Question 12.17

[jensen]

In this grouping of signs question:

n1 = 10
n2 = 10
G = 8

The critical value (from the tables is 3).

Since the critical value is 3 and G = 8 (therefore G>3) then shouldn't we reject null hypothesis and and that results is SIGNIFICANT?

The solution says "the observed value of 8 is greater than 3 and therefore is not significant" and no mention of whether we accept or reject Ho.

 

[didster]

Always need to think about what you're testing.
Here a higher number of groups are better, so if you have more than the critical value, you don't have significant data to reject H1.

Strictly speaking, a hypothesis test is a test of whether you have significant data to accept/reject H1 in favour of H0.
If you reject H1, it's not that you have significant data to accept H0.
You don't have significant data to accept H1. A very subtle difference.

Significant = Accept H1
Not Significant = Reject H1

"Accepting H0" is more saying "We can't find a reason not to" rather than "We have a specific reason to accept H0"

 

[jensen]

Always need to think about what you're testing.
Here a higher number of groups are better, so if you have more than the critical value, you don't have significant data to reject H1.

-- So you reject Ho, right?

Strictly speaking, a hypothesis test is a test of whether you have significant data to accept/reject H1 in favour of H0.
If you reject H1, it's not that you have significant data to accept H0.
You don't have significant data to accept H1. A very subtle difference.

Significant = Accept H1
Not Significant = Reject H1

"Accepting H0" is more saying "We can't find a reason not to" rather than "We have a specific reason to accept H0"

Significant = Accept H1 -- Or sufficient evidence to reject Ho
Not Significant = Insufficient evidence to reject H1 -- Or Accept Ho, right?

didster,

So back to the original question, shouldn't the answer be "significant,and sufficient evidence to reject Ho, ie accept H1." I just want to confirm my understanding.

 

[didster]

Forgeting all the statistical nitty gritty for a while.

If you have enough groups the graduation fits OK in this regard.
More groups is better, so you are more consistently "in between" the data values.
That is, the data is not consistently higher/lower than your graduation in any area.

Now bring in the stats.
How few is not "enough" to say the fit is bad?
This is the critical value.
Less actual groups than critical value => fit is bad.
More actual groups than critical value => fit ok.

Now onto the H0/H1
H0 is always what you have (and trying to prove wrong).
H1 is what you think is better than H0.
so,
H0 - Fit is good;
H1 - Graduation ABC is better. loosely speaking "Current fit is bad"

 

[jensen]

Thanks didster!

I went to read the formula again, and I noticed (like you mentioned) the bigger the G, then bigger the p-value is hence result is insignificant (just as stated in the notes) and so we reject H1 in favour of H0, ie what we have is better than H1 proposes? I think I got it ??

 

[didster]

Always helpful in any test, to take a moment and think back to basics.
Eg, is it unexpected/good/bad to get a high/low observed value?

This way, you avoid making mistakes by mixing up tests, eg higher than critical in grouping of signs test is "good fit" whereas higher than critical in chi-squared test is "bad fit"

 

[jensen]

thanks, that is a good tip indeed. I'm going to go back to the tests and list out the conditions so i wont get mixed up again.

 

[didster]

Was thinking more of a "common sense" approach.
Eg for "best fit"
Want many switches in deviations from +/-, ie plenty groups (grouping of signs)
Want aproximately as many + as - (signs test)
Want small deviations from data to graduation (chi squared test)
etc

But your way works too, and you can add things like formulae (useful for the last minute cram session).

 

[jensen]

right, common sense. Now if only i could remember where I left mine...

Thanks for everything. You have been very helpful.