Statistics: The Conceptual Approach (Hardcover, 1997)

1 Statistics: Randomness and Regularity.- 1.1 Statistics: What’s in a word?.- 1.2 Knowing how statistics is used: Goals for the reader.- Understanding what can go wrong.- Understanding statistical terms.- 1.3 Central ideas in statistics.- Randomness and regularity: Twins in tension.- Randomness in regularity.- Two examples in the study of randomness and regularity.- Probability: What are the chances?.- Variables: The names we give things.- Variables, values, and elements.- Theoretical variables and empirical variables.- Constants.- 1.4 Users of statistics.- 1.5 Relationship of statistics to mathematics, pencils, and computers.- 1.6 Summary.- Additional Readings.- Exercises.- 2 Collection of Data.- 2.1 Defining the variables.- 2.2 Observational data: Problems and possibilities.- Population versus sample.- Selection of the sample: Making sure the pot is stirred.- Random sample: What is it?.- Convenience sample: How to produce a “poor” sample.- Selecting proper samples.- Selection of variables on which to collect observational data.- 2.3 Errors and “errors” in collecting observational data.- Sampling error: The “error” that is not a mistake.- Nonresponse error: Result of rude, rushed, and reticent respondents.- Response errors.- 2.4 Experimental data: Looking for the causes of outcomes.- Experimental group and control group.- Selecting the experimental and control groups.- Problems with experimenting on people.- Role of statistics in experimentation.- Putting it all together: Does class size affect school performance?.- 2.5 Data matrix/Data file.- 2.6 Summary.- Additional Readings.- Exercises.- 3 Description of Data: Graphs and Tables.- 3.1 Graphs: Picturing data.- Creating statistical graphs.- Types of graphs.- 3.2 Categorical variables: Pie charts and bar graphs.- Graphing one categorical variable.- Graphing two categorical variables.- 3.3 Metric variables: Plots and histograms.- Graphing one metric variable.- Graphing two metric variables.- Time series plot.- 3.4 Creating maps from data.- 3.5 Graphing: Standards for excellence.- “The least ink”: Is the simplest graph best?.- “Chartjunk”: A new name for garbage.- Data density.- “Revelation of the complex”.- 3.6 Tables: Turning can be timely.- 3.7 Summary.- Additional Readings.- Exercises.- 4 Description of Data: Computing Summary Statistics.- 4.1 Averages: Let us count the ways.- Mode: The hostess with the mostes’.- Median: Counting to the middle.- Mean: Balancing the seesaw.- Mode, median, or mean?.- 4.2 Variety: Measuring the spice of life.- Range: Lassoing the two extreme values.- Standard deviation: The crucial deviant.- 4.3 Standard error of the means.- 4.4 Standard scores: Comparing apples and oranges.- 4.5 Gain in simplicity, loss of information.- Replacing the data with a graph.- Replacing the data with a summary value.- 4.6 Real estate data: Out-of-sight prices.- 4.7 Summary.- Additional Readings.- Formulas.- Exercises.- 5 Probability.- 5.1 How to find probabilities.- Equally likely events.- Relative frequency.- Using subjective probabilities.- 5.2 Computations with probabilities.- Adding probabilities.- Multiplying probabilities.- 5.3 Odds: The opposite of probabilities.- 5.4 Probability distributions for discrete variables.- Binomial distribution.- Poisson distribution.- Hypergeometric distribution.- Displaying probabilities in graphs and tables.- Computations with probabilities.- 5.5 Probability distributions for continuous variables.- Standard normal distribution: The bell curve.- The t-distribution.- Chi-square distribution.- F-distribution.- Need for normally distributed data.- 5.6 Using probabilities to check on assumptions.- Is it a fair coin?.- Is it a fair workplace?.- Is it an evenly split electorate?.- 5.7 Decision analyis: Using probabilities to make decisions.- 5.8 Summary.- Additional Readings.- Formulas.- Exercises.- 6 Drawing Conclusions: Estimation.- 6.1 Sample statistic and population parameter.- 6.2 Point estimation.- What is a “good” point estimate?.- A strategic use of the point estimate: How many tanks did the Germans have?.- 6.3 Interval estimation: More room to be correct.- Length of confidence interval.- Confidence intervals for differences.- 6.4 Summary.- Additional Readings.- Formulas.- Exercises.- 7 Drawing conclusions: Hypothesis testing.- 7.1 The hypothesis as a question.- Null hypothesis.- Alternative hypothesis.- Errors in answering the question.- 7.2 How to answer the question posed by the null hypothesis.- Probability: The p-value.- Mechanics of hypothesis testing.- To reject or not to reject the null hypothesis.- Causal effect: A skip too far.- A little statistical theory and a game on the computer.- 7.3 Significance level.- 7.4 Testing a population proportion.- 7.5 Difference between two population proportions.- Testing the null hypothesis.- Estimating the difference.- 7.6 Testing hypotheses versus constructing confidence intervals.- 7.7 Statistical versus substantive significance.- 7.8 Applications: When to reject the null hypothesis.- Psychology experiment on cooperation and competition.- Community study of blue-collar workers.- 7.9 Summary.- Additional Readings.- Formulas.- Exercises.- 8 Relationships Between Variables.- 8.1 Four questions about two variables and their relationship.- Question 1. Relationship between the variables in the data?.- Question 2. Strength of the relationship?.- Question 3. Relationship in the population?.- Question 4. Causal relationship?.- 8.2 Prediction.- 8.3 Independent and dependent variables.- 8.4 Different types of variables: Categorical, rank, metric.- 8.5 Return to the question of causality.- Role of other variables.- Role of time.- Multiple causal factors.- 8.6 Summary.- Additional Readings.- Exercises.- 9 Chi-square Analysis for Two Categorical Variables.- 9.1 Analysis of the data: Are there trustworthy differences in attitude?.- Bar graphs.- Summary computations with categorical variables.- 9.2 Question 1. Relationship between the variables?.- 9.3 Question 2. Strength of the relationship?.- Phi in the sample.- Phi in the population.- 9.4 Question 3. Relationship in the populations?.- Setting up the null hypothesis.- Testing the null hypothesis.- From chi-square to p-value.- Degrees of freedom for chi-square analysis.- 9.5 Question 4. Causal relationship?.- 9.6 Larger tables: A banquet of possibilities.- Question 1. Relationship between the variables?.- Question 2. Strength of the relationship?.- Question 3. Relationship in the populations?.- Question 4. Causal relationship?.- 9.7 Summary.- Additional Reading.- Formulas.- Exercises.- 10 Regression and Correlation for Two Metric Variables.- 10.1 Question 1. Relationship between the variables?.- Graphing the data in a scatterplot.- Learning from the scatterplot.- Linear relationships.- 10.2 Question 2a. Strength of the relationship?.- Is r positive or negative? Large or small?.- Four scatterplots: From strong to weak relationships.- Interpretation of r: An issue of inexactness.- 10.3 Question 2b. Form of the relationship?.- A line through the middle of the points.- How to find the regression line: The least squares principle.- Predicting with regression analysis: From fat to calories.- Magnitudes of effects: Interpretation of r-square.- Correlation or regression? The more the merrier.- Regression analysis for data on change.- 10.4 Question 3. Relationship in the population?.- Confidence interval approach.- Hypothesis testing using t.- Hypothesis testing using F.- 10.5 Warning: What you measure is what you get.- 10.6 How to be smart using dummy variables.- Categorical independent variable with two values and metric dependent variable.- Categorical dependent variable with two values and metric independent variable.- 10.7 Question 4. Causal relationship?.- 10.8 Summary.- Additional Readings.- Formulas.- Exercises.- 11 Analysis of Variance for a Categorical and a Metric Variable.- 11.1 Analysis of variance: Comparing the mean-ings of things.- 11.2 Question 1. Relationship between violent crime rate and region?.- Scatterplot.- Boxplot: A simpler view of the data.- 11.3 Question 2. Strength of the relationship?.- Region variable.- Residual variable.- Effect of both region and residual variable: Total sum of squares.- Measuring the strength of the relationship.- Explained amounts of variation.- 11.4 Question 3. Could the relationship have occurred by chance alone?.- The null hypothesis.- p-value from F.- Going beyond the F-test: Making mean comparisons.- 11.5 Question 4. Causal relationship?.- 11.6 Analysis of variance: A bird’s-eye review.- 11.7 Matched pair analysis: Two observations per unit.- A t-test.- The sign test: A simple yes or no.- 11.8 Summary.- Additional Readings.- Formulas.- Exercises.- 12 Rank Methods for Two Rank Variables.- 12.1 Two rank variables with words as the values.- Question 1. Relationship between identification and interest?.- Question 2. Strength of the relationship?.- Question 3. Relationship in the population?.- Question 4. Causal relationship?.- 12.2 Ranking numbers as values: How are the Phillies doing?.- Question 1. Relationship in the data?.- Question 2. Strength of the relationship?.- Question 3. Did the relationship occur by chance?.- Question 4. Causal relationship?.- 12.3 Summary.- Additional Readings.- Formulas.- Exercises.- 13 Multivariate analysis.- 13.1 Partial phis: Three categorical variables.- Control for a third variable: The neutralizing game.- Partial phi.- 13.2 Multiple regression with metric variables.- Question 1. Relationship in the data?.- Question 2b. Form of the relationship? Partial regression coefficients.- Question 2a. Strength of the relationship? Partial correlation coefficients.- Question 3. Relationship in the population?.- 13.3 Multiple regression with a dummy variable.- 13.4 Two-way analysis of variance.- One-way analysis with time of day only.- One-way analysis with route only.- Two-way analysis with time of day and route.- A second study with interaction effects.- 13.5 Establishing causality.- 13.6 Summary.- Additional Readings.- Formulas.- Exercises.- 14 Statistics in Everyday Life.- 14.1 Stepping stones to statistical sophistication.- 14.2 Approaching numbers with care.- 14.3 Data and statistical methods.- 14.4 How things can go wrong.- Dangers in the collection of data.- Special problems of survey research.- Misuses of analysis methods.- Misuses of statistical inference.- Misuses in interpretation of numbers.- 14.5 Statistics and Big Brother.- 14.6 Ending on the upbeat.- Additional Readings.- Exercises.- Statistical Tables.- Answers to Odd-Numbered Exercises.