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Authors: Alan Graham
ISBN-13: 9780071583053, ISBN-10: 007158305X
Format: Paperback
Publisher: McGraw-Hill Companies, The
Date Published: October 2008
Edition: New
Alan Graham has lectured in mathematics education at the Open University for over 30 years. His particular interest is statistics and he has written a number of books and OU course units in this field.
Bet the odds on Teach Yourself
Teach Yourself Statistics introduces you to the
key concepts and principles of statistics. It will help you understand statistics as they occur in your everyday life.
Foreword | xii | |
1 | Introducing Statistics | 1 |
Some good reasons to learn about statistics | 1 | |
What sort of statistical questions can be asked? | 2 | |
Can you summarize the data? | 2 | |
Is there a significant difference between these two sets of results? | 3 | |
Is there a close relationship between the two things under consideration? | 3 | |
How are statistical questions investigated? | 4 | |
Choosing and using your calculator | 6 | |
2 | Some basic maths | 8 |
Algebra | 8 | |
Why letters? | 8 | |
Algebraic logic | 10 | |
Graphs | 15 | |
Notation | 21 | |
(Capital) Sigma | 21 | |
X bar | 22 | |
Summary | 23 | |
Comments on exercises | 23 | |
3 | Graphing data | 28 |
Bar charts | 28 | |
Pie charts | 34 | |
Pictograms | 36 | |
Histograms | 36 | |
Stemplots | 39 | |
Scattergraphs | 42 | |
Time graphs | 44 | |
Summary | 44 | |
Comments on exercises | 45 | |
4 | Choosing a suitable graph | 47 |
Types of data | 47 | |
Discrete and continuous data | 47 | |
Single and paired data | 50 | |
Types of statistical judgement | 52 | |
Summarizing | 52 | |
Comparing | 53 | |
Inter-relating | 55 | |
Getting the right graph | 56 | |
Bar charts and pie charts | 56 | |
Stemplots and histograms | 60 | |
Summary | 62 | |
Comments on exercises | 63 | |
5 | Summarizing data | 65 |
Introducing averages - finding a middle value | 65 | |
Calculating and choosing averages | 68 | |
Mode | 68 | |
A simple mean (X) | 70 | |
A weighted mean (X) | 71 | |
Median (Md) | 74 | |
Spread | 76 | |
5-figure summary | 77 | |
Boxplot | 79 | |
Range | 81 | |
Inter-quartile range (dq) | 81 | |
Mean deviation | 83 | |
Variance ([sigma][superscript 2]) and Standard deviation ([sigma]) | 84 | |
Summary | 87 | |
Comments on exercises | 88 | |
6 | Lies and statistics | 89 |
Misleading graphs | 89 | |
Data set A | 90 | |
Data set B | 93 | |
Data set C | 97 | |
Confusing percentages | 99 | |
Inappropriate averages | 104 | |
Summary | 108 | |
Comments on exercises | 108 | |
7 | Choosing a sample | 109 |
The sampling frame | 110 | |
Random sampling | 112 | |
Generating random numbers | 115 | |
Using random numbers to select a sample | 116 | |
Register of Electors | 117 | |
Sampling variation | 121 | |
Systematic sampling | 121 | |
Human error and sampling error | 124 | |
Summary | 129 | |
8 | Collecting information | 130 |
Secondary source data | 131 | |
Social Trends | 131 | |
Data accuracy | 133 | |
Primary source data | 135 | |
Experimental design | 135 | |
Questionnaire design | 138 | |
Summary | 142 | |
Comments on exercises | 142 | |
9 | Reading tables of data | 144 |
Spreadsheets | 145 | |
What is a spreadsheet? | 145 | |
Why bother using a spreadsheet? | 146 | |
Using a spreadsheet | 146 | |
What else will a spreadsheet do? | 150 | |
Turning the tables | 151 | |
Reading the small print | 158 | |
Summary | 160 | |
Comments on exercises | 160 | |
10 | Regression: describing relationships between things | 164 |
Paired data | 164 | |
The 'best-fit' line | 167 | |
Making predictions | 172 | |
Summary | 178 | |
Calculating the regression coefficients using the formula | 179 | |
Comments on exercises | 181 | |
11 | Correlation: measuring the strength of a relationship | 187 |
Scatter | 187 | |
Product-moment correlation coefficient | 191 | |
Rank correlation | 197 | |
Cause and effect | 202 | |
Summary | 207 | |
12 | Chance and probability | 208 |
Measuring probability | 208 | |
Odds | 208 | |
Statistical probability | 210 | |
Myths and misconceptions about probability | 213 | |
Mutually exclusive outcomes and adding probabilities | 215 | |
Independence and multiplying probabilities | 218 | |
Summary | 226 | |
Comments on exercises | 226 | |
13 | Probability models | 228 |
Compared to what? | 228 | |
The uniform distribution | 229 | |
The Normal distribution | 233 | |
Calculating probabilities from the Normal curve | 238 | |
The binomial distribution | 242 | |
The binomial expansion | 247 | |
Linking the binomial distribution and the binomial expansion | 248 | |
Summary | 252 | |
Comments on exercises | 252 | |
14 | Deciding on differences | 254 |
Picturing differences | 255 | |
Contexts for investigating differences | 260 | |
Some basic terminology | 261 | |
What is a test of significance? | 266 | |
Stage 1 Set up the hypothesis | 266 | |
Stage 2 Calculate the test statistic, S | 268 | |
Stage 3 Look up the critical value | 268 | |
Stage 4 Is S [less than or equal] C? | 269 | |
The z test | 269 | |
The binomial test | 275 | |
Summary | 280 | |
Comments on exercises | 281 | |
Appendix | 286 | |
Choosing the right statistical technique | 286 |