Statistical Analysis for Education and Psychology Researchers

In statistics an event refers to an observable or measurable outcome of an
‘experiment’. The term experiment is unfortunate because it does not mean an
experiment in the sense of research design, rather it means a conceptual experiment in
which something is done or observed and for which there are various possible outcomes.
For example, the sex of a child at birth is an observable outcome, counting the percentage
of 15-year-old pupils in a school who achieve 5 or more GCSE grades A to C is an
observable outcome, the number of children who improve their reading skills in a reading
recovery programme is an observable outcome, and improvement in a school’s average
A-level points score is a measurable outcome.
Most of these events or outcomes have a degree of uncertainty attached to them and
could be considered to be random. We use the idea of a random variable to describe
events of interest. For example, if we role two dice, a random variable could be the value
we obtain when we multiply the two totals on the upturned dice, another random variable
might be the value of the sum of the two scores on the upturned dice. If we administer a
standardized maths achievement test to a class of 8-year-old school children, a random
variable could be the value of one pupil’s test score, yet another random variable could be
the average test score for the class. The sex of a child, percentage of GCSEs and average
A-level points score could all be random variables of interest. Use of the term random
variable has gained such widespread use in probability theory it needs a mention here.
The term random in this context does not mean outcomes that are equally likely as in the
term simple random sample or random selection. It denotes a variable whose outcome
is determined by an element of chance and has a degree of uncertainty associated with it.
We can say the outcome of the experiment is not predictable but is one of many possible
outcomes, each with a numerical value or probability.

Probability Models

One of the aims of educational and psychological research is to describe and predict the
world in which we live and thereby gain an insight into all kinds of educational and
psychological phenomena. One way to do this is by empirical quantitative research.
When we use statistical inference, we want to model our random experiments and to be
able to give values to the probabilities associated with each outcome. To do this we
construct a probability model which adequately describes that part of the world we are
interested in.
It would be almost impossible to model the outcome of a single random event such as
a birth, or a flip of a coin, or a single test score for an individual, because by its random
nature the sex of a child at birth, whether a coin lands heads or tails, or an achieved test
score is uncertain. However, in the long run, and provided the experiment is random, a
pattern of outcomes is detectable. This predictable pattern is the basis of probability
models and is the reason why we can use statistical inference and statistical tests. It may
seem strange, but random uncertainty, in the long run, leads to predictability, and the
long-run regularity of random phenomena can be described using a mathematical or
probability model.
In the long-run refers to repeated flips of a coin, repeated births, repeated test scores,
that is each experiment repeated many times under the same conditions. In many flips of

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