Univariate descriptive

For metric variables having many values, you should consider whether univariate descriptive analysis may be more appropriate than frequency. Univariate descriptive analysis is a method of describing how the cases are distributed over the values of a particular variable. The technique results in several descriptive measures that portray central tendencies and distribution for metric variables. In other words, instead of listing all the values, it provides details on the distribution of a metric variable.

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 perform a univariate descriptive analysis:

  • Open the "Trust" dataset.
  • Find the variable you are interested in, in the variable list in the left margin.
  • Select the "Tabulation" tab, left-click the variable and select "Add as measure".

Table 2 shows the descriptive results for the variable "Age". Please note that the data are weighted according to the two weights.

Table 2: Example of univariate descriptive analysis: Age

Let us start the interpretation of Table 2 with N. N is the number of observations with valid values. Because of the population size weight, N is not interpretable in this table. This weight variable causes each respondent from the smaller countries to count as less than 1, so the number of respondents reported, 37 307, is less than the real number (which is 42 101).

The maximum value is 109, which means that the oldest person in the sample was 109 years old in 2002. The minimum value is 4, which means that the youngest person in the sample was 4 years old in 2002. This is obviously a mistyping in the data, which illustrates that it is easy to make mistakes when preparing large datasets. The sum is less important in this analysis. The ages of all respondents are added together and the total is 1694190.

The median is a measure of the central tendency for ordinal or metric variables. The median is the value that divides a sorted distribution into two equal parts, i.e. 50 % of the cases will be above it, and 50 % below.

The arithmetic mean shows the central tendency for metric variables. It is the sum of all values divided by the number of cases. Since the variables must have metric characteristics to make it possible to calculate the mean, this measure should not be used for nominal and ordinal variables.

As you can see from Table 2, there is a small discrepancy between the two measures of the central tendency, the mean being slightly greater in this case than the median. This indicates that there may be some older people in the sample, pulling the mean higher. For metric variables you could use both measures, but you should be aware that the measures might be telling different stories. The mean is more vulnerable to extreme values, so for instance if Bill Gates lived in a small municipality, the mean income in this municipality would be extremely large. The median would be a better measure of the income most commonly earned.

Standard deviation is a measure of statistical dispersion based on the intervals between the individual data values and the arithmetic mean of these values. A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean. Standard deviation can only be used for metric variables. In Table 2 we can see that the standard deviation for the age variable is quite large, 18.01, indicating that the respondents are well spread around the mean.

For an explanation of the rest of the output, please look up Confidence interval and Box-and-whisker plot in the keyword section.