# Further Stats query regarding May 16th paper

Discussion in 'Mathematics' started by chris592, May 17, 2019 at 10:44 AM.

1. ### chris592New commenter

Hi I wonder if someone can answer a really dumb question. I am sure there is an obvious answer I am missing

In Yesterdays paper Question 1 had a contingency table 3 by 5.

Part c of the question said "explain why there are 6 degrees of freedom."

I would have thought there were 8.

Can anyone wo has seen the paper give a quick explanation as to why there could be 6?

Thanks

2. ### nervousnedSenior commenter

I haven't seen the paper but assume there was an expected frequency less than 5

3. ### chris592New commenter

Dear Chris,

Thank you for your query regarding the 8FM0_23 examination that was taken on 16th May.
I have been in contact with the Chief Examiner for this paper and have included their comments below:
There is a convention for carrying out chi-squared tests that the expected frequencies should be greater than 5. If this is not the case in a contingency table then a row or column should be combined to ensure that this condition IS met.
Part (b) of the question drew the attention of the students to the small observed frequencies for snooker and checked that for the age of 60 or more the expected frequency was OK. The students should therefore be on the “look out” for the cell which would have the smallest expected frequency. This would clearly be snooker for those under 20.
Calculation of this expected frequency (= 3.6) shows that this value is less than 5 and so some combining of cells needs to take place. The best way to do this (it combines related variables of age and gives the greatest degrees of freedom) is to combine the first two rows thus giving a 4x3 table which would give rise to 6 degrees of freedom.

I hope that this helps with your query and if you have any further questions please do not hesitate to get in contact.
Kind regards,
Alexa

4. ### chris592New commenter

ITs just a shame that the text book the students have been using have not had this 'convention' stated or used in any example. it seems quite important to miss from a text book

5. ### briceanusNew commenter

Welcome to the rushed-out text books.
Unfortunately there are errors / omissions / sloppy methods contained throughout.
BUT, expected value <5 is standard practice, just as Yate's correction would be expected process.
Bric

p.s. anyone else really struggled/struggling to get through the new content in the hours provided ?

6. ### gainlyEstablished commenter

So Edexcel are now using Alexa to answer queries!

Piranha likes this.

It’s on page 97 of the Pearson textbook. Thanks to everyone on Twitter who contributed to the discussion.

8. ### chris592New commenter

I see. We don’t have that book. If it’s important enough it ought to be mentioned in any endorsed text book.

9. ### chris592New commenter

Yes the rushed out books have been shoddy
And it’s a shame that students, who are using texts as a representation of the curriculum , aren’t necessarily able to determine an ‘expected process’ unless they are shown it’s an ‘expected process’

And yes getting through content is hard at only five hours a fortnight - although I’m sure some are struggling with fewer.

10. ### briceanusNew commenter

"And it’s a shame that students, who are using texts as a representation of the curriculum , aren’t necessarily able to determine an ‘expected process’ unless they are shown it’s an ‘expected process’"

That's why there are teachers who know the content and know the expected process !! Any stats teacher delivering contingency tables would, most certainly, cover Yates and expected < 5, even if not specifically covered in the textbook. In a similar way, teachers delivering vectors will be showing students the dot product, even though this is not in the textbook.
Bric

11. ### chris592New commenter

It is not true to say Any Stats teacher would. Contingency tables have not been in most delivered curriculum for many years. I have known many dedicated and able professionals who would all agree that they don’t know every party of every possible syllabus. They ask and they learn. In this day and age saying to any teacher something like ‘any stats teacher would’ could demoralise and demotivate and add to stress. These teachers rely heavily on produced curriculum material being detailed about what content the curriculum demands and not to be made to feel foolish for asking the questions.

12. ### pi r squaredNew commenter

Perhaps not, but this is why it's also extremely important to pay close attention to the exam board specification and any teacher guidance they offer. I've just had a quick look at the Edexcel spec and it does state quite clearly on p32 the expectation that cells should be combined whenever Ei<5. I can't access any teacher guidance from Edexcel but the AQA teaching guidance makes a pretty big deal of it:

and also provides three example questions reinforcing that skill.

It is pretty shocking for an endorsed textbook to have missed this out, sure - but it's also a good reminder of why students and, more importantly, teachers should not be relying solely on textbooks to determine curriculum content.

Piranha likes this.
13. ### chris592New commenter

Yes we read the Edexcel spec many times. 'Clear' is obviously open to the interpretation of the reader. It puts Goodness of fit and Contingency together and says "cells should be combined whenever Ei<5". We considered that vague and decided to look for clarity within the textbook, that does Goodness of fit merging well, but has no statement or example for a contingency table. That's why we asked the question.

14. ### PiranhaStar commenter

I seem to recall from the old A-levels that odd things that were not mentioned either in the textbook or the specification suddenly appeared in the exam.

15. ### pi r squaredNew commenter

I'm not trying to be belligerent here but I am interested to hear an example from the textbook of "Goodness of fit merging", involving combining cells, that did not also suggest that a contingency table should also be merged if Ei<5. Cells would automatically imply a table to me, though admittedly I am coming at this as someone who has taught Chi Squared as part of the old AQA S2 module not completely afresh. Do Edexcel not also provide teacher guidance to the same level as that quoted above from AQA?

Textbooks for sure but I'd be intrigued to hear an example of a thing that appeared in an exam that was not part of the official specification (nor the assumed knowledge from GCSE), as that would surely be grounds for complaint?

16. ### chris592New commenter

The textbook actually tells the student to apply Yates Correction in a cell in a contingency table with any cell where the O<5. But only shows one example with a 2x2 contingency table. Nowhere does it suggest merging rows

17. ### henlyjuNew commenter

I'm a Maths teacher who has taught Further Maths for over 20 years.
Our department talked long and hard about this Contingency Table, degrees of freedom question yesterday. In the end we decided it was only worth a few marks and hoped are candidates weren't thrown by it.

I agree with most of this thread...
We switched boards from MEI to Edexcel since we liked their third applied paper model, (50% Stats, 50% Mechanics).

No text book is perfect but we chose Oxford over Pearson at the beginning. My Maths department have continually discussed about switching to Pearson's and the jury's still out. I generally like Oxford but the section A questions are not differentiated enough. Surely any sensible person would start with easier questions and progressively work towards harder questions! Apparently not!
Rushing textbooks out is a disgrace.

A complete revised edition is needed for Oxford, (not just a Bridging Edition, that was cobbled together after the event).
Also, Oxford's Further Mechanics 1 book, looks like someones notes thrown together. Oblique Impact questions bear no resemblance to the Sample Assessment Material! I'll be buying Pearson's FM M1 next year.

I could go on but I have L6th reports to write...