Statistical Analysis for Education and Psychology Researchers

of U can be used. For example, assume the total number of + and − signs is 44, of which
the first 21 are + and the remaining 23 are −. The number of runs equals 2 and the
frequency in both binary categories is >20. In this example the large sample
approximation could be used.

Test Assumptions

This is a simple one-sample test with few assumptions, namely:

• Observations can be classified as binary (data may be dichotomized—above or below a
  median value).


• Observations are recorded in the sequence (order) of their occurrence.

Example from the Literature

An example of use of the runs test can be found in a paper by Cliffe (1992) who
investigated symptom-validity and testing of feigned sensory or memory deficits.
Symptom validity testing has been used to detect feigning in patients claiming sensory
and memory deficits. Such patients typically give fewer correct responses on forced
choice testing than would be expected by chance (non-random). In an experiment in
which six subjects were asked to feign blindness (the task was to identify which of two
numbers, 0 or 1 was presented on a display monitor), it was hypothesized that subjects
would simply decide which stimulus, 0 or 1 to nominate prior to each forced choice.
To test the hypothesis it was necessary to identify non-randomness in the sequence of
observed responses to a series of trials. The investigator reported 148 runs in 240 trials
(the number of observations in each binary category was not reported) and concluded that
this number exceeded the number expected for a random sequence, p<0.00046 (two-
tailed). The null hypothesis of random choice of digits (1 or 0) was rejected. The
investigator reported that in subsequent interviews subjects confirmed this strategy.

Worked Example

Small sample

In a study of teachers’ classroom interactions a research student video-recorded fifteen
science lessons taught by two teachers. Each lesson was subsequently coded and
classified as either teacher interaction predominantly with boys (B) or teacher interaction
predominantly with girls (G). As the lessons were recorded during different times of the
day and week and considering the possibility of the teachers awareness of being observed
influencing their behaviour (this might change over the study period) the researcher
wanted to test the randomness of the fifteen observed lessons. The sequence of lessons
were coded as:

LESSON 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CODE BBGBBGBBB G GGGBB

Inferences involving rank data 215