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
100
80
60
East
40
West
20
North
0
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
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
2
3
• ________________________________
___________
• 1. Vocab 1.000 .38
.66
• 2. Grammar
1.00
.60
• 3. 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 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.
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 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?
Kanchana Prapphal, Chulalongkorn University
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, Chulalongkorn University
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**
Kanchana Prapphal, Chulalongkorn University
Practice (continued)
•
•
•
•
•
•
•
•
Source
df
Instructional methods (A) 1
Subject matters (B)
1
Science interest levels (C) 1
AxB
1
AxC
1
BxC
1
AxBxC
1
MS
F
439.35 4.85*
67.33
1.13
1116.94 12.34**
111.83
225.92
760.03
8.39***
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
Kanchana Prapphal, Chulalongkorn University