Math Is Fun Forum

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Degree of freedom for a Chi-squared test?

Hi, may I know the degree of freedom for a chi-squared test? What is given on my notes is k-p-1 where k denote the no. of classes, p denote estimated parameter. However this is one question that really confused me:

30 passengers on a flight took part in an experiment to investigate if a new drug suppresses jet lag. The subjects were divided into two group, one given the course of treatment and the other was given a placebo.

                                   Jet lag                 No jet lag
Treatment group             3                           12
Placebo group                 10                         5

With data above, use a chi-squared test to investigate if the treatment suppressed jet lag.

Solution is given as:

There is no association between experiencing jet lag and the treatment

Treatment suppressed jet lag

The expected frequencies are as follows:

                                  Jet lag                 No jet lag
Treatment group             6.5                        8.5
Placebo group                 6.5                        8.5

Hence the test statistic is:

Degree of freedom:

.
.
.
.

My question is, why is the degree of freedom (2-1)(2-1)=1 ? Isn't it 4-1=3? since no. of classes is 4 and there are no estimated parameter?

Thanks a bunch in advance, I have an exam this week.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Degree of freedom for a Chi-squared test?

This is a 2x2 contingency table.
When a comparison is made between one sample and another, the rule is that the degrees of freedom equal (number of columns minus one) x (number of rows minus one). For your data this gives (2-1) x (2-1) = 1.

The other answer is for a One Sample Test.
That test compares a collection of categorical data with some theoretical expected distribution.

It confuses me too.

Last edited by bobbym (2009-05-12 01:19:55)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Degree of freedom for a Chi-squared test?

That it! You are the MAN! How could I have forgotten about this? Thanks a bunch.:D

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Degree of freedom for a Chi-squared test?

Thanks coffeeking, let me know how you do on your exam.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.