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E-raamat: Using Statistics to Make Educational Decisions

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  • Ilmumisaeg: 07-Sep-2011
  • Kirjastus: SAGE Publications Inc
  • Keel: eng
  • ISBN-13: 9781483314686
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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 07-Sep-2011
  • Kirjastus: SAGE Publications Inc
  • Keel: eng
  • ISBN-13: 9781483314686

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An accessible introduction to statistics written specifically for Education students in the changing educational landscape

Government scrutiny and intensified oversight have dramatically changed the landscape of education in recent years. Observers want to know how schools compare, which district is best, which states are spending the most per student on education, whether reforms are making a difference, and why so many students are failing. Some of these questions require technical answers that educators historically redirected to outside experts, but the questions leveled at all educators have become so acute and persistent that they can no longer be outsourced. This text helps educators develop the tools and the conceptual understanding needed to provide definitive answers to difficult statistical questions facing education today.

Arvustused

This text seems to cover the basics of educational decision making. It would make an excellent text for a course preceding the one I am teaching. -- Mack C. Shelley The content is very specific to my design for the course. The book addresses a wide range of prior content affiliation by the student. It reads very well but still provides necessary mathematical rigor for understading the concepts presented...extremely appropriate for most EdD programs and could also function as an excellent transistion from a mathematics, statistical background into the world of research in the social sciences. -- Benjamin Brown

Preface xvii
Acknowledgments xxiii
PART I DEVELOPING A CONTEXT FOR STATISTICAL ANALYSIS
1(40)
1 A Context for Solving Quantitative Problems
3(12)
About Statistics
4(1)
Regarding the Math
5(1)
Answers the Old-Fashioned Way
6(1)
It's Greek to Me!
7(1)
Different Kinds of Statistics
8(1)
Samples and Populations
8(1)
The Connection Between Quantitative Analysis and Research Design
9(1)
Testing Issues
10(1)
Chapter Organization
10(1)
Software and Hardware
11(1)
Studying for Statistics
12(1)
And Finally
13(2)
2 Describing Data
15(26)
The Scale of the Data
16(4)
Nominal Scale Data
17(1)
Ordinal Scale Data
17(1)
Interval Scale Data
18(1)
Ratio Scale Data
19(1)
Descriptive Statistics
20(5)
Measures of Central Tendency
20(1)
The Mode
21(1)
The Median
22(2)
The Mean
24(1)
The Effect of Outliers
25(7)
Measures of Variability
26(1)
The Range
26(1)
Dividing up the Range
27(3)
The Variance
30(2)
Degrees of Freedom
32(9)
The Standard Deviation
33(3)
Looking at SPSS Output
36(1)
A Reminder
36(1)
Other Measures of Variability
36(1)
Another Word About Samples and Populations
37(1)
Summary
37(4)
PART II PRESENTING DATA
41(66)
3 Data Distributions: Picturing Statistics
43(34)
The Frequency Distribution
44(6)
Apparent Versus Actual Limits
47(1)
Guidelines for Developing a Grouped Frequency Distribution
47(2)
Frequencies, Relative Frequencies, and Cumulative Relative Frequencies
49(1)
Stem-and-Leaf Displays
50(2)
Interpreting Tables and Figures
52(1)
Preparing Data Figures
53(17)
Pie Charts
53(2)
Bar Charts
55(1)
Histograms
56(1)
Frequency Polygons
57(2)
The Normal Distribution
59(1)
Central Tendency and Normality
60(2)
Why Do We Care?
62(3)
The Standard Deviation and Normality
65(2)
s = 1/6th R
67(3)
Determining What Is Representative
70(2)
Summary
72(5)
4 Working With the Normal Curve: z Scores
77(30)
The z Distribution
78(4)
Calculating z Scores
79(1)
Interpreting z
79(1)
Determining the "Best" Performance
80(2)
z and the Percent of the Population Under the Curve
82(1)
Table A
82(1)
Extending z Scores
83(1)
From z to Percentiles
84(2)
Probabilities and Percentages
86(2)
The Probability of Scoring Between Two Points
88(5)
Two Values on Opposite Sides of the Mean
88(2)
Two Values on the Same Side of the Mean
90(1)
The Percentage of the Distribution Outside an Interval
91(1)
Rules for Determining the Percentage of the Population Under Areas of the Curve
91(2)
Using SPSS
93(1)
From Percentages to z Scores
94(1)
Working Backward From z
94(2)
Other Standard Scores
96(7)
The T Score
96(1)
The Normal Curve Equivalent
97(1)
The Standard Nine-Point Scale
98(2)
The Nonstandard Grade Equivalent Score
100(1)
Standard Scores With Specified Characteristics
101(2)
Summary
103(4)
PART III EXAMINING DIFFERENCES
107(146)
5 Probability and the Normal Distribution
109(30)
A Little Review
110(1)
The Distribution of Sample Means
110(5)
The Central Limit Theorem
111(3)
Sampling Error and the Law of Large Numbers
114(1)
The Effect of Extreme Scores
114(1)
Describing the Distribution of Sample Means
115(1)
The z Test
116(3)
Deriving the Values for the z Test
117(1)
Calculating the z Test
118(1)
Representativeness and Statistical Significance
119(4)
Back to the Gaussian Distribution
121(1)
Mr. Forsythe's Question
121(1)
Another Example
122(1)
Probability, the Alpha Level, and Decision Errors
123(4)
Decision Errors Continued
125(1)
On the Horns of a Dilemma
126(1)
Who Decides? Determining Statistical Significance
127(1)
Confidence Intervals
127(2)
Calculating the Confidence Interval
128(1)
Interpreting the Confidence Interval
129(1)
Sample Size and Confidence
129(4)
Convenience Samples
133(1)
Summary
133(6)
6 t for One, or Two
139(34)
A Little History
139(1)
From the z Test to the One-Sample t-Test
140(5)
The Estimated Standard Error of the Mean, SEm
141(1)
The One-Sample t-Test
142(1)
Interpreting the t Value
142(1)
Degrees of Freedom and the t Distribution
143(2)
Inferential Statistics
145(2)
Looking at SPSS Output
147(1)
The Independent t-Test
148(7)
The Distribution of Difference Scores
149(1)
The Logic of the Independent t-Test
149(1)
The Test Statistic
149(2)
Calculating the Independent t
151(1)
Interpreting the t Statistic
151(1)
SEd for Unequal Samples
152(1)
Another t-Test Example
152(1)
The Sign of t
153(1)
Harmony Among the Tests
154(1)
Looking at SPSS Output
155(1)
The Confidence Interval of the Difference
156(1)
Research Design
157(2)
The Scale of the Independent and Dependent Variables
159(1)
Hypothesis Testing
159(2)
Two-, Versus One-Tailed Tests
161(2)
The Risk of Using One-Tailed Tests
163(1)
Tails Versus Samples
163(1)
Requirements for Independent t-Tests
163(1)
A Reminder About Decision Errors
164(3)
Power and Statistical Testing
164(1)
Practical Significance
165(2)
Summary
167(6)
7 One-Way Analysis of Variance
173(26)
A Context for Analysis of Variance
174(3)
A Look Backward
175(1)
The Advantages of Analysis of Variance
175(2)
The One-Way ANOVA
177(17)
The Hypotheses
178(1)
The Sources of Variance
179(1)
The Total Sum of Squares
179(3)
The Between and Within Sums of Squares
182(4)
Interpreting the Variability Measures
186(1)
Degrees of Freedom and the ANOVA
186(1)
The F Ratio
187(1)
The Critical Values of F
188(1)
The ANOVA Table
188(1)
Understanding the Calculated Value of F
189(1)
The Post-Hoc Test
189(2)
The Effect Size
191(1)
Requirements for the One-Way ANOVA
192(2)
Looking at SPSS Output
194(1)
Summary
194(5)
8 The Factorial ANOVA
199(22)
Limitations in the Independent t-Test and One-Way ANOVA
199(2)
The Factorial ANOVA
201(17)
Describing the Factorial ANOVA
202(1)
How Many Variables?
203(1)
The Components of SSbet
203(1)
Calculating the SSbet Components
204(2)
The First Factor
206(1)
The Second IV
206(1)
The Within Sum of Squares (SSwith)
207(2)
The Interaction
209(1)
The Results
210(1)
Checking Results
210(1)
The Degrees of Freedom for a Factorial ANOVA
210(1)
The F Ratios
210(1)
The ANOVA Table
211(1)
The Post-Hoc Test
212(1)
Using a Graph to Explain the Interaction
212(3)
The Effect Sizes
215(2)
Looking at SPSS Output
217(1)
Summary
218(3)
9 Dependent Groups Tests for Interval Data
221(32)
Working Backward to Move Forward
221(1)
Statistical Power and the Standard Error of the Difference
222(1)
The Dependent Samples t-Tests
223(12)
The Matched Pairs Design
224(1)
Interpreting Result
225(1)
Calculating the t Statistic
225(1)
An Example
226(1)
Interpreting the Result
227(1)
The Give and Take of the Before/After t
228(1)
A Matched Pairs Design
228(2)
The Dependent Samples t-Test Versus the Independent t
230(2)
Looking at SPSS Output
232(3)
The Within-Subjects F
235(11)
The Difficulty of Matching Multiple Groups
235(1)
Examining Sources of Variability
236(1)
Calculating the Within-Subjects F
237(1)
Summarizing the Results
238(1)
Interpreting the F Value
239(1)
Another Within-Subjects F Example
240(1)
Locating Significant Differences
241(1)
How Much of the Variance Is Explained?
242(1)
Comparing the Within-Subjects F With the One-Way ANOVA
243(1)
A Comment on the Within-Subjects F and SPSS
244(2)
Summary
246(7)
PART IV ASSOCIATION AND PREDICTION
253(76)
10 Correlation
255(30)
A Context for Correlation
255(1)
A Little History
256(1)
What Correlation Offers
257(1)
The Scatter Plot
258(3)
Variations on the Correlation Theme
261(1)
The Pearson Correlation
262(12)
The Correlation Hypotheses
267(1)
Looking at SPSS Output
267(2)
Assumptions and Attenuated Range
269(1)
Interpreting the Correlation Coefficient: Direction and Strength
270(1)
Regarding the Strength of the Correlation
270(2)
The Coefficient of Determination
272(1)
The Correlation Coefficient Versus the Coefficient of Determination
273(1)
Significance and Sample Size
273(1)
The Point-Biserial Correlation
274(3)
Another Thought on Interpreting Correlation Values
277
Nonparametric Correlations
276(1)
A Partial List of Bivariate Correlations
276(3)
Summary
279(6)
11 Regression With One Predictor
285(22)
Regression Analysis
286(9)
Back to Scatter Plots
288(2)
The Least Squares Criterion
290(1)
The Regression Equation With One Predictor
290(1)
Calculating the Intercept and the Slope
291(1)
Interpreting the Slope
292(1)
Interpreting the Intercept
292(2)
Regress Which Variable on Which?
294(1)
Prediction Errors
295(8)
Calculating the Standard Error of the Estimate
296(1)
Understanding the SEest
297(1)
Another Example of Calculating SEest
297(1)
A Confidence Interval for the Estimate of y
298(2)
From the Top
300(2)
Looking at SPSS Output
302(1)
Summary
303(4)
12 Regression With More Than One Predictor
307(22)
Multiple Regression
307(18)
Multiple R, or Multiple Correlation
308(1)
Calculating Multiple R
308(2)
Another Multiple R Problem
310(1)
The Second Problem
311(1)
Partial Correlation
311(2)
Making the Application to Regression
313(1)
The Multiple Regression Equation
313(4)
Using Multiple Regression
317(3)
A Comment About SPSS Output
320(1)
The Standard Error of the Multiple Estimate
320(2)
The Confidence Interval for v'
322(1)
Another Confidence Interval Example
323(1)
Overfitting the Data and Shrinkage
324(1)
Significance Tests
324(1)
Summary
325(4)
PART V TESTS FOR NOMINAL AND ORDINAL DATA
329(58)
13 Some of the Chi-Square Tests
331(24)
The Chi-Square Tests
332(10)
The Goodness-of-Fit Chi-Square
333(1)
Calculating the Test Statistic
334(1)
The Chi-Square Hypotheses
335(1)
Interpreting the Test Statistic
336(1)
A1xk (Goodness-of-Fit) Chi-Square Problem With Unequal fe Values
337(1)
Calculating fe Values for Unequal Categories
337(2)
Interpreting the Results
339(1)
Another 1 x k Problem With Equal Categories
339(1)
The Chi-Square and Statistical Power
339(2)
Looking at SPSS Output
341(1)
The Chi-Square Test of Independence
342(1)
An Example Problem
343(8)
The Contingency Table
343(2)
The fo and fe Values in the Chi-Square Test of Independence
345(1)
Degrees of Freedom for the Chi-Square Test of Independence
345(1)
The Yates Correction
346(1)
Interpreting the Chi-Square Test of Independence
346(1)
Phi Coefficient and Cramer's V
346(1)
Phi Coefficient
347(1)
Cramer's V
347(1)
Another Example of the Test of Independence
348(2)
Looking at SPSS Output
350(1)
Summary
351(4)
14 Working With Ordinal, More-, or Less-Than Data
355(32)
A Little History
356(1)
The Hypothesis of Association for Ordinal Data: Spearman's rho
356(7)
The Formula
357(1)
Calculating rho
358(2)
Interpreting Spearman's rho
360(1)
Looking at SPSS Output
361(2)
The Hypothesis of Difference for Ordinal Data
363(14)
Two Independent Groups: Mann-Whitney U
364(1)
Calculating the Mann-Whitney U
364(1)
An Example
365(2)
The Mann-Whitney and Power
367(1)
Looking at SPSS Output for Mann-Whitney
367(1)
Two or More Independent Groups: Kruskal-Wallis H
368(1)
Calculating the Kruskal-Wallis H
368(1)
An Example
369(2)
Looking at SPSS Output for Kruskal-Wallis
371(1)
Two Related Groups: Wilcoxon T
371(1)
Calculating the Wilcoxon T
372(1)
Interpreting the Test Statistic, T
373(1)
Two or More Related Groups: Friedman's ANOVA
373(2)
A Friedman's ANOVA Example
375(2)
Interpreting the Test Value
377(1)
Keeping It All Straight
377(3)
Summary
380(7)
PART VI TESTS, MEASUREMENT ISSUES, AND SELECTED ADVANCED TOPICS
387(60)
15 Testing Issues
389(32)
Classical Test Theory
390(1)
Score Reliability
391(4)
The Relationship Between Reliability and Measurement Error
391(1)
Calculating Reliability: An Example
392(2)
Alternate Forms Reliability
394(1)
What's a High Reliability Coefficient?
394(1)
Expanding Reliability
394(1)
The Spearman-Brown Prophecy Formula
395(1)
Other Applications for Spearman-Brown
396(1)
Lee Cronbach
397(9)
Cronbach's Alpha
398(1)
Calculating Coefficient Alpha
399(2)
Looking at SPSS Output
401(1)
The Kuder and Richardson Formulae
401(1)
Score Versus Test Reliability
402(2)
Strengthening Reliability
404(1)
Classification Consistency
404(2)
The Standard Error of Measurement
406(2)
Interpreting SEM
407(1)
Reliability for the Group Versus the Individual
408(1)
Score Validity
408(1)
The Most Tested Generation
409(6)
Bias in Admissions Testing
409(1)
An Example
410(2)
Another Point of View
412(2)
Teaching the Test
414(1)
Summary
415(6)
16 A Brief Introduction to Selected Advanced Topics
421(26)
Analysis of Covariance
422(5)
An ANCOVA Example
423(1)
Understanding the Results: The Covariate
424(1)
The Independent Variable
425(1)
Another ANCOVA Example
425(1)
Some Final Considerations
426(1)
Multivariate Analysis of Variance
427(5)
Combining the Dependent Variables
427(1)
A MANOVA Example
427(2)
Understanding MANOVA Results
429(2)
MANOVA Variations
431(1)
Another MANOVA Example
431(1)
Some Final Considerations
431(1)
Discriminant Function Analysis
432(5)
A dfa Example
433(1)
Understanding dfa Output
434(2)
Another dfa Example
436(1)
Some Final Considerations
436(1)
Other Procedures
437(7)
Regression Methods
437(1)
A Forward Regression Solution
438(1)
A Backward Regression Solution
438(1)
A Stepwise Regression Solution
438(1)
A Hierarchical Regression Solution
439(1)
Canonical Correlation
439(1)
Factor Analysis
440(1)
Cluster Analysis
441(1)
Path Analysis
441(3)
Summary
444(3)
Glossary
447(10)
Appendices
457(52)
Tables of Critical Values
458(15)
A Primer in SPSS
473(26)
Solutions to Selected Problems
499(10)
Index 509(14)
About the Author 523
David Tanner is a Professor in the Department of Educational Research and Administration at California State University, Fresno, where he was the Department Chair from 1990-1995. He received his Ph.D. in Curriculum and Instruction/Measurement from Texas A&M University, and his areas of interest include educational psychology; statistics and measurement; educational research; quantitative and qualitative evaluation; assessing student achievement; evaluating classroom assessment instruments; and evaluating the performance of teachers and teacher candidates. He has authored several journal articles and the textbook Assessing Academic Achievement (©2001).