chi 2 Contingency Tests Flashcards
What is chi sqaured about
You want to compare if the expected frequency or whatever matched the collected and so if theredsome sssocistiom?
How to find the CHI saaured static
Yiu want the expected frequencies
- these are the frequency you would expect assuming everything is INDEPENDENT , probably of one event doesn’t effect the probability of another event occurring!
- anyways formula ends up being row x column total/ total
- and these frewuencies should add up to normal totals anyways
Once you have these, use chi sqaured statistic, which is observed - expected sqaured/ expected
Put this in another table, and add them
Will now come lade to critical value which will form basis of tedt
Null hypothesis / alternative
Null same thing no association
Alter Wirbel only there is some association
Bevause you just testing if they are ascosited or not, independent or not, if there are indecent then not ssdocsited
How to calc degrees of freedom,
Rows - 1 x coloumns -1
What is the left side of table of cricitsl vs,Jed for
In the case where chin2 very small it means expected and observed are almost too close
So maybe cheating
Then use those to help
What are degrees of freedom
Bsdicslly how many numbers you defo need to work out all the rest, as yiu csn use the total to work out
How to do hypothesis for chi sqaured
1) H0 there is no asscostion between x and y
2) H1 there is some association between x and y
Critical value for x degrees of freedom at y significance is
Work out chi
If chi is greater reject H0
How to work out chi sqaured
Work out totals
Work out exprevte frewuency and check them
Work out observed - expected sqaured / expected
Sum this up
What does the contributions tsble mean , how to comment on it
Basically break down each contribution from highest to smallest
Look at the highest contribution, and check the expected vs observed. Wheat er the difference, the difference is FAR more or less than expected
Look at the middle contributors and check . Whatever it is the difference is just MORE OR LESS THAN EXPECTED
Look at the contributions really close to 0. These will give observed and expected values very similar. Thus these ones are just EXPECTED
What does contributions have in relation to expected snd observed
The higher the contribution aoprentlty the difference between observed and expected is greater, such thst if contributions are basically 0, then the observed values are basically EXPECTED
Why is ther a problem if there are SMALL EXPECTED FREQUENCIES LESS THAM 5?
In the calculation for contributions, the expected frewuency is denominator
The more small this becomes the greater the contribution is .
The greater the overall contribution the likelier chance you reject ti null hypothesis
In this Cade the contributions that a small number may give may outweighs what a decent size sample will give, and so unfair snd not correvt picture
How do you fix small frewuency problem in reality
You would collect more data
If you cantcollect more data how to fix small frewuency problem
Bsdicslly once you idenfit one less than 5 you’ll need to combine groups and remember this is EXPECTED FREWUENCY ONLY
Have to pick wisely what groups to combine, can do ages but the age category would be a it ridiculous
Can combine other into already low one and this makes sense
So combine and refund the expected , should be above 5, find contributions, chi sqaured compared with degree freedom and reject null
What does having a small x 2 compared to critical value mean (like a bit over)
Well done you reject h0 but this quite weak, turn down the significance level and you’re finished
