"Most people at this point will "reject" the hypothesis, but what does that mean? "
To suppliment it,my question is: even based on all circumstatial evidence, whether a (non) convicted person is always(not) guilty?
If the answer is 'no', then we need to know about Type-I & Type-II errors.
After all we are dealing with all kinds of chance events, and (perhaps)that is why we first study probability,then distribution , then sampling,then sampling distribution of statistic(s) and then proceed to Inference.
And , my personal view is , inference(be it estimation, be it testing) is nothing but (enlightened) statistical guesswork....
Coming to the point : rejection never implies falseness;neither acceptance implies correctness. Rejection implies that the probability(calculated under certain assumptions)of the falseness is high.(In other words, when we 'feel' that the parbability of the falseness of the null hypothesis is 'high', we reject it)
What is high or what is low....depends upon the context.
From: Andrew Hartley <khahstats@...>
To: Statisticians_group@...
Sent: Wednesday, February 4, 2009 6:01:42 PM
Subject: Re: [Statisticians_group] Please Help me
|
Harika,
sorry about your paper. I don't know how your course is being taught, but many courses don't, in my opinion, adequately explain something that is strange about the usual methods for statistical inference: Those methods start by stating this or that hypothesis concerning the larger population, & then make statements about how often such & such would be observed in the smaller sample if that hypothesis were true. This reasoning is from the general to the specific, whereas statistical inference would be from the data to the hypotheses (i.e., the specific to the general, as reflected in the ppt Sasikumar mailed you). You're then supposed to observe the data, & use your creative imagination to invent the meaning those data indicate concerning the hypothesis about the larger population.
E.g., in hypothesis testing, we assume the tested ("null") hypothesis. That hypothesis might indicate that, if you repeated the experiment many times, 95% of the time, the sample means will fall between -5 & +5. Now, say you observe the sample mean & it is -7. That was not in the range you expected with 95% confidence. Everything up to this point is the "general to specific" part. Now comes the "creative imagination" part: Having observed something in the sample that seemed unlikely given your hypothesis, to do inference you need to say something about the hypothesis itself.
Most people at this point will "reject" the hypothesis, but what does that mean? Does it mean we are 95% sure the hypothesis is false? Or simply that our confidence in the hypothesis has decreased to some unspecified degree? Disparate answers to this question abound among statisticians, which is probably part of why you "didn't understand even a problem or a sentence."
I could go on to explain what I think is a more sensible approach than the standard statistical methods, but want to ask now whether any of the above makes sense to you.
--- On Wed, 2/4/09, harikabhardwaj <harikabhardwaj@ yahoo.com> wrote: From: harikabhardwaj <harikabhardwaj@ yahoo.com> |
Offline 
Send Email