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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

Statistics for Language Teachers

Kanchana prapphal

May 23, 2002

Kasetsart University

contents
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)
frequency distributions
Frequency Distributions
  • Class interval
  • Graphic Presentation of Data (Bar graph, Histogram, Frequency Polygon, Line graph)
  • Percentage
measures of central tendency
Measures of Central Tendency
  • Mode
  • Median
  • Arithmetic mean (X = sum X/N)
measures of variability
Measures of Variability
  • Range
  • Variance
  • Standard deviation
  • The normal distribution
correlation
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
pearson correlation matrix
Pearson Correlation Matrix
  • ___________________________________________
  • Tests 1 2 3
  • ___________________________________________
  • 1. Vocab 1.000 .38 .66
  • 2. Grammar 1.00 .60
  • 3. Sound Perception 1.00
  • ___________________________________________
regression bivariate
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
regression multiple variables
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.
inferential statistics
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
t test for one factor with 2 groups
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
f test
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.
two way anova
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
three way anova
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
factorial design
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
non parametric statistical tests
Non-parametric Statistical Tests
  • Chi-square Test
  • frequency, category, nominal data
  • Spearman Rank Order Correlation
  • rank, N < 30, ordinal data
practice
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?
practice continued
Practice (continued)
  • Interpret the following correlation coefficients.
  • Structure Listening CU-TEP Spelling
  • Structure .723** .560 * -.300*
  • Listening .840 ** -.010
  • Spelling
  • *p< .05 **p< .01
practice continued1
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
practice continued2
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***
research questions
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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