# s3 new AQA

step by step instructions on how to answer each question.

- Created by: riya
- 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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