Contingency Tables

[sfischer]

In the example 12.21, we combine 2 groups because character present has a value or 3.5 and 1.9 in the 2 groups we combine (both <5). Would we combine them if only one value was <5? If we didn't combine them would the test be still valid (in this case) - I thought we were only concerned if >20% of the Ei were <5? Could we arbitrarily decide to group say 21-25 and 26-30 and the test would still be valid? Sorry 3 questions for the price of 1 there just trying to get a full understanding of when to combine and when not to.
Thanks.

 

[Tim.Sullivan]

Examples 12.18 and 12.19 seem to indicate that we should combine groups when any ei is <5. I'll be going through past papers in coming weeks - it would be good to know if anyone else has followed the 20% "conservative" approach?

Tim

 

[John Lee]

Apologies - I thought I had answered this question!

In the example 12.21, we combine 2 groups because character present has a value or 3.5 and 1.9 in the 2 groups we combine (both <5). Would we combine them if only one value was <5?

You'd certainly need to combine the one which was less than 5 but you could choose which group you'd combine it with.

If we didn't combine them would the test be still valid (in this case) - I thought we were only concerned if >20% of the Ei were <5?

There are 8 cells and two of them (ie 25%) are less than 5 so that is >20% of them.

Could we arbitrarily decide to group say 21-25 and 26-30 and the test would still be valid?

Yup - the test just compares numbers in the groups - doesn't matter wherre they're from.

 

[sfischer]

Thanks for that. 2 out of 8=25%...Ok missed the simple maths there. But on your response to the first part - eg. if I only had 1 out of the 8 <5, I would still need to combine it - where does the >20% rule come in if we need to combine all values <5 anyway?

 

[John Lee]

Thanks for that. 2 out of 8=25%...Ok missed the simple maths there. But on your response to the first part - eg. if I only had 1 out of the 8 <5, I would still need to combine it - where does the >20% rule come in if we need to combine all values <5 anyway?

There's two rules:

the easy-to-remember-but-harsher-than-it-needs-to-be "combine if <5" rule

the harder-to-remember-but-not-so-harsh "combine if more than 20% <5 or if any are <1" rule

the second is more accurate - but the first is a nice easy to remember rule.

In the exam use whichever you like.

 

[sfischer]

That's clear - thanks.