Chi ^2 Contingency

Question 1

What is chi ^2 used for

Answer 1

Where you want to see if there is association brgerrn two variables , which take MORE THAN ONE VALUE

such as school and way to get to school , primary secondary vs car table bike etc

But overall association. Is type of school and way they get there

Question 2

How does chi^2 work

Answer 2

Assumed it’s independent
- this finds the expected frequencies
- find the difference in expected frequencies in terms of contingency
- and then sums this up

Now it compares it to critical value, if it is above then that means it’s unlikely they independent, hence MUST BE CONNECTED
if below then likely I repent hence not connected and no association

So tests for dependence by assuming they are independent!

Question 3

Null alternative

Answer 3

No underlying population hence again words

H0: there is NO ASSOCIATION between x and y
H1: again there is SOME associajton ( not positive negative for chi^2)

All we can determine is are they associated or not

Question 4

Degrees of freedom

Answer 4

Row -1 coloumn -1

Don’t use TOTALS

This gives total numbers needed to predict every other number on the table

Question 5

Hypotension test

Answer 5

Expected f
- adjust for small f

Build contributions.

Add chi ^2

And then compare to critical table

H0 no association
H1 there is some

Context

Find degrees of freedom, at significant level, critical table is

Question 6

What happens if Expecyed f is LESS THAN 5 and what do we do about it and why

Answer 6

Less than 5 we don’t use
- this because f0-fe will give us some huge number, and thus will contribute to contributions too much for no reaosn
- hence combine rows or columns picking sensible that won’t really take away spread of data

And then re do
- not wreklebrr reduced column size degree freedom gonna decrease

Question 7

How to use contributions table to comment on expected vs observed

Answer 7

The highest contributions = the bigger the difference brgeeen f0 and fe
- therefore look at highest
- compare therefore the observed and frequency
- so say highest contributions , means we got less than expected by a lot , more , etc

Do it for highest middle and low to show far from expected kond of or pretty much as expected

Question 8

In reality how would we fix small expected frequency

Answer 8

Higher sample

Question 9

Small x^2 above the cortical?

Answer 9

Okay calm you reject but increase significance then your finished