You are Here: Home >< Maths

# S3 Degrees of Freedom

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
1. For part d), why isn't a constraint the fact that the expected frequencies have to equal the observed frequencies? Or does the mark scheme answer mean the same thing?

Also, when working out the degrees of freedom, do you miss out the cell where x=0?

Thanks for any help.
Attached Images

2. (Original post by PhyM23)
For part d), why isn't a constraint the fact that the expected frequencies have to equal the observed frequencies? Or does the mark scheme answer mean the same thing?

Also, when working out the degrees of freedom, do you miss out the cell where x=0?

Thanks for any help.
6 cells.

Merge two together because you need all expected frequencies to be >5.

5 cells left.

You need all the expected frequencies to add up to (number of trials).

One degree of freedom gone.

So 5 cells, gives 5 degrees of freedom. One degree is used on adding up expected frequencies. So 4 degrees of freedom.
3. (Original post by Zacken)
6 cells.

Merge two together because you need all expected frequencies to be >5.

5 cells left.

You need all the expected frequencies to add up to (number of trials).

One degree of freedom gone.

So 5 cells, gives 5 degrees of freedom. One degree is used on adding up expected frequencies. So 4 degrees of freedom.
Ah so the -1 is from the EFs equalling the OFs, and not from the cells being combined because of one being <5?
4. (Original post by PhyM23)
Ah so the -1 is from the EFs equalling the OFs, and not from the cells being combined because of one being <5?
Yep. There are 6 cells, then you merge them into 5 cells to get 5 degrees of freedom and one is lost from the total EF being the total OF for a total of 4.
5. (Original post by Zacken)
Yep. There are 6 cells, then you merge them into 5 cells to get 5 degrees of freedom and one is lost from the total EF being the total OF for a total of 4.
Awesome. Thank you for clearing that up.

Just another question, in the textbook it says if the estimate of a parameter is calculated then it's a restriction, but it isn't a restriction when when using an estimate that seems sensible from observations.

Is a sensible estimate like saying the probability of getting a 6 with a fair dice equalling 1/6? So would that not be a restriction?
6. (Original post by PhyM23)
Awesome. Thank you for clearing that up.

Just another question, in the textbook it says if the estimate of a parameter is calculated then it's a restriction, but it isn't a restriction when when using an estimate that seems sensible from observations.

Is a sensible estimate like saying the probability of getting a 6 with a fair dice equalling 1/6? So would that not be a restriction?
If you calculate a parameter from the observed data (so adding it up and dividing or whatevs) then it's a restriction, if you assume the parameter then it's not a restriction. So if you had some observed data about a fair dice then you could:

(i) do a test with assuming the probability of it being a 6 as 1/6 and your degree of freedom is unchanged
(ii) calculate the probability of it being a 6 as (whatever, even if it's 1/6, you've calculated it) then you lose a degree of freedom.
7. (Original post by Zacken)
If you calculate a parameter from the observed data (so adding it up and dividing or whatevs) then it's a restriction, if you assume the parameter then it's not a restriction. So if you had some observed data about a fair dice then you could:

(i) do a test with assuming the probability of it being a 6 as 1/6 and your degree of freedom is unchanged
(ii) calculate the probability of it being a 6 as (whatever, even if it's 1/6, you've calculated it) then you lose a degree of freedom.
PRSOM

8. (Original post by PhyM23)
PRSOM

No problem.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: May 20, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams