# Workshop and discussion exercises

Practice with these exercises to prepare for your seminars and wider research.

1. Constructing contingency tables and scattergrams:
(a) Using this data matrix, construct contingency tables that show the relationship between: Sex and Working; Sex and Jobsat; Working and Jobsat. Ensure that each cell contains a count and column and row percentages. Describe the character of the relationships which you find.
(b) Draw a scattergram, plotting Age against Jobsat. Describe the character of this relationship.
(c) Using the recoded version of Age construct contingency tables showing the relationship between this variable and each of the other three variables. Describe the character of the relationships you find.(d) If you are learning SPSS or another statistical package, try inputting these data. You will find it easier to get the computer to do the analyses specified above. You can also generate tests of association and significance and consider the meaning of these. Try using the software to produce output in the form of graphs (e.g. pie charts, histograms).

2. Here are four contingency tables (a)–(d), each demonstrating different types of relationship between the two variables of social class and home ownership. Below each is a p-value and the result of a test of association (Q). For each table, describe the character of the relationship and explain why the p-values and tests of association vary.

3. Cross-tabulation and the chi-squared test:

The first part of the exercise, Cross-Tabulation and the American National Election Study (2012): Party Identification and Same-Sex Marriageguides you through cross-tabular analysis of a data set. Full instructions and downloadable data, which you can analyse with SPSS or other statistical software programs, are located on the site.

The second part of the exercise, Pearson’s Chi-Squared Test and the American National Election Study (2012): Gender and Views on Same-Sex Marriage, guides you in the use of the chi-squared test.

4. The t-test to test whether the means of two groups are significantly different:

The exercise, Difference of Means t-test and the British Crime Survey (2007–2008): Confidence in the Police and Area of Residence, guides you in the use of the t-test. Full instructions and downloadable data, which you can analyse with SPSS or other statistical software programs, are located on the site.

5. The Pearson’s correlation coefficient to examine the relationship between two continuous variables:

The exercise, Pearson's Correlation Coefficient and the UK Living Cost and Food Survey (2010): The Relationship between Income and Expenditure, guides you in the use of the Pearson’s correlation coefficient. Full instructions and downloadable data, which you can analyse with SPSS or other statistical software programs, are located on the site.

6. This is a structured exercise in reading a statistical table that aims to give you a general strategy for perceiving the main messages of such tables.

You could apply this approach to this table or you could find a table by doing this:

Choose a topic of interest to you, for example, ethnicity, gender differences, class inequalities, educational inequalities, family structure, health differences. Find some tables of official statistics and/or government survey data on your chosen topic in the reference section of your library. Do not choose data that are already presented in graph form. Some examples of UK statistical series that you are likely to find are: Social Trends; General Household Survey; Annual Abstract of Statistics; Population Trends; Mortality Statistics; Decennial Census; Marriage and Divorce Statistics. Use Google to search for them.

You will find that not all of the questions are relevant to every table, but experience has shown that these steps, if followed carefully, enable a deeper understanding of any statistical table.
(a) Read the title before you look at any numbers. What does this reveal about the content of the table?
(b) Look at the source: who produced the data, with what purpose? Was it a census or a sample?
(c) Look at any notes above or below the table. How will they influence its scope and your interpretation?
(d) Read the column and row titles. They indicate which variables are applied to the data.
(e) How many variables are there and what are they? Can any be considered independent or dependent?
(f) How are the variables measured? Are there any omissions or peculiarities in the measurement scale? How else might such a measure have been constructed?
(g) What units are used – percentages, thousands, millions? If you are dealing with percentages, then which way adds up to 100 per cent?
(h) Look at the ‘All’ or ‘Total’ column. These are usually found on the right-hand column and/or the bottom row (the ‘margins’ of a table). What do variations in the row or column tell you about the variables concerned?
(i) Now look at some rows and/or columns inside the table. What do these tell you about the relationships between variables? What social processes might have generated the trends you find?
(j) Is it possible to make causal statements about the relationship between variables? If so, do any of these involve the interaction of more than two variables?
(k) What are the shortcomings of the data in drawing conclusions about social processes?
(l) What other enquiries could be conducted to take this analysis further?
(m) Finally, consider the issue of whether the table reveals something about social reality, or creates a particular way of thinking about reality.