s2 contingency tables question help needed!

My query is about chi squared tests. In the aqa s2 textbook (p.g 99) it is written " For an approximation to be valid, each value of O must be greater than 5"
There isn't anything tricky about that, i guess its just something you have to except. When i tried the aqa jan 10 question q4

http://store.aqa.org.uk/qual/gce/pdf/AQA-MS2B-W-QP-JAN10.PDF

I though you would have to combine 19-30 and 40-60 due to not enough O values. but it the mark scheme :
http://store.aqa.org.uk/qual/gce/pdf/AQA-MS2B-W-MS-JAN10.PDF

It only mentions of combining the final column (40-60). Could someone explain why this is as in the 19-30 there is an O value less than 5 so to me, from what i understand this doesn't really work. The examiners report doesn't really help either but here it is anyway:

http://store.aqa.org.uk/qual/pdf/AQA-MS2B-W-WRE-JAN10.PDF

Reply 1

coolstorybrother

anyoneeee

really confused on this now... it just doesn't makes sense

Reply 2

ghostwalker

Original post by coolstorybrother

anyoneeee

really confused on this now... it just doesn't makes sense

According to my book, Statistics by Crawshaw and Chambers, you only need to combine classes when the Expected value is 5 or less.

A bit of googling seems to support it being the Expected value, and not the Observed value that's important.

(edited 11 years ago)

Reply 3

coolstorybrother

Original post by ghostwalker

According to my book, Statistics by Crawshaw and Chambers, you only need to combine classes when the Expected value is 5 or less.

hmmm, can both conditions still stand in unison?
EDIT: im thinking a massive typo in the book then? so unfair for those who sat this exam using this book, endorsed by AQA no less :/
These are the book for anyone interested
http://www.amazon.co.uk/Statistics-AQA-SMP-AS-Mathematics/dp/0521605318/ref=sr_1_1?s=books&ie=UTF8&qid=1340054166&sr=1-1

(edited 11 years ago)

Reply 4

ghostwalker

Original post by coolstorybrother

hmmm, can both conditions still stand in unison?
EDIT: im thinking a massive typo in the book then?

I'd go with typo.

Edit: Unfortunately most books have some errors; makes learning from the book rather difficult. If they have any worked examples in the book that might prove fruitful, in showing up their error, but equally might support it.

(edited 11 years ago)

Reply 5

coolstorybrother

Original post by ghostwalker

Yea... but whats even more weird is that they try to show how the combining of rows work, but again they are using observed frequencies..a direct quote from the book " If a value of O is less than 6, some categories in the data must be combined to make O large enough." (a whole example wrong? :s-smilie:

unfortunately thats all they mention about it in the book)
Could you link some the website which validate that it's all about the Expected frequency, not observed? cheers :smile:

Reply 6

ghostwalker

Original post by coolstorybrother

Could you link some the website which validate that it's all about the Expected frequency, not observed? cheers :smile:

Just google the two character strings "contingency tables" "combining classes"

First hit is http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch11.pdf and search through for "combining".

Reply 7

coolstorybrother

Original post by ghostwalker

Just google the two character strings "contingency tables" "combining classes"

First hit is http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/stats_ch11.pdf and search through for "combining".

thanks, i think i get it, so if the expected was 5.5, that would be okay? it's just if it's five or less, in the actual process of combining, does it actually matter which other row you combine it too?

Reply 8

ghostwalker

Original post by coolstorybrother

thanks, i think i get it, so if the expected was 5.5, that would be okay?

Yes.

it's just if it's five or less, in the actual process of combining, does it actually matter which other row you combine it too?

It is important, but I'm not an expert.

If your data is ordered, as here, it wants to be one of the neighbouring classes.

If it's not ordered, then, I believe, it should be one that has roughly the same proportions as the data you're combining it with.