Correlation

By investigating a cross table, as described above, one is often able to detect whether there is a relationship between two variables, and also what the relationship is. Often this is not enough. Sometimes we would like to know how strong the connection is, or we would like to compare several relationships.

Correlation is a mathematical method summarising the statistical relationship between two variables. Different coefficients are developed for the analysis of different types of variables. We will limit ourselves to Pearson's r, which has been developed for metric variables.1 Pearson's r can range from –1 to 1, and represents the linear relationship between two variables. Using survey data, it is very rare to find correlations above 0.6.

In the following example, we will investigate the relationship between the variables "age", "gender" and "personal use of Internet/e-mail". The interesting correlations here are between age and use of Internet, and between gender and use of Internet.

Please see the text on weighting and how to weight data.

Weighting is a very important concept in the analysis of sample data. Weighting allows you to assign different weights to the different cases in the analysis file. Weighting is usually used to correct skewness in a sample that is meant to represent a particular population.

If, for example, you have measured the height of 50 men and 10 women in a country with an equal gender distribution, the mean height of this sample is not the same as the one you would have found if you had measured all the people in the whole population. Because men generally are taller than women, the sample must be weighted so that it can be used for inferential purposes. To make the sample more representative of a "true" population, it is necessary to reduce the effect of the male majority in the sample. By multiplying each male height by 0.2, and each female height by 1, you can adjust for the effect of the male dominance in the sample (male: 50*0.2=10, female: 10*1=10).

There are two weights in the ESS data that may and often should be switched on. The first is the design weight (dweight). Several of the sample designs chosen by countries participating in the ESS were not able to give all individuals in the population aged 15+ precisely the same chance of selection. Thus, for instance, the unweighted samples in some countries over- or under-represent people at certain types of addresses or in certain types of households, such as those in larger households. The design weight corrects for these slightly different probabilities of selection, thereby making the sample more representative of a "true" sample of individuals aged 15+ in each country.

The second weight is the Population Size weight (pweight). This is used when examining data for two or more countries combined. This weight corrects for the fact that most countries taking part in the ESS had very similar sample sizes, no matter how large or small their population. The mathematics of probability proves that a sample of, for example, 1000 respondents is equally useful in examining the opinions in a country with 10 million inhabitants as it would be in a country with a population of only 1 million.

Without weighting, any figures that combine data for two or more countries would over-represent smaller countries at the expense of larger ones. So the population size weight makes an adjustment to ensure that each country is represented in proportion to its population size.

When computing any tables or percentages, you should always use weighted data. However, different types of tables require different combinations of weights. The general rules of thumb are:

  • You should always use the design weight.
  • When you are comparing data of two or more countries and with reference to the average (or combined total) of those countries, and when you are combining countries into a group, such as "EU member states", both design and population size weights should be applied.

The following example illustrates some of the effect of weighting. If we want to find the general political interest in the population covered by all the countries participating in the ESS survey, we could create a frequency table using the variable "How interested in politics". The example below gives the weighted and unweighted valid frequencies for this variable. The unweighted frequencies tell us the level of political interest in this sample only. If we want to say something about the population in these countries, we must use the weighted frequencies. The discrepancy may not seem very large, but it will have an important impact in many analyses. You should note that the N is less in the weighted column, and not directly interpretable. This is because respondents from smaller countries count less than one, and in this way make the samples more proportional to the population size.

"How interested in politics": Weighted and unweighted valid frequencies.

Please visit European Survey Data for guidance on how to get reliable estimates.

Follow these steps to switch on the weights:

  • Open the Trust data set.
  • Click the icon for weighting.
  • Select the appropriate weights from the box "Weighting variables defined in the dataset", and press the ">" button. In analyses where both weights need to be applied, you could use the combined weight instead of the design and population weights. The combined weight is simply the two weights multiplied.
  • Click "OK". Now you can proceed with the analyses.

To establish the correlations in Table 5:

  • Open the Trust dataset.
  • Switch the combined weight on.
  • Select the "Analysis" tab.
  • Find the variable gender, left-click and select "Add to correlation".
  • Find the variables age and personal use of Internet and add them to the correlation.

Table 5: Bivariate correlations (Pearson's r): Age, Gender, Personal use of Internet

Open this table in Nesstar WebView

From Table 5 we can see that the correlation between age and personal use of Internet is -.35, while the correlation between gender and personal use of Internet is - .11. Both correlations are significant, that is, the results are unlikely to be due to chance.

It is not straightforward to compare the size of these coefficients. Gender is a variable with only two categories, while age is a metric variable with many categories. When the number of categories is low, it is nearly impossible to obtain a very high correlation using survey data.

To be able to interpret the direction of the correlations - in our example they are both negative- we need to know how the variables are coded: Gender (0 = male, 1 = female), Personal use of internet/e-mail (1 = No access, 2 = Never use, 3 = Less than once a month, 4 = Once a month, 5 = Several times a week, 6 = Every day), Age in number of years 2002 (20, 21 etc.)

A negative correlation means that there is a tendency for a respondent with a low value on one variable to have a high value on the other variable. (Positive correlation means that a high value on one variable is associated with a high value on the other). Thus, the negative correlation between gender and Internet means that male (low value) is connected to frequent use (high value), and female to less frequent use. Similarly, the result reveals that young people (low value) use the Internet more often (high value) than old people.

  • [1] In research it is common to use Pearson's r for nominal or ordinal variables as well. To do so, it is necessary to assume that the variable has metric characteristics. For nominal variables (male - female) this is done be recoding the variables into dummy variables: Either you are a man (=1), or you are not (=0) (but then we know you are a woman). For ordinal variables (very positive ? quite positive ? quite negative ? very negative), we assume that this is a scale.