Statistics for Language Teachers

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Statistics for Language Teachers

• Kanchana prapphal
• May 23, 2002
• Kasetsart University

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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)

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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)

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Measures of Variability

• Range
• Variance
• Standard deviation
• The normal distribution

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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

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Pearson Correlation Matrix

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

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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

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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.

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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

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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

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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 lt .05
• The three groups differed in terms of the test
  form they received.

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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

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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

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Factorial Design

• More than one factor
• Two main effects and one interaction
• Example
• Factors Time limit (Yes, No)
• Item order (syllabus,
  backward, random)
• 23 ANOVA

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Non-parametric Statistical Tests

• Chi-square Test
• frequency, category, nominal data
• Spearman Rank Order Correlation
• rank, N lt 30, ordinal data

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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?

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Practice (continued)

• Interpret the following correlation coefficients.
• Structure Listening
  CU-TEP Spelling
• Structure .723
  .560 -.300
• Listening
  .840 -.010
• Spelling
• plt .05 plt .01
  

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Practice (continued)

• Read the following table.
• Criterion variables
  R
• Aptitude
  AptitudeAffective F
• Reading .792
  .810 6.094
• Listening .723
  .740 3.200
• Writing .570
  .608 5.111
• Speaking .578
  .624 6.182
• plt .01

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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

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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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