Title: Introduction: Correlation and regression
Course: UGQuants (SSPS) > Section: Correlation and Regression

Introduction - Relationships between variables: 'bivariate statistics'

Quantitative data analysis is a powerful way to investigate relationships between variables. If, for example, we can demonstrate that the value of one variable increases as another variable decreases, or that two variables tend to rise in tandem, we are able to understand the relationships among variables and the way different concepts relate to each other.  This relationship is known as correlation; i.e. the extent to which two (or more) variables relate together (or co-relate).

This is not to say that studying a single variable on its own – for example through univariate statistics such as the mean and median or standard deviation  - is not important.  If we can catalogue support for a particular political party we might be able to predict the result of the next election. But if we can link voting intentions with other variables, such as social class, age, gender, income, or ethnic background, then we might be able to understand not just what the election result might be but why certain types of people support different political parties.  This helps us not only to understand voting intentions, but the political system as a whole.  This notion of looking at two variables at the same time is referred to as bivariate statistics: studying the relationships between variables allow us to build models and test theories of social relations.

Relationships between two variables

In a sense, our task as social scientists is made easier in two situations: (i) if there is no relationship between variables and (ii) if there is a perfect relationship between variables.   If there is no relationship at all, then knowing the value of one variable will not help us to understand the second variable.  Imagine for example if we have data on a group of people’s views on whether euthanasia ought to be legal, and on their sex and age.  We might find that sex was not associated with any difference in views: men might be as likely to support the legalisation of euthanasia as women. In such a situation, knowing the gender of an individual will not help us to gauge their views of euthanasia.  This is a feature known as statistical independence.  On the other hand, we might find that all the older people (say 55 and over) in our dataset, both male and female, were in favour of legalising euthanasia while all the younger respondents in our dataset were opposed.  In such a situation, knowing a person’s age would allow us to predict with perfect certainty their views on euthanasia.

In reality, we tend to find situations between these two poles.  Certainly finding that a relationship is not present is more likely than finding a perfect relationship but often we have to decide whether we think there is a relationship between two variables or not.  Keeping with our euthanasia example, older people might bemore likely to support euthanasia than younger people, but we might find older people who are opposed and younger people in support of euthanasia.  Our task as social scientists, then, is to identify methods for determining whether a relationship is present or not and, often, for identifying the strength and direction of that relationship.