Statistical Analysis for Education and Psychology Researchers

fragments for the same set of twelve words. The number of fragment words completed
were counted. A new set of twelve fragment words were also presented, these had not
been previously presented in a reading passage. This was a matched pairs design, that is
each student attempted to complete two sets of fragment words, twelve that had
previously been read in passage and twelve that had not. If the student completed more
word fragments for the set of twelve words previously presented in the reading passage,
(compared with the twelve words that had not been presented) this constituted a priming
effect.
For the twenty-four students, seventeen showed a priming effect and three had tied
scores, that is completed equal numbers of word fragments for both sets. The investigator
concluded that there was a significant priming effect for items that had been read
previously, p <0.001, by the sign test.
In a numerical example of the sign test given by Sachdeva (1975), twelve randomly
selected pairs of students (each pair matched on age, sex and IQ) were randomly assigned
to two different conditions. The obtained data are:
Pair No. 1 2 3 4 5 6 7 8 9 10 11 12
Condition I 17 18 26 24 26 14 17 29 36 25 44 30
Condition II 22 32 25 22 27 21 14 41 37 24 43 31
Sign for difference− − + + − − + − − + + −

The investigator wanted to find out whether there was any difference between the two
experimental conditions in the average performance of students.
The sign test was used and alpha was set to 5 per cent, with a two-tailed test. The null
hypothesis of no difference in the average performance of students under the two
experimental conditions was not rejected, and the investigator concluded that the average
performance of students under the two conditions was the same.

Worked Examples

Data from the study by Gardiner (1989) on the influence of priming on implicit memory
is used to illustrate the paired difference sign test. The sign test determines the probability
associated with an observed number of +’s and −’s when in this case the probability of a

• or a − is 0.5. The test statistic is the count of the number of pairs with a difference in
  the desired direction. Pairs with a zero difference are not included in the analysis and n,
  the number of pairs, is reduced accordingly.
  Gardiner reported that 17/21 students showed a basic priming effect, that is seventeen
  subjects completed more word fragments for the set of twelve words previously presented
  in the reading passage, compared with the twelve new words not previously presented
  (here 17 +’s). Three subjects had tied scores, that is, completed an equal number of word
  fragments for both sets of twelve words. Under the null hypothesis of an equal number of
  +’s and −’s, the null hypothesis is rejected if too few differences of one sign occur. The
  probability of obtaining the observed distribution of 17/21 +’s, or a more extreme
  distribution (fewer differences for the sign with the smallest count) is evaluated using the
  binomial equation (see Chapter 4, section 4.1). The binomial equation with probability
  0.5, sample size twenty-one and number of successes set to four or fewer evaluates
  whether four or fewer subjects would be expected to occur by chance (four is the smaller

Statistical analysis for education and psychology researchers 190