Statistics

Section 1
This section is based on

Lee, S.-K. (2007). Effects of textual enhancement and topic familiarity on Korean EFL students’ reading comprehension and learning of passive form. Language Learning, 57, 1, 87-118.

Questions in this section are :

Q. 1

In table 4 (p. 101), Lee reports the results of the reading proficiency test and the form correction task at pretest time. On p. 99 he presents the results of ANOVAs, comparing the scores of the 4 groups.

1.1 From Table 4, which relationship is apparent between the reading proficiency test results and the form correction task results?

1.2 Looking at the means and standard deviations of the form correction task results in Table 4, what can you conclude about the distribution of the results in the groups?

1.3 Lee writes:
A one-way ANOVA revealed that the four groups were not statistically different from one another in terms of their general reading ability, F(3, 255)=.35, p=.79; nor did they differ from one another in their performance on the form correction task at the onset of the study, F(3, 255) = 1.01, p = .39. (p. 99)
In what way(s) is this statement not completely correct?

Q. 2

On pp. 101 to 103, Lee describes the results of the form correction task.

2.1. On page 102, Lee reports the results of a two-way ANOVA, investigating effects of enhancement and topic familiarity. You can consider this as two separate ANOVAs, one for enhancement and the other for topic familiarity. In your own words, what was the outcome of the ANOVA for topic familiarity?

2.2 Lee shows in Figure 1 that lines of the two +E groups are far steeper than the lines of the two –E groups. What does this indicate?

2.3 In table 6 (p. 103), Lee shows the results of dependent t-tests, comparing pre- and post scores for the four groups. What is the p-value for the +E / -F group?

Q. 3

On pp. 102 to 105, Lee describes the results of the free-recall task. Again running a two-way ANOVA (which you can consider equivalent to two separate ANOVAs), Lee shows that both features, topic familiarity and textual enhancement, significantly affected recall.

3.1 Looking at Table 7, which feature (textual enhancement or topic familiarity) actually hindered recall? How can you tell? (2 points)

3.2 Again looking at Table 7, which feature (textual enhancement or topic familiarity) had the stronger effect? How can you tell? (2 points)

3.3 How do you explain the effects of topic familiarity and textual enhancement on recall?

Q. 4

On p. 105, Lee describes the results of a correlation between scores from the form correction and free recall tasks.

4.1 Was this probably a Pearson or a Spearman correlation? Why? (2 points)

4.2 As Lee shows in Table 8, the correlation for the total population is far lower than the correlation for each of the four groups. How is that possible?

4.3 Lee finds higher correlations between task scores for students who had the unenhanced texts than for students who had enhanced texts. What do you think is the reason for these higher correlations?

Section 2

R. (2004) ran a Test of Idiomatic English (TIE) at two ELICOS institutions in Melbourne: Gumtree Language School and Kangaroo Paw English Institute. The test measured pragmalinguistic knowledge and consisted of three sections (Implicatures, Routines, Speech Acts). 68 students took part.

Q. 1
R. wanted to check whether there was a significant relationship between length of residence in Australia and self-rating of oral proficiency. Length of residence was reported in months, and students self-rated their oral proficiency on a scale of 1-5.

1.1    What statistical procedure would be appropriate to use?

1.2 Why?

Q. 2

Were native languages equally distributed between language schools? A chi-square analysis was conducted to investigate this question.

Crosstabs

2.1    Were languages equally distributed?

2.2    For which two languages was the distribution most unbalanced?

2.3    Why is the result potentially problematic?

Q. 3

Was students’ pragmalinguistic knowledge equal at both language schools? A t-test was conducted with total score as the dependent variable and institution as the independent variable.

T-Test

3.1 Was students’ pragmalinguistic knowledge significantly different between language schools?

3.2 Which group has greater knowledge?

3.3 Was this is a dependent or independent t-test?

Q. 4

What is the relationship between the test sections? The construct assumed the existence of some shared variance with some unique variance. A Pearson correlation was run to check this assumption.

Correlations

4.1 Which sections correlated the least and what was the size of the correlation?

4.2 What was the significance level of the correlation for the sections that correlated the least?

4.3 How much of the variance on the implicature section is accounted for by the speech act section?

4.4 Is the construct’s assumption of some shared variance between sections and some unique variance for each section justified?

Q. 5

Do students at different proficiency levels differ in their performance on the three sections? Test-takers rated themselves on their speaking proficiency on a scale of 1-5, which was collapsed into 3 levels for this analysis. An ANOVA was run to find differences between groups.

Oneway

Post Hoc Tests

Homogeneous Subsets

5.1 On what section(s) did students perform significantly differently depending on their proficiency?

5.2 For the section(s) with significant differences, what was the F-value?

5.3 Which groups differed significantly from each other?

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