# Independence Day

'Is political persuasion dependent on Gender? How can we tell - an introduction to independence tests'

When two data sets are numerical we can look for correlation using scatter graphs and linear regression and so on. So what do we do when they are not numerical? Independence tests are a way of looking for a relationship between categorical data sets. In this case we will experiment with the question above about whether or not political persuasion is dependent on gender. The process hinges on a couple of key points. What would you expect survey results to show if there was no relationship between the two and how different is this from actually happened. This activity aims to show that the first question can be answered intuitively and that from that you can begin to understand the significance of the differences between what you might expect to happen and what actually does. Have some fun using the power of social networks to collect data to answer the question so that comparisons can be made. All of this provides a good context for going through the independence test for the first time.

## Aims

To explore the idea of 'expected outcomes' by building on intuition. To recognise that the difference between what you would expect to happen given independence and what actually does happen becomes a measure of the dependence. You might follow this with some more Real independence tests

### Resources

The following video can be used to help students understand...

This activity runs from the following two activity sheets.

Independence day - part 1

Independence day - Part 2

For the data collection part of the activity you can use the Is political persuasion dependent on gender questionnaire. This is also embedded below.

### Collecting data

The following is an online questionnaire to collect data to answer this question. Having completed the exercises above, you can use the data collected or better yet, collect even more data. Use the power of your social networks, post it on twitter, facebook etc and see how many people you can get to answer the question. Watch the live data pour in here and export it for your own use!

### Description

This is an outline of how the activity might run

• Ask the question about political persuasion and have a conversation both about perceptions and how it might be possible to test out the theory.
• Use the first activity sheet to explore how expected frequencies can be worked out intuitively. It is good to do this before the observed values are actually considered.
• Use the first activity sheet to introduce frequency tables and expected values. This is the first chance to consider what you might expect to happen.
• Use the questionnaire to collect data to answer the question (it might be an idea to get the questionnaire out there earlier so there is time to collect some responses)
• Use the data from the questionnaire to work out some expected frequencies assuming independence and then use this real data to go through the stages on an independence test.

### I did it my way!

As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collect of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at jamesn@inthinking.co.uk In time some of these twists may appear here....

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