s3 new AQA

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  • Created on: 04-04-10 17:00
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Page 1 of 8 Riya Nawaz
STATISTICS UNIT 3
Contingency Tables
General contingency tables
1. Always start by writing your H0 and H1. In the case of contingency tables, you write weather the
two variables are dependent or independent of each other.
Remember: H0 is the null hypothesis. This means that H0 will always be that the variables are
INDEPENDENT of each other.
Also remember: Contingency table tests are always 1 TAILED.
2. Each value that appears on the table is an observed value. You have to find the expected values by
using this formula:
row total x column total
grand total
3. When you have all your expected values, you must use a formula to find your test statistic:
(O-E)2
E
4. Once you have worked out this formula for all your values, you must add up the totals. This will
give you your test statistic:
.
5. The critical value comes from the degrees of freedom which are simple:
(m-1)(n-1)
If you have a 2 x 3 table, you would use the formula to get 1 x 2, giving you 2, which you would
then look up 2 in the X2 tables. Because contingency tables are always 1 TAILED, you would look
up the upper tail of your significance level. So if it was a 5% significance level, you would look up
0.95 and 2.
6. To finish, you must make a suitable conclusion, rejecting H1 or H0. Because it is a one tailed test,
you can make a rough sketch of the diagram below. The critical value must be written on the
divide between accepting and rejecting H0.
If the test statistic is greater than the critical value, you reject H0.
If the test statistic is less than the critical value, you accept H0.
Small expected values
When you work out , the value for each observed value must be over 5. If you get a number
smaller than five, you will have to combine rows. You should combine rows that are similar. Make sure you
keep an eye on this before you work out your critical value as it will affect your degrees of freedom.

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Yates correction (2 x 2)
1. Always start by writing your H0 and H1. In the case of contingency tables, you write weather the
two variables are dependent or independent of each other.
Remember: H0 is the null hypothesis. This means that H0 will always be that the variables are
INDEPENDENT of each other.
2. Each value that appears on the table is an observed value.…read more

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H0 Population median = 300
H1 Population median </> 300
Remember: H0 is the null hypothesis. This means that H0 will always have no change. This means, in
the case of the sign test, H0 will always be `Population median = x'
2. You will be given a population median and a sample of numbers.…read more

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Paired sample Wilcoxon signed-rank test
1. Always start by writing your H0 and H1. Because you are not given a population median, your H0
and H1 for a two tailed test will be:
H0 Population median difference = 0
H1 Population median difference 0
For a one tailed test it would be:
H0 Population median difference = 0
H1 Population median difference </> 0
Remember: H0 is the null hypothesis. This means that H0 will always have no change.…read more

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Distribution-free methods for two or more unpaired samples
Man-Whitney U Test
1. Always start by writing your H0 and H1.
Say for example, we are talking about the difference in cholesterol in men and women.…read more

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2. The exam question may ask you to state H0 and H1. In any case, they would be:
H0 Ranks in population are independent.
H1 Ranks in population are dependent.
Remember: H0 is the null hypothesis. This means that H0 will always have no change. This means, in
the case of this test, H0 will always be `ranks in population are independent'.
3. The test statistic is the value or r that you find on your calculator.
4.…read more

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