Chapter 4
Probability and Inference
In this chapter basic statistical concepts involved in the design and subsequent data
analysis of empirical investigations are introduced. These ideas are considered in the
context of planning and implementing a quantitative empirical research study. Unlike in
the previous chapter where we explained that the purpose of initial data analysis was to
describe and summarize data, in this chapter we will focus on another aspect of statistical
analysis, namely, how statistics can help answer specific research questions and provide
evidence on the trustworthiness of our conclusions.
Two of the most important statistical ideas which are central to the use of statistical
tests and indeed are fundamental to the empirical research process are probability and
statistical inference. These statistical ideas play an essential role when a researcher’s
interest turns from describing data to answering more specific research questions.
4.1 Research ProcessA good way to begin an empirical investigation is with a research question, for example:
- ‘Do teachers’ expectations of students’ abilities influence students’ performances?’
- ‘Is illness perceived by young children as a form of punishment?’
- ‘Are secondary school pupils’ academic achievements in the most part determined by
their academic performance in primary school?’
Selection of focused research question(s) and definition of a population of interest is the
first step in what is typically a four-stage empirical research process. The statistical
concepts of probability and inference, which are often not explicitly recognized as part of
the researeh process, are introduced in the context of these four stages of research, see
Figure 4.1.