The chisquared test, , of independence contingency tables

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The chi-squared test, , of
independence (contingency tables)

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The chi-squared test can be used to test for
independence or goodness of fit. This slideshow
is for the independence of data.
That is you will be given two (or more) sets of
data and we will test to see if the data is
independent.
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The procedure to test for the independence
1. State a hypotheses based on the fit of the data
2. Make a table of the observed and expected
values. You will most likely be given the
observed values.
3. Calculate the chi-squared test statistic, this
is
4. Look up the chi-squared critical value from
your chi-squared tables in the information
booklet.
5. Compare your test statistic with your critical
value and make a conclusion. If the test
statistic lies in the critical region then reject
H0 in favour of H1. Otherwise do not reject H0 in
favour of H1.
At first glance this is similar to the goodness
of fit test, but the test statistic is worked out
differently.
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Degrees of freedom, v.
When undertaking a chi-squared test you will have
a table of observed and expected values. The
degrees of freedom will be defined as
v(number of rows-1)(number of columns-1)
The chi-squared distribution.
The distribution will alter depending on the
value of v. The general curve is shown opposite.
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Example of Chi-squared independence test
The headmaster of a large IB school is concerned
that the maths results are dependent on the maths
teacher. There are 3 SL teachers and the results
for each class have been shown below. These are
the observed values. Test at the 5 level of
significance to see if the grades are independent
of the teacher.
Make your hypotheses
H0 the grade at maths SL is independent of the
teacher. H1 the grade at maths SL is not
independent of the teacher.
Make a table of expected values. To do this take
each row total x column total and divide by the
grand total. This is shown opposite.
Find the expected number of grade 2s that Mr. P
gets.
This value is the expected value for this cell.
Complete a table of expected values.
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continued ....
Calculate the chi squared test statistic
Observed
the p value
Find the critical value from your
tables. v(7-1)(3-1)12
Critical value 21.026
Expected
Make your conclusion
Do not reject the null hypothesis. At the 5
level of significance there is no evidence to
suggest that the choice of teacher influences the
grade achieved.