Statistical Analysis for Education and Psychology Researchers

interval you are in a better position to make a judgment about the author’s conclusions.
You should read the article for yourself.

In the previous example, individual pupils can either interpret graphs or they cannot. If
they can, they are given a score of 1, and if they cannot, a score of 0.

Why then do individuals always have a score (1 or 0) which lies outside

the 95 per cent confidence intervals of 0.18 to 0.42?

We should not forget that the confidence interval represents the probable limits around an
AVERAGE number of pupils who can perform the task. We interpret the 95 per cent CI
as inferring that if another random sample of sixty pupils were to complete the graphical
task, then this sample would have an average proportion of success in the confidence
interval 0.18 to 0.42.
You should be aware of one small problem when estimating confidence intervals for a
discrete random variable. When the underlying distribution is binomial, probabilities of
events can only change one whole unit at a time. Interpretation of the confidence
intervals, however, is on a continuous scale. This does not present a problem when
samples are large, that is when n>30 or when the minimum value of P or 1−P≤0.10. With
smaller samples a correction for continuity, 1/2n should be applied;

CI0.95

for a

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on—4.6

This chapter has been ‘heavy going’ so we will pause at this point to sum up. If you have
followed the story so far you will have an understanding of the tricky ideas of probability
and statistical inference and how they relate to research design and statistical analysis.
The next section extends these ideas to continuous distributions and introduces the formal
procedure of hypothesis testing.
To summarize so far:

1 Data are summarized by statistics such as means, standard deviations, counts,
percentages and proportions. Statistics are stochastic or random variables, provided
data on which they are based have been generated by a random process.
2 Statistics can be considered to be random variables which follow the laws of
probability. The variability of a sample statistic is shown in the sampling distribution
of that statistic. Empirically, this is obtained by calculating the statistic for many
samples of a fixed size, drawn at random from a specified population. In practice, with

Statistical analysis for education and psychology researchers 102