Kanchana Prapphal, ChulalongkornUniversity
Statistics for Language Teachers
Kanchana prapphal May 2 3 , 2 0 0 2
Kasetsart University
Kanchana Prapphal, ChulalongkornUniversity
Contents
• Descriptive Statistics (Frequency Dis tributions, Measures of Central Tend
ency, Measures of Variability)• Correlation and Regression• Inferential Statistics - -(t test, F test)• - Non parametric Statistical Tests (Chi
- square Test, Spearman Rank OrderCorrelation)
Kanchana Prapphal, ChulalongkornUniversity
Frequency Distributions
• Class interval• Graphic Presentation of Data (Bar
graph, Histogram, Frequency Polygon, Line graph)
• Percentage0
20
40
60
80
100
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
East
West
North
Kanchana Prapphal, ChulalongkornUniversity
Measures of Central Tendency
• Mode• Median• Arithmetic mean (X = sum X/N)
Kanchana Prapphal, ChulalongkornUniversity
Measures of Variability
• Range• Variance • Standard deviation• The normal distribution
Kanchana Prapphal, ChulalongkornUniversity
Correlation
• 2Relationship between variables• :• +.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, ChulalongkornUniversity
Pearson Correlation Matrix
• ___________________________________________• 1 2 3Tests• ___________________________________________• 1 1000 38. Vocab . . .66
• 2 100 6. Grammar . .0
• 3 100. Sound Perception .• ___________________________________________
Kanchana Prapphal, ChulalongkornUniversity
Regression (Bivariate)
• 2Prediction of the relationship between variablee
• e e = + 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, ChulalongkornUniversity
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, ChulalongkornUniversity
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, ChulalongkornUniversity
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, ChulalongkornUniversity
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• * 05p < .• The three groups differed in terms of the test form th
ey received.
Kanchana Prapphal, ChulalongkornUniversity
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, ChulalongkornUniversity
Three-Way ANOVA
•7Fs• e eee eeeeeee3• - 3 first order interactions (AxB, AxC,
BxC)• - 1 second order interaction (AxBxC)• eeeeeeee ee eeeeeeeeee ee eeeee e
et hods of t eachi ng Engl i sh
Kanchana Prapphal, ChulalongkornUniversity
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, ChulalongkornUniversity
Non-parametric Statistical Tests
• - Chi square Test• frequency, category, nominal da
ta• Spearman Rank Order Correlation• rank, N < 3 0 , ordinal data
Kanchana Prapphal, ChulalongkornUniversity
Practice
• tests mean % sd items• 3157 4209 15structure . ( . ) .
05 75
• 1933 3866 84listening . ( . ) . 3 50
• - 4454 4454 163CU TEP . ( . ) . 6 100
• ee eee eeeeeee eeeee?• Which is the most difficult test?• What do you learn from the standard deviations of t
he 3 tests?
Kanchana Prapphal, ChulalongkornUniversity
Practice (continued)
• Interpret the following correlation coefficients.• - Structure Listening CU TEP
Spelling• Structure .723** .560 *
-.300*• Listening .840 **
-.010• Spelling• *p< .05 **p< .01
Kanchana Prapphal, ChulalongkornUniversity
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
Kanchana Prapphal, ChulalongkornUniversity
Practice (continued)
• Source df MS F• 1 43935Instructional methods (A) .485*
• Subject matters (B) 1 67.33• Science interest levels (C) 1 1.13• 1 111694A x B .
1234**.• 1 11183A x C .• 1 22592B x C .• e e e ee e 17600 3
839***.
Kanchana Prapphal, ChulalongkornUniversity
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, ChulalongkornUniversity