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Statistics for Language Teachers

Statistics for Language Teachers. Kanchana prapphal May 23, 2002 Kasetsart University. Contents. Descriptive Statistics (Frequency Distributions, Measures of Central Tendency, Measures of Variability) Correlation and Regression Inferential Statistics (t-test, F-test)

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Statistics for Language Teachers

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  1. Statistics for Language Teachers Kanchana prapphal May 23, 2002 Kasetsart University

  2. Contents • Descriptive Statistics (Frequency Distributions, Measures of Central Tendency, Measures of Variability) • Correlation and Regression • Inferential Statistics (t-test, F-test) • Non-parametric Statistical Tests (Chi-square Test, Spearman Rank Order Correlation)

  3. Frequency Distributions • Class interval • Graphic Presentation of Data (Bar graph, Histogram, Frequency Polygon, Line graph) • Percentage

  4. Measures of Central Tendency • Mode • Median • Arithmetic mean (X = sum X/N)

  5. Measures of Variability • Range • Variance • Standard deviation • The normal distribution

  6. Correlation • Relationship between 2 variables • Interpretation: • +.95, +.93, +.87, +.85 = high positive correlation • +.23, +.20, +.18, +.17 = low positive correlation • +.02, +.01, .00, -.03 = no systematic correlation • -.21, -.22, -.17, -.19 = low negative correlation • -.92, -.89, -.90, -.93 = high negative correlation

  7. Pearson Correlation Matrix • ___________________________________________ • Tests 1 2 3 • ___________________________________________ • 1. Vocab 1.000 .38 .66 • 2. Grammar 1.00 .60 • 3. Sound Perception 1.00 • ___________________________________________

  8. Regression (Bivariate) • Prediction of the relationship between 2 variables • y = a + bx • y = the predicted college GPA • a = constant or the point at which the regression line intersects the y axis • b = the slope of the regression line,I.e. the amount of y is increasing for each increase of one unit in x • x = the x value used to predict y

  9. Regression (Multiple Variables) • Multiple regression prediction equation • y = a + bx1 + bx2 + bx3 • y = the predicted college GPA • x1 = the high school GPA • x2 = the score on the entrance exam • x3 = the absence rate in high school • y = 2.80 = He would be predicted to obtain a B- average in his first quarter of college work.

  10. Inferential Statistics • T-test (independent samples, correlated samples) • F-test • One-way analysis of variance (ANOVA) • Factorial analysis of variance • -two-way ANOVA • -three-way ANOVA • -factorial design

  11. T-test (for one factor with 2 groups) • A. Independent samples e.g. • An experiment between a control group and an experimental group • B. Dependent or correlated samples e.g. • The difference between the pre-test and the post-test

  12. F-test • One-way ANOVA (with more than two groups) • The ANOVA Summary Table • Source df SS MS F • Test formats 2 16 8 4* • Within groups 15 30 2 • Total 17 46 • *p < .05 • The three groups differed in terms of the test form they received.

  13. Two-Way ANOVA • 3 Fs • 2 main effects (two factors or two independent variables) • 1 interaction (the effect the dependent variable of the two independent variables operating together) • Example: an experiment of two methods of teaching English

  14. Three-Way ANOVA • 7Fs • 3 main effects • 3 first-order interactions (AxB, AxC, BxC) • 1 second-order interaction (AxBxC) • Example: an experiment on three methods of teaching English

  15. Factorial Design • More than one factor • Two main effects and one interaction • Example: • Factors = Time limit (Yes, No) • Item order (syllabus, backward, random) • 2*3 ANOVA

  16. Non-parametric Statistical Tests • Chi-square Test • frequency, category, nominal data • Spearman Rank Order Correlation • rank, N < 30, ordinal data

  17. Practice • tests mean % sd items • structure 31.57 (42.09) 15.05 75 • listening 19.33 (38.66) 8.43 50 • CU-TEP 44.54 (44.54) 16.36 100 • Which is the easiest test? • Which is the most difficult test? • What do you learn from the standard deviations of the 3 tests?

  18. Practice (continued) • Interpret the following correlation coefficients. • Structure Listening CU-TEP Spelling • Structure .723** .560 * -.300* • Listening .840 ** -.010 • Spelling • *p< .05 **p< .01

  19. Practice (continued) • Read the following table. • Criterion variables R • Aptitude Aptitude+Affective F • Reading .792 .810 6.094** • Listening .723 .740 3.200** • Writing .570 .608 5.111** • Speaking .578 .624 6.182** • **p< .01

  20. Practice (continued) • Source df MS F • Instructional methods (A) 1 439.35 4.85* • Subject matters (B) 1 67.33 • Science interest levels (C) 1 1.13 • A x B 1 1116.94 12.34** • A x C 1 111.83 • B x C 1 225.92 • A x B x C 1 760.03 8.39***

  21. Research Questions • Is there a significant relationship between X and Y? • Do A, B, and C have any effect on Y? • Which method (A or B) is better for first-year Arts students? • Can field trips, case studies and mini-theses predict career success of graduate students?

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