Statistics: The Conceptual Approach

ISBN-13: 9781461274704 / Angielski / Miękka / 2011 / 735 str.

Gudmund R. Iversen; Mary Gergen

Opis

An imaginative introduction to statistics, reorienting the course towards an understanding of statistical thinking and its meaning and use in daily life and work. Gudmund Iversen and Mary Gergen bring their years of experience and insight into teaching the subject, incorporating such innovations and insights as a sustained emphasis on the process of statistical analysis and what statistics can and cannot do as well as careful exposition of the ideas of developing statistical and graphical literacy. In the spirit of contemporary pedagogy and by using technology, the authors break down the traditional barriers of statistical formulas and lengthy computations encountered by students without strong quantitative skills. Further, formulas are grouped at the end of each chapter along with related problems, and, with only algebra as a prerequisite, the book is ideal for students in the liberal arts and the behavioural and social sciences.

Spis treści

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.