Statistical Methods in Education and Psychology

This book is intended for use in the elementary statistics course in Educa­ tion or in Psychology. While it is primarily designed for use in the first semester of a two-semester course, it may also be used in a one-semester course. There are not five or ten competing texts; the number is much closer to fifty or a hundred. Why, then, should we write still another one? A new statistics text for use in Education and Psychology is, to some slight extent, comparable to a new translation or edition of the Bible. Most of it has been said before-but this time with a difference. The present writers realize that elementary statistics students know very little about the subject-even the meaning of I is all Greek to them. This text covers the basic course in depth, with examples using real data from the real world. It, of course, contains the usual reference tables and several new ones; it gives the appropriate formulas every time; and it accurately depicts all graphs. It is so comprehensive that if instructors can't find their own special areas of interest covered, then those interests probably don't belong in a basic text.

1 The Nature of Statistical Methods.- General Interest in Numbers.- The Purposes of Statistical Methods.- Preview of This Text.- Rounding, Significant Figures, and Decimals.- Supplement 1.- Rounding.- 2 Averages.- Raw Data.- The Mean Computed from Raw Data.- Grouping of Data.- The Mean Computed from Grouped Data.- The Median.- Choice of Mean or Median.- The Histogram and the Frequency Polygon.- Summary.- Supplement 2.- Other Averages.- Proof that Error Due to Grouping Is Small.- Cumulative Graphs.- Bar Diagrams.- 3 The Standard Deviation.- Need for a Measure of Variability.- Formula for the Standard Deviation.- Computing the Standard Deviation with Grouped Data.- Standard Deviation of a Finite Population.- Standard Scores.- Other Measures of Dispersion.- Summary.- Supplement 3.- How to Square Numbers.- Methods of Extracting Square Roots.- How to Check Square Roots.- How to Compute and Check the Standard Deviation.- Sheppard’s Correction for Coarseness of Grouping.- Some Other Measures of Dispersion.- Types of Standard Scores.- 4 Normal Probability Curve.- The Nature of the Normal Probability Curve.- The Ordinates of the Normal Probability Curve.- Binomial Coefficients and the Normal Probability Curve.- Applications of the Binomial Coefficients.- The Area under the Normal Probability Curve.- Summary.- Supplement 4.- Simplifying the Equation for the Normal Curve.- Fitting a Normal Probability Curve to Any Frequency Distribution.- 5 Statistical Inference.- Dependability of Figures.- Speculation.- Samples and Populations.- Sampling Distributions and Standard Error of the Mean.- The t Test for Means.- Levels of Significance.- The z Test for Means.- Point and Interval Estimates.- Statistical Inference.- Sampling Distribution and Standard Error of the Median.- Sampling Distribution and Standard Error of the Standard Deviation.- Hypothesis Testing.- Summary.- Supplement 5.- Stability of the Median.- Standard Error of a Proportion.- 6 Percentiles and Percentile Ranks.- Percentiles.- Percentile Ranks.- Computation of Percentiles.- Percentiles and Percentile Ranks Compared.- Deciles.- Quartiles.- Standard Error of a Percentile.- Summary.- Supplement 6.- Method of Obtaining Percentile Ranks for Grouped Data.- Measures of Variability Based upon Percentiles.- The Range.- Relative Value of Measures of Variability.- 7 Skewness and Transformed Scores.- Skewness.- Kurtosis.- Transformed Scores.- The Description of Frequency Distributions.- Summary.- Supplement 7.- Additional Measures of Skewness and Kurtosis.- 8 Pearson Product Moment Coefficient of Correlation.- Definition of Pearson r.- Plotting a Scatter Diagram.- Illustrations of Pearson r’s of Various Sizes.- Published Correlation Coefficients.- Some Characteristics of Pearson r.- Computing r Without Plotting the Data.- Plotting the Data and Computing r from the Scatter Diagram.- The z’ Transformation and Its Standard Error.- Assumptions upon Which Pearson r Is Based.- Interpretation of Pearson r.- Summary.- Supplement 8.- Other Formulas for Pearson r.- Alternate Ways to Test the Significance of an Obtained Pearson r.- Reliability and Validity.- 9 Regression Equations.- The Purpose of a Regression Equation.- Formulas for Regression Equations.- The Use of Regression Equations.- The Graphic Representation of Prediction.- A Second Illustration of Regression Equations.- Further Interpretations of r.- Summary.- Supplement 9.- Making a Large Number of Predictions.- 10 More Measures of Correlation.- Why Other Correlations.- Biserial r.- Multiserial Correlation.- Point Biserial r.- Classification of Dichotomous Variables.- Tetrachoric r.- Phi.- Interrelations among rbis , rpb , rt, and ?.- Summary.- Supplement 10.- Cosine Pi Correlation Coefficient.- Rank Correlation Coefficient.- 11 Chi Square.- Nature of Chi Square.- Illustration of Correct Use of Chi Square.- Sources of Error in Chi Square.- Chi Square in the General Contingency Table.- The Exact Test of Significance in 2 × 2 Tables.- Use of Chi Square in Curve Fitting.- Advantages and Disadvantages of Chi Square.- Summary.- Supplement 11.- Unique Characteristics of Chi Square.- 12 Nonparametric Statistics Other than Chi Square.- The Purposes of Nonparametric Statistics.- The Sign Test.- The Runs Test.- The Median Test.- The Mann-Whitney U Test.- Which Nonparametric Statistic Should Be Used?.- Other Nonparametric Statistics.- Summary.- 13 Simple Analysis of Variance.- Why Not the t Test.- The Basis of Analysis of Variance.- A First Example.- Assumptions.- Checking.- Technicalities.- A Second Example.- Summary.- Supplement 13.- 14 Standard Errors of Differences.- Standard Error of Any Difference.- Standard Error of the Difference between Means.- Standard Error of the Difference between Standard Deviations.- The Standard Error of Other Differences.- Summary.- Supplement 14.- 15 Reorientation.- Moments.- Correlation.- Popular Concepts.- Future Courses.- Using Statistics.