Inferring differences and relationships

One way you can begin to look for relationships between variables in your categorical data is by creating a cross-tabulation (often referred to as a ‘crosstab’ by statistical software). This enables you to summarise information about two categorical variables at the same time – for instance, gender and age. Using statistical software, crosstabulations can also give you the percentage of individuals in each combination of categories that you have chosen – for instance, where gender and age are concerned, the percentage of women who are aged 20–29. Cross-tabulations present data in tables.

The usefulness of cross-tabulations is that you can move on from them to conduct statistical tests to find out whether there is a link between the two variables of concern – in formal language, infer whether there is a significant relationship between the two identified variables or if the difference, for example in the number of males and females within each age group, is significant. As we have already noted, the statistical tests you might use to do this are called inferential statistics because they allow you to draw conclusions or inferences about a population on the basis of the data in your sample.

5. Complete the following sentences:

• Categorical data are concerned with ….

• Categorical data tend to…

• With numerical data, the variables that you are concerned with include …

• What is comforting is that these descriptive statistics can often be done without …

• Descriptive statistics allow you to describe where the centre is; that is, ….

• The method that you choose to find the centre of a data set …

• Crosstab enables you to summarise ….

6. Ask 10 general questions to the text.

7. Answer the following questions:

• What are categorical data concerned with?

• How are categorical data described?

• How do one calculate a percentage?

• How are numerical data expressed?

• What is the “center” of your data?

• Why is the method of finding the center so important?

• What is cross-tabulation?

• What is the usefulness of cross-tabulation?

8. Give examples of graphs you know. Identify and name the different types of graphs and charts bellow: line graph, pie chart, flow chart, pictogram, bar chart, scatter diagram

9. Look at the picture of the line graph. What verbs could you use to describe what is happening. What other verbs do you know to describe ‘going up’ or ‘going down’ (Increase, decrease, plummet, soar etc.)

10. The verbs in the box can all be used to describe changes commonly represented on line graphs. Answer the following questions using the dictionary if necessary:

Plummet	decrease	fluctuate	peak	rise	drop
Rocket	increase	decline	level out	soar	fall

1 Which 5 verbs mean go up? ___________________________________________________

2 Of these, which 3 mean go up suddenly/a lot? _____________________________________

3 Which 5 verbs mean go down? _________________________________________________

4 Which verb means reach its highest level? ________________________________________

5 Which verb means stay the same? ______________________________________________

6 Which verb means go up and down? _____________________________________________