Figure 4.1: Overview of the empirical
research process
Generally our research questions refer to whole populations of interest, such as all
teachers, all young children, all secondary school pupils. However, after having specified
a population (step 1), it is often impossible to collect data for the whole population of
interest. Instead, a sample from the population is selected (step 2). A wise researcher
should give careful thought to the kind of statistical inference(s) required to address the
research question(s) at the planning and design stage, that is before data is collected.
You may recall from the previous chapter that initial data analysis of the achieved
sample is the first phase in our overall data analysis strategy. We used graphical
techniques and summary statistics to describe our sample data and to identify underlying
data distributions and possible statistical models (step 3). In so doing, we were preparing
for the next phase of analysis which involves more formal procedures of statistical
inference.
Fundamentals of InferenceThe idea of statistical inference is involved whenever we go beyond the numeric
findings obtained from sample data to suggest what the situation is, or what would
happen, in the parent population. There are two aspects to statistical inference—
estimation and hypothesis testing. Whereas both hypothesis testing and estimation make
use of the same concepts: sample, statistic, population and parameter, fundamentally they
address different questions.
Estimation addresses the question, ‘What is the value of a population parameter?’.
For example, what is the mean maths achievement score in the specified population?
Hypothesis testing addresses the question, ‘What is the probability or likelihood that
the population parameter is equal to a specified value?’ For example, what is the
probability that the mean maths achievement score is 100? A test of significance is used
to assess the strength of evidence against the hypothesis (step 3). The central tenet of our
research question(s) is usually concerned not so much with the findings from a particular
sample per se, but rather with generalizing these findings beyond the immediate
experimental or survey setting (step 4).
Probability and inference 85