Statistical analysis

The chosen statistical methods and reasons

Three research questions were used in the study in order to explore the effective ways of improving young EFL learners’ writing ability. First, we sought to find out whether PI, TBI, and eclectic instruction are effective in enhancing the participants’ writing ability.

Second, we examined the relative contribution of the three instructions. Third, we further analyzed if the three instructions can benefit the participants’ writing ability in particular aspects.

In order to answer the three research questions, the study employed two sets of statistical analysis.

For the first and second research questions, the tests (pretest and posttest) and the treatments (PI, TBI, and eclectic instruction) were defined as independent variables in the

first set of statistical analysis. The total scores of the pretest and posttest were defined as the dependent variable. In order to find out which treatments could effectively improve the participants’ writing ability, the current study viewed the tests as one independent factor.

Because the pretest score of a specific participant was used to compare with her own posttest score, the variable of tests was a within subject factor. Also, in order to find out the

relative contribution of the writing instructions, the treatments were viewed as another independent factor. Because one participant could only receive one type of treatment and the comparison was between groups, the variable of treatments was a between subject factor in the study. Furthermore, in order to examine the general effectiveness of the three instructions, the total scores of the pretest and posttest would be a better indicator to answer the first and second research questions. In the current study, repeated measures analysis of variance (ANOVA) in mix design would be adopted to answer the first and second questions for the following reasons. First, by controlling family wise error rate, ANOVA could prevent the problem of high type I error of post hoc comparison if the pair t-test was conducted several times. Second, both the first and second research questions could be answered based on the interaction effect of tests and treatments. Thus, 3 (the treatments: PI, TBI, and eclectic) × 2 (the tests: pretest and posttest) repeated measure ANOVA in mixed

design was conducted as the first set of statistical analysis in the study.

For the third research question, in order to find out whether certain treatments could benefit specific writing aspects, the current study viewed both the aspects (fluency, accuracy, and complexity) and the treatments (PI, TBI, and eclectic instruction) as independent variables in the second set of statistical analysis. The sub-scores of the posttest were defined as the dependent variable. Because the three writing aspects were parts of writing ability of one specific participant, the variable of aspects was a within subject factor. As noted above,

the variable of treatments was a between subject factor in the study. Furthermore, in order to examine the different aspects of one’s writing ability, the sub-scores of the posttest would be a better indicator to answer the third research questions. In the current study, the pretest scores were viewed as a covariate variable and controlled in order to prevent the participants from having a different baseline in the pretest. The reasons for the method are as follows. First, the covariate could control the proficiency difference between the participants if there were any. Second, there would not be an extra factor (pretest, posttest) which would make the second set of statistical analysis complicated. Thus, 3 (the treatments:

PI, TBI, and eclectic) × 3 (the tests: pretest and posttest) repeated measure ANOVA in

mixed design was conducted as the second set of statistical analysis in the study.

The Procedure of the statistics

The examination procedures were as follows. For the first and second research questions, the first set of statistical analysis would be conducted. First, the interaction effect would be examined to see if the total scores would be influenced by the types of treatments.

If there were significant differences in the examination of interaction effect, then the post hoc comparison of the treatments and the tests would be done respectively using Tukey post-hoc analysis. By examining the simple main effect of the treatments, we could see whether the writing performances of the participants were different in the experiment after the eight-week writing instruction. The results would be the answer to the first research

question. Next, examination of the simple main effect of the tests would show whether the participants were at the same baseline at the beginning of the experiment and whether the participants of the three treatment groups showed any significant differences at the end of the experiment. The results would be the answer to the second research question.

For the third research question, the second set of statistical analysis would be conducted with the three sub-scores in the pretest as covariate. First, the interaction effect would be examined to see if the sub-scores of the posttest would be influenced by the types of treatments. If there were significant difference in the examination of interaction effect, then the simple comparison of the treatments and the sub-scores would be done respectively, also using Tukey post-hoc analysis. Examination of the simple main effect of the sub-scores would show whether the participants of the three treatment groups had significant difference in the sub-scores at the end of the experiment. The results would be the answer to the third research question.