Statistical Analysis for Education and Psychology Researchers

have to, as Hayes (1981) comments, ‘judge the reinterpretability of the numerical results
into a valid statement about properties of things’ (p. 64).
The researcher may interpret results as real quantities of an attribute, or simply as test
scores, leaving readers to judge their meaning. In either case, this amounts to a problem
of interpretation and not of statistics. It is quite possible for statistical procedures to
produce correct numbers but ones which have no meaning whatsoever because little
thought has been given to what is being measured and what are appropriate levels of
measurement. Some statistical measures do lend themselves to nominal and rank order
levels of measurement (for example, see Chapters 5, 6 and 7). Researchers should use
these procedures if they have serious doubts about their measurement assumptions. The
simple message here is that one should not neglect measurement issues, but at the same
time, one should not be over concerned about attaining interval levels of measurement for
tests and scales. The tacit assumption of interval level of measurement is often reasonable
provided interpretations are judicious.

2.4 Psychological Tests and Scales

Psychological testing is a form of measurement and many tests relating to learning are
concerned with measures of mental processes, such as intelligence, motivation, aptitude,
knowledge and understanding. These tests are referred to as cognitive and attainment
tests and are frequently employed by teachers and educational psychologists. Another
category of tests concerned with, for example, an individual’s feelings, attitudes,
personality, creativity, anxiety or identity status are generally referred to as affective or
personality type tests.
In practice, none of these psychological constructs can be measured directly. Instead,
psychological tests have been designed which produce either quantitative scores or some
qualitative diagnostic outcome. In essence, one measures what people say about their
feelings, mental states, traits, behaviours and what they know. These statements, which
are usually assessed on a quantitative scale, provide raw scores which are often
manipulated using statistical techniques. Psychological test procedures may be designed
for either individual or group administration. If individual test procedures are used,
different test materials are administered.

Criterion and Norm Referenced Tests

Psychological and, particularly, attainment tests can be categorized by the way in which
meaning is given to the raw scores. If the questions in a test represent specific material,
such as specified knowledge or skills, and the overall test is designed to show or describe
what an individual knows or can do, then this is called a criterion referenced test. This
category of tests has a long history in the United States where they are called content
referenced or domain referenced tests. Criterion tests were developed to evaluate
objective based curricular programmes of study. The content of such tests would be
directly related to the objectives of a programme of study and to the criteria by which
these objectives could be judged to have been met. Test scores would indicate what had
or had not been achieved in a specified domain or following a specified programme of

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