (Obs_i - Exp_i)
>both increase the "lack-of-fit", then that is universally recognised.
>
The definition of chi squared density function is probability to get a
sum of squared random variables which follow centered normal
distribution. As they are squared this means that when we look at the
right of our value on the chi squared density graph we look for 1
minus cumulative density which basically corresponds to two tailed
test.
You states that this is universally recognied but take a look at
Dennis Roberts message quoted above to see that you are wrong.
large snip
>For me, the only important practical (as opposed to theoretical)
>objection to carrying out a 1-tailed test is ethical. If an amateur
>statistician decides that applying 10mg Cu per square metre is no
>better for wheat yield than applying 10mg K per square metre,
>then deciding to apply 10mg Cu/m^2 is their prerogative, their problem,
>and an example of evolution in action. However, if they chose to
>apply poison to my grandmother because it is no better than medically-
>accepted standard treatment for multiple sclerosis, then I would object.
>Forcibly. See "Decision Theory".
There is a huge gap between test and decision. I do not think that
your example is a good one. No better vs no difference ie 1tailed vs
2tailed does not make difference at all because in medicine these are
never used by decision making authorities. So you won't have to
object.
Indeed in this particular case you are talking about a slightly
different problem. In fact we are faced to dilemma. Usually any
treatment is tested against placebo. Thus if it is not different or no
better with2.5% we throw that molecule to recycle bin. Things are
quite different if there is already an effective (although never
perfect) treatement for your grand mom's multiple sclerosis. Helsinki
declaration exlicitly prohibits testing against placebo where such
treatment exists. If we think that a new treatment is just as
efficatious as the old one we have to use the so called equivalence
tests wich are far from perfect.
But this is another discussion which is far from our original subject.
>More importantly, I would say: DON'T DO TESTS. Instead, try to find
>models that you would be prepared to use to predict the response
>in as-yet untried circumstances.
For me "TO DO TEST" means to test my model. Yet that concept is never
tought at medical school. We are usually tought some cabbalistic
calculations then compare result to that table. This is probably why
some people may think that when the result in table of chi squred
table corresponds to cumulative distribution we are doing one tailed
test.
Alexandre Kaoukhov
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