kanchana prapphal, chulalongkorn university statistics for language teachers kanchana prapphal may...

Kanchana Prapphal, ChulalongkornUniversity

Statistics for Language Teachers

Kanchana prapphal May 2 3 , 2 0 0 2

Kasetsart University


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)


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


Measures of Central Tendency

• Mode• Median• Arithmetic mean (X = sum X/N)


Measures of Variability

• Range• Variance • Standard deviation• The normal distribution


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


Pearson Correlation Matrix

• ___________________________________________• 1 2 3Tests• ___________________________________________• 1 1000 38. Vocab . . .66

• 2 100 6. Grammar . .0

• 3 100. Sound Perception .• ___________________________________________


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


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

• 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)• 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

• - 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.


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

•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


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

• - Chi square Test• frequency, category, nominal da

ta• Spearman Rank Order Correlation• rank, N < 3 0 , ordinal data


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?


Practice (continued)

• Interpret the following correlation coefficients.• - Structure Listening CU TEP

Spelling• Structure .723** .560 *

-.300*• Listening .840 **

-.010• Spelling• *p< .05 **p< .01



• 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



• 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***.


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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