Statistics Essentials For Dummies

by Rumsey, Deborah J.

• ISBN13: 9780470618394
• ISBN10: 0470618396
• Format: Paperback
• Copyright: 2010-05-17
• Publisher: For Dummies

Summary

Statistics Essentials For Dummies not only provides students enrolled in Statistics I with an excellent high-level overview of key concepts, but it also serves as a reference or refresher for students in upper-level statistics courses. Free of review and ramp-up material, Statistics Essentials For Dummies sticks to the point, with content focused on key course topics only. It provides discrete explanations of essential concepts taught in a typical first semester college-level statistics course, from odds and error margins to confidence intervals and conclusions. This guide is also a perfect reference for parents who need to review critical statistics concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Author Biography

Deborah Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies.

Table of Contents

Introduction	p. 1
About This Book	p. 1
Conventions Used in This Book	p. 2
Foolish Assumptions	p. 2
Icons Used in This Book	p. 3
Where to Go from Here	p. 3
Statistics in a Nutshell	p. 5
Designing Studies	p. 5
Surveys	p. 5
Experiments	p. 6
Collecting Data	p. 7
Selecting a good sample	p. 7
Avoiding bias in your data	p. 8
Describing Data	p. 8
Descriptive statistics	p. 8
Charts and graphs	p. 9
Analyzing Data	p. 10
Making Conclusions	p. 10
Descriptive Statistics	p. 13
Types of Data	p. 13
Counts and Percents	p. 14
Measures of Center	p. 15
Measures of Variability	p. 17
Percentiles	p. 19
Finding a percentile	p. 19
Interpreting percentiles	p. 20
The Five-Number Summary	p. 21
Charts and Graphs	p. 23
Pie Charts	p. 23
Bar Graphs	p. 24
Time Charts	p. 26
Histograms	p. 27
Making a histogram	p. 27
Interpreting a histogram	p. 29
The distribution of the data in a histogram	p. 29
Variability in the data from a histogram	p. 29
Center of the data from a histogram	p. 30
Evaluating a histogram	p. 30
Boxplots	p. 31
Making a boxplot	p. 31
Interpreting a boxplot	p. 32
Distribution of data in a boxplot	p. 32
Variability in a data set from a boxplot	p. 34
Center of the data from a boxplot	p. 34
The Binomial Distribution	p. 35
Characteristics of a Binomial	p. 35
Checking the binomial conditions step by step	p. 36
Non-binomial examples	p. 36
No fixed number of trials	p. 37
More than success or failure	p. 37
Probability of success (p) changes	p. 37
Trials are not independent	p. 38
Finding Binomial Probabilities Using the Formula	p. 38
Finding Probabilities Using the Binomial Table	p. 40
Finding probabilities when p ≤ 0.50	p. 40
Finding probabilities when p > 0.50	p. 41
Finding probabilities for X greater-than, less-than, or between two values	p. 42
The Expected Value and Variance of the Binomial	p. 43
The Normal Distribution	p. 45
Basics of the Normal Distribution	p. 45
The Standard Normal (Z) Distribution	p. 46
Finding Probabilities for X	p. 48
Finding X for a Given Probability	p. 51
Normal Approximation to the Binomial	p. 53
Sampling Distributions and the Central Limit Theorem	p. 55
Sampling Distributions	p. 55
The mean of sampling distribution	p. 57
The standard error of a sampling distribution	p. 57
Sample size and standard error	p. 58
Population standard deviation and standard error	p. 60
The shape	p. 61
Distribution of X is normal	p. 61
Distribution of X is unknown or not normal	p. 61
Finding Probabilities for X	p. 62
The Sampling Distribution of the Sample Proportion	p. 63
What proportion of students need math help?	p. 64
Finding Probabilities for p	p. 66
Confidence Intervals	p. 69
Making Your Best Guesstimate	p. 69
The Goal: Small Margin of Error	p. 71
Choosing a Confidence Level	p. 71
Factoring In the Sample Size	p. 73
Counting On Population Variability	p. 75
Confidence Interval for a Population Mean	p. 75
Confidence Interval for a Population Proportion	p. 77
Confidence Interval for the Difference of Two Means	p. 78
Confidence Interval for the Difference of Two Proportions	p. 80
Interpreting Confidence Intervals	p. 82
Spotting Misleading Confidence Intervals	p. 84
Hypothesis Tests	p. 87
Doing a Hypothesis Test	p. 87
Identifying what you're testing	p. 88
Setting up the hypotheses	p. 88
What's the alternative?	p. 88
Knowing which hypothesis is which	p. 89
Finding sample statistics	p. 90
Standardizing the evidence: the test statistic	p. 90
Weighing the evidence and making decisions: p-values	p. 91
Finding the p-value	p. 92
Interpreting a p-value	p. 93
General steps for a hypothesis test	p. 94
Testing One Population Mean	p. 94
Testing One Population Proportion	p. 96
Comparing Two Population Means	p. 97
Testing the Mean Difference: Paired Data	p. 99
Testing Two Population Proportions	p. 102
You Could Be Wrong: Errors in Hypothesis Testing	p. 104
A false alarm: Type-1 error	p. 105
A missed detection: Type-2 error	p. 105
The t-distribution	p. 107
Basics of the t-Distribution	p. 107
Understanding the t-Table	p. 108
t-distributions and Hypothesis Tests	p. 109
Finding critical values	p. 110
Finding p-values	p. 110
t-distributions and Confidence Intervals	p. 112
Correlation and Regression	p. 113
Picturing the Relationship with a Scatterplot	p. 113
Making a scatterplot	p. 114
Interpreting a scatterplot	p. 114
Measuring Relationships Using the Correlation	p. 115
Calculating the correlation	p. 116
Interpreting the correlation	p. 117
Properties of the correlation	p. 118
Finding the Regression Line	p. 119
Which is X and which is Y?	p. 119
Checking the conditions	p. 119
Understanding the equation	p. 120
Finding the slope	p. 121
Finding the y-intercept	p. 121
Interpreting the slope and y-intercept	p. 122
Interpreting the slope	p. 122
Interpreting the y-intercept	p. 123
The best-fitting line for the crickets	p. 123
Making Predictions	p. 124
Avoid Extrapolation!	p. 125
Correlation Doesn't Necessarily Mean Cause-and-Effect	p. 125
Two-Way Tables	p. 127
Organizing and Interpreting a Two-way Table	p. 127
Defining the outcomes	p. 128
Setting up the rows and columns	p. 128
Inserting the numbers	p. 129
Finding the row, column, and grand totals	p. 130
Finding Probabilities within a Two-Way Table	p. 131
Figuring joint probabilities	p. 31
Calculating marginal probabilities	p. 131
Finding conditional probabilities	p. 132
Checking for Independence	p. 134
A Checklist for Samples and Surveys	p. 137
The Target Population is Well Defined	p. 138
The Sample Matches the Target Population	p. 138
The Sample Is Randomly Selected	p. 139
The Sample Size Is Large Enough	p. 139
Nonresponse Is Minimized	p. 140
The importance of following up	p. 140
Anonymity versus confidentiality	p. 141
The Survey Is of the Right Type	p. 142
Questions Are Well Worded	p. 142
The Timing Is Appropriate	p. 143
Personnel Are Well Trained	p. 143
Proper Conclusions Are Made	p. 144
A Checklist for Judging Experiments	p. 147
Experiments versus Observational Studies	p. 147
Criteria for a Good Experiment	p. 148
Inspect the Sample Size	p. 148
Small samples - small conclusions	p. 148
Original versus final sample size	p. 149
Examine the Subjects	p. 149
Check for Random Assignments	p. 150
Gauge the Placebo Effect	p. 150
Identify Confounding Variables	p. 151
Assess Data Quality	p. 152
Check Out the Analysis	p. 152
Scrutinize the Conclusions	p. 153
Overstated results	p. 153
Ad-hoc explanations	p. 154
Generalizing beyond the scope	p. 154
Ten Common Statistical Mistakes	p. 155
Misleading Graphs	p. 155
Pie charts	p. 155
Bar graphs	p. 156
Time charts	p. 156
Histograms	p. 157
Biased Data	p. 157
No Margin of Error	p. 158
Nonrandom Samples	p. 158
Missing Sample Sizes	p. 159
Misinterpreted Correlations	p. 159
Confounding Variables	p. 160
Botched Numbers	p. 160
Selectively Reporting Results	p. 161
The Almighty Anecdote	p. 162
Appendix: Tables for Reference	p. 163
Index	p. 171
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