Fundamentals of Statistical Reasoning in Education / Edition 22

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Overview

A statistics text specifically geared towards the education community. This text gives educators the statistical knowledge and skills necessary in everyday classroom teaching, in running schools, and in professional development pursuits. It emphasises conceptual development with an engaging style and clear exposition.

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Product Details

  • ISBN-13: 9780470084069
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 6/22/2007
  • Edition description: REV
  • Edition number: 22
  • Pages: 480
  • Product dimensions: 7.40 (w) x 9.10 (h) x 0.80 (d)

Table of Contents


Introduction     1
Why Statistics?     1
Descriptive Statistics     2
Inferential Statistics     3
The Role of Statistics in Educational Research     4
Variables and Their Measurement     5
Some Tips on Studying Statistics     9
Descriptive Statistics     13
Frequency Distributions     15
Why Organize Data?     15
Frequency Distributions for Quantitative Variables     15
Grouped Scores     17
Some Guidelines for Forming Class Intervals     18
Constructing a Grouped-Data Frequency Distribution     19
The Relative Frequency Distribution     21
Exact Limits     22
The Cumulative Percentage Frequency Distribution     24
Percentile Ranks     25
Frequency Distributions for Qualitative Variables     27
Summary     28
Graphic Representation     37
Why Graph Data?     37
Graphing Qualitative Data: The Bar Chart     37
Graphing Quantitative Data: The Histogram     38
The Frequency Polygon     42
Comparing Different Distributions     43
Relative Frequency and Proportional Area     44
Characteristics of Frequency Distributions     46
The Box Plot     49
Summary     51
Central Tendency     59
The Concept of Central Tendency     59
The Mode     59
The Median     60
The Arithmetic Mean     62
Central Tendency and Distribution Symmetry     64
Which Measure of Central Tendency to Use?     66
Summary     67
Variability     75
Central Tendency Is Not Enough: The Importance of Variability     75
The Range     76
Variability and Deviations from the Mean     77
The Variance     78
The Standard Deviation     79
The Predominance of the Variance and Standard Deviation     81
The Standard Deviation and the Normal Distribution     81
Comparing Means of Two Distributions: The Relevance of Variability     82
In the Denominator: n vs. n - 1     85
Summary     85
Normal Distributions and Standard Scores     91
A Little History: Sir Francis Galton and the Normal Curve     91
Properties of the Normal Curve     92
More on the Standard Deviation and the Normal Distribution      93
z Scores     95
The Normal Curve Table     97
Finding Area When the Score Is Known     99
Reversing the Process: Finding Scores When the Area Is Known     102
Comparing Scores from Different Distributions     104
Interpreting Effect Size     105
Percentile Ranks and the Normal Distribution     107
Other Standard Scores     108
Standard Scores Do Not "Normalize" a Distribution     110
The Normal Curve and Probability     110
Summary     111
Correlation     119
The Concept of Association     119
Bivariate Distributions and Scatterplots     119
The Covariance     124
The Pearson r     130
Computation of r: The Calculating Formula     133
Correlation and Causation     135
Factors Influencing Pearson r     136
Judging the Strength of Association: r[superscript 2]     139
Other Correlation Coefficients     141
Summary     142
Regression and Prediction     149
Correlation versus Prediction     149
Determining the Line of Best Fit     150
The Regression Equation in Terms of Raw Scores      153
Interpreting the Raw-Score Slope     156
The Regression Equation in Terms of z Scores     157
Some Insights Regarding Correlation and Prediction     158
Regression and Sums of Squares     161
Measuring the Margin of Prediction Error: The Standard Error of Estimate     163
Correlation and Causality (Revisited)     168
Summary     169
Inferential Statistics     179
Probability and Probability Distributions     181
Statistical Inference: Accounting for Chance in Sample Results     181
Probability: The Study of Chance     182
Definition of Probability     183
Probability Distributions     185
The Or/addition Rule     187
The And/multiplication Rule     188
The Normal Curve as a Probability Distribution     189
"So What?" Probability Distributions as the Basis for Statistical Inference     192
Summary     192
Sampling Distributions     197
From Coins to Means     197
Samples and Populations     198
Statistics and Parameters     199
Random Sampling Model     200
Random Sampling in Practice     202
Sampling Distributions of Means     202
Characteristics of a Sampling Distribution of Means     204
Using a Sampling Distribution of Means to Determine Probabilities     207
The Importance of Sample Size (n)     211
Generality of the Concept of a Sampling Distribution     212
Summary     213
Testing Statistical Hypotheses about [Mu] When [sigma] Is Known: The One-Sample z Test     221
Testing a Hypothesis about [Mu]: Does "Homeschooling" Make a Difference?     221
Dr. Meyer's Problem in a Nutshell     222
The Statistical Hypotheses: H[subscript 0] and H[subscript 1]     223
The Test Statistic z     225
The Probability of the Test Statistic: The p Value     226
The Decision Criterion: Level of Significance ([alpha])     227
The Level of Significance and Decision Error     229
The Nature and Role of H[subscript 0] and H[subscript 1]     231
Rejection versus Retention of H[subscript 0]     232
Statistical Significance versus Importance     233
Directional and Nondirectional Alternative Hypotheses     235
Prologue: The Substantive versus the Statistical     237
Summary     239
Estimation     247
Hypothesis Testing versus Estimation      247
Point Estimation versus Interval Estimation     248
Constructing an Interval Estimate of [Mu]     249
Interval Width and Level of Confidence     252
Interval Width and Sample Size     253
Interval Estimation and Hypothesis Testing     253
Advantages of Interval Estimation     255
Summary     256
Testing Statistical Hypotheses about [Mu] When [sigma] Is Not Known: The One-Sample t Test     263
Reality: [sigma] Often Is Unknown     263
Estimating the Standard Error of the Mean     264
The Test Statistic t     266
Degrees of Freedom     267
The Sampling Distribution of Student's t     268
An Application of Student's t     270
Assumption of Population Normality     272
Levels of Significance versus p Values     273
Constructing a Confidence Interval for [Mu] When [sigma] Is Not Known     275
Summary     275
Comparing the Means of Two Populations: Independent Samples     283
From One Mu to Two     283
Statistical Hypotheses     284
The Sampling Distribution of Differences Between Means     285
Estimating [Characters not reproducible]     288
The t Test for Two Independent Samples     289
Testing Hypotheses about Two Independent Means: An Example     290
Interval Estimation of [Mu subscript 1] - [Mu subscript 2]     293
Appraising the Magnitude of a Difference: Measures of Effect Size for X[subscript 1]-X[subscript 2]     295
How Were Groups Formed? The Role of Randomization     299
Statistical Inferences and Nonstatistical Generalizations     300
Summary     301
Comparing the Means of Dependent Samples     309
The Meaning of "Dependent"     309
Standard Error of the Difference Between Dependent Means     310
Degrees of Freedom     312
The t Test for Two Dependent Samples     312
Testing Hypotheses about Two Dependent Means: An Example     315
Interval Estimation of [Mu subscript D]     317
Summary     318
Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance     327
Comparing More Than Two Groups: Why Not Multiple t Tests?     327
The Statistical Hypotheses in One-Way ANOVA     328
The Logic of One-Way ANOVA: An Overview     329
Alison's Reply to Gregory     332
Partitioning the Sums of Squares     333
Within-Groups and Between-Groups Variance Estimates     337
The F Test     337
Tukey's "HSD" Test     339
Interval Estimation of [Mu subscript i] - [Mu subscript j]     342
One-Way ANOVA: Summarizing the Steps     343
Estimating the Strength of the Treatment Effect: Effect Size ([Omega superscript 2])     345
ANOVA Assumptions (and Other Considerations)     346
Summary     347
Inferences about the Pearson Correlation Coefficient     357
From [Mu] to [rho]     357
The Sampling Distribution of r When [rho] = 0     357
Testing the Statistical Hypothesis That [rho] = 0     359
An Example     359
Table E     361
The Role of n in the Statistical Significance of r     363
Statistical Significance versus Importance (Again)     364
Testing Hypotheses Other Than [rho] = 0     364
Interval Estimation of [rho]     365
Summary     367
Making Inferences from Frequency Data     375
Frequency Data versus Score Data     375
A Problem Involving Frequencies: The One-Variable Case     376
X[superscript 2]: A Measure of Discrepancy Between Expected and Observed Frequencies     377
The Sampling Distribution of X[superscript 2]     379
Completion of the Voter Survey Problem: The X[superscript 2] Goodness-of-Fit Test     380
The X[superscript 2] Test of a Single Proportion     381
Interval Estimate of a Single Proportion     383
When There Are Two Variables: The X[superscript 2] Test of Independence     385
Finding Expected Frequencies in the Two-Variable Case     386
Calculating the Two-Variable X[superscript 2]     387
The X[superscript 2] Test of Independence: Summarizing the Steps     389
The 2 x 2 Contingency Table     390
Testing a Difference Between Two Proportions     391
The Independence of Observations     391
X[superscript 2] and Quantitative Variables     392
Other Considerations     393
Summary     393
Statistical "Power" (and How to Increase It)     403
The Power of a Statistical Test     403
Power and Type II Error     404
Effect Size (Revisited)     405
Factors Affected Power: The Effect Size     406
Factors Affecting Power: Sample Size     407
Additional Factors Affecting Power     408
Significance versus Importance     410
Selecting an Appropriate Sample Size      410
Summary     414
References     419
Review of Basic Mathematics     421
Introduction     421
Symbols and Their Meaning     421
Arithmetic Operations Involving Positive and Negative Numbers     422
Squares and Square Roots     422
Fractions     423
Operations Involving Parentheses     424
Approximate Numbers, Computational Accuracy, and Rounding     425
Answers to Selected End-of-Chapter Problems     426
Statistical Tables     448
Index     461
Useful Formulas     479
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