Kanchana Prapphal, Chulalongkorn University Statistics for Language Teachers Kanchana prapphal May 23, 2002 Kasetsart University

Kanchana Prapphal, Chulalongkorn University 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)

Kanchana Prapphal, Chulalongkorn University Frequency Distributions Class interval Graphic Presentation of Data (Bar graph, Histogram, Frequency Polygon, Line graph) Percentage

Kanchana Prapphal, Chulalongkorn University Measures of Central Tendency Mode Median Arithmetic mean (X = sum X/N)

Kanchana Prapphal, Chulalongkorn University Measures of Variability Range Variance Standard deviation The normal distribution

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University Pearson Correlation Matrix ________________________________ ___________ Tests ________________________________ ___________ 1. Vocab Grammar Sound Perception 1.00 ________________________________ ___________

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University 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.

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University F-test One-way ANOVA (with more than two groups) The ANOVA Summary Table Source df SS MS F Test formats * Within groups Total *p <.05 The three groups differed in terms of the test form they received.

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University 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

Kanchana Prapphal, Chulalongkorn University Non-parametric Statistical Tests Chi-square Test frequency, category, nominal data Spearman Rank Order Correlation rank, N < 30, ordinal data

Kanchana Prapphal, Chulalongkorn University Practice tests mean % sd items structure (42.09) listening (38.66) CU-TEP (44.54) Which is the easiest test? Which is the most difficult test? What do you learn from the standard deviations of the 3 tests?

Kanchana Prapphal, Chulalongkorn University Practice (continued) Interpret the following correlation coefficients. Structure Listening CU-TEP Spelling Structure.723**.560 * -.300* Listening.840 ** Spelling *p<.05 **p<.01

Kanchana Prapphal, Chulalongkorn University Practice (continued) Read the following table. Criterion variables R Aptitude Aptitude+Affective F Reading ** Listening ** Writing ** Speaking ** **p<.01

Kanchana Prapphal, Chulalongkorn University Practice (continued) Source df MS F Instructional methods (A) * Subject matters (B) Science interest levels (C) A x B ** A x C B x C A x B x C ***

Kanchana Prapphal, Chulalongkorn University 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?

Kanchana Prapphal, Chulalongkorn University