ISBN-10:
0470574798
ISBN-13:
2900470574798
Pub. Date:
10/12/2010
Publisher:
Wiley
Fundamentals of Statistical Reasoning in Education / Edition 3

Fundamentals of Statistical Reasoning in Education / Edition 3

by Theodore Coladarci
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  • Product Details

    ISBN-13: 2900470574798
    Publisher: Wiley
    Publication date: 10/12/2010
    Edition description: Older Edition
    Pages: 480
    Product dimensions: 6.00(w) x 1.25(h) x 9.00(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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