Inferential statistical analysis procedures and resources for EAP (Objectives 1A–1D)


Objective 1A: To investigate relationships between two different entities (Bachman, 2004, pp. 80–85; Dörnyei, 2007, pp. 223–225; Gorard, 2001, pp. 167–170).


Correlation coefficients are statistics calculated from data which summarize the strength and direction of the relationship between two variables. Correlation coefficients range between negative one (-1.00) and positive one (+1.00). Positive coefficients indicate direct relationships, while negative coefficients indicate inverse relationships. The larger the coefficient, positive or negative, the stronger the relationship. A correlation near to zero suggests a weak relationship and a correlation near to one (either positive or negative) shows a strong relationship. In EAP, this kind of procedure could be used to calculate the correlation between students’ results in, for example, separate reading and writing tests to ascertain whether there is a correlation between high or low grades in reading and high or low grades in writing.


Pearson product-moment correlation coefficient


This technique requires the relationship between the two variables to be linear; both variables should constitute interval scales and both should be normally distributed. For example, the data below were collected from the results obtained by 28 students, each of whom completed two 50-item tests, one test focusing on academic vocabulary and the other on broader academic reading skills. In each case, the maximum score was 50.


Student S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 Vocab


8 9 15 16 17 19 21 21 21 22 23 24 25 26 Reading 9 7 17 15 18 18 20 19 22 24 46 25 26 25


Student S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 Vocab


26 27 28 29 29 29 30 31 35 36 39 41 43 44 Reading 25 26 30 27 29 28 31 30 32 35 37 40 42 46


Chapter 10: Inferential statistics and applications in EAP assessment


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