Statistical Analysis for Education and Psychology Researchers

Example from the Literature

Christensen and Cooper (1992) examined the research hypothesis that 6-7-year-old
children achieve greater proficiency in simple problems of addition when they use
cognitive strategies compared with children who do not use them. Study participants
included twenty-two girls and eighteen boys from two classes of a suburban public
school in Australia. This was a pre-test-post-test design but only pre-test data is analysed
here. Students were given a screening pre-test on written and oral problems of addition.
Pre-testing confirmed all children had conceptual understanding of addition and that no
child utilized cognitive strategies. All children participated in an intervention (involving a
variety of instructional activities) over a twelve-week period. Post-testing was completed
immediately following the period of intervention. Children were assigned to cognitive
strategy and non-cognitive strategy groups after the intervention when strategy group
could be identified.
Response variables analysed included written score (number of correct responses on a
written test), oral latency score (time interval between initial display of test item and
student correct response), error score (number of errors on oral test) retrieval score
(number of items retrieved from memory), and counting score (number of items
answered by counting). For memory and counting scores it was not specified whether
only ‘number correct’ items were counted.
Table 1 in Christensen and Cooper’s paper presents data on mean pre-test and post-test
scores for the two groups of students. Part of this table showing pre-test data only, is
reproduced as follows:

Table 8.5: Means, standard deviations and results

of significance tests for strategy and non-strategy

groups at pretest

(^) Strategy group Non-strategy group
(^) Mean SD Mean SD Test p
Written 20.05 13.04 12.70 11.07 t38=2.04 .048
Oral latency 5.87 2.07 8.53 2.53 t 38 =3.64 .001
Errors 7.70 9.35 5.75 4.66 t 38 =0.83 .409
Proficient 1.55 2.01 0.60 1.43 t 38 = 1–72 .093
Retrieval 37.70 13.15 21.85 15.36 t 38 =3.51 .001
Counting 17.30 13.15 33.15 15.36 t 38 =3.51 .001*

• Statistically significant
  With respect to this pretest data, six research questions were addressed, one question for
  each response variable. In each case the question is of the form, Is the average pre-test
  score for students who are strategy users different to the average pre-test score for
  students who are non-strategy users? The population of interest in this study is the
  population of students who might participate in a twelve-week instructional programme.
  Implicitly this is the population to which the authors generalize their results.
  Statistical analysis for education and psychology researchers 296