Chapter 4: Analysing the Data Part II : Descriptive Statistics

Descriptive statistics describe patterns and general trends in a data set. In most cases, descriptive statistics are used to examine or explore one variable at a time. However, the relationship between two variables can also be described as with correlation and regression. Inferential statistics test hypotheses about differences or relationships in populations on the basis of measurements made on samples. Inferential statistics can help us decide us if a difference or relationship can be considered real or just a chance fluctuation.

One of the goals of psychological science is to understand human behaviour. But before we can understand it, we have to be able to describe it. In some sense, descriptive statistics is one of the bridges between measurement and understanding. Use of inferential and descriptive statistics is rarely an either-or proposition. With a data set and array of research questions, we are usually interested in both describing and making inferences about the results. We describe the data, find reliable differences or relationships, and estimate population values for the reliable findings

Statistics can be viewed as a means of finding order and meaning in apparent chaos. At the end of the data collection phase of a research project, really all we've got is a bunch of numbers with no apparent order or meaning. The first phase of data analysis involves the placing of some order on that chaos. Typically the data are reduced down to one or two descriptive summaries like the mean and standard deviation or correlation, or by visualisation of the data through various graphical procedures like histograms, frequency distributions, and scatterplots.

As an example, we will be using a real data set from a study by Andrew Hayes. The study was concerned with the sexual behaviour of university students. The data come from a questionnaire where respondents were asked a number of questions about their beliefs, values, and sexual behaviour. The variable we will examine is the number of sexual partners each respondent reported having in the past year. 177 people have provided data on this variable. The raw scores can be found in Figure 4.1.

 Question: "How many sexual partners have you had in the last year?" Respondents: UNE students Data: 1, 0, 2, 4, 5, 1, 1, 1, 2, 1, 1, 4, 1, 1, 10, 2, 6, 1, 1, 1, 1, 1, 1, 2, 5, 2, 1, 1, 6, 2, 4, 2, 1, 4, 1, 0, 1, 5, 0, 1, 0, 1, 1, 4, 2, 1, 1, 0, 1, 3, 1, 1, 3, 1, 4, 1, 0, 1, 1, 1, 0, 1, 8, 1, 15, 1, 1, 1, 2, 3, 1, 4, 3, 3, 1, 1, 2, 1, 1, 1, 1, 1, 4, 3, 2, 1, 0, 0, 1, 2, 1, 2, 3, 1, 7, 1, 2, 2, 1, 1, 1, 1, 0, 2, 0, 2, 1, 3, 0, 0, 2, 1, 1, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 7, 1, 0, 1, 2, 2, 7, 2, 8, 0, 1, 3, 14, 1, 1, 0, 1, 3, 3, 1, 1, 4, 1, 1, 2, 1, 1, 0, 1, 1, 3, 3, 1, 0, 0, 1, 2, 5, 0, 6, 2, 2

Figure 4.1 Data for "number of sexual partners" variable.