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## PowerPoint Slideshow about 'Statistics for Language Teachers' - Olivia

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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)

Frequency Distributions

- Class interval
- Graphic Presentation of Data (Bar graph, Histogram, Frequency Polygon, Line graph)
- Percentage

Measures of Central Tendency

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

Measures of Variability

- Range
- Variance
- Standard deviation
- The normal distribution

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

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

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)

- 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
- *p < .05
- The three groups differed in terms of the test form they 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
- 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

- 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 data
- Spearman Rank Order Correlation
- rank, N < 30, ordinal data

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)

- Interpret the following correlation coefficients.
- Structure Listening CU-TEP Spelling
- Structure .723** .560 * -.300*
- Listening .840 ** -.010
- Spelling
- *p< .05 **p< .01

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 (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

- 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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