Statistical Methods And Calculation Skills

Description

As with its predecessors, this fourth edition of Statistical Methods and Calculation Skills aims to equip students with the skills to apply statistical analysis and quantitative techniques in the research and working environments, and to make effective decisions. Part A: – statistical methods – covers the collection and presentation of data; descriptive and inferential methods of analysis; index numbers; regression and correlation analysis; time series; probability and probability distributions; statistical estimation; and hypothesis testing. Part B: Calculation skills are revised in Part B, which deals with elementary calculations such as exponents, decimals, scientific notation, logarithms and rounding. Students with no mathematics background can learn how to do basic calculations before going on to statistical applications. For some courses, calculations such as interest, future values of investments, graphs and ratios form part of the core module and are also covered here. Of Interest and Benefit to: For Diploma courses that use multiple choice for assessments. This is just for students to get used to the format of multiple choice questions. Key Benefits: • A theoretical framework for statistical problem-solving • A practical step-by-step approach to applying methods and calculations • A complete list of outcomes in each unit • Worked examples with detailed explanations • Guided activities and a range of self-test questions. Front cover......Page 1 Title page......Page 2 Imprint page......Page 3 Table of contents......Page 4 Part 1: Statistical methods......Page 8 Unit 1: Introduction......Page 10 1.1 Problem-solving steps......Page 11 1.2 Definition......Page 12 1.3 The language of statistics......Page 13 1.4 Measurement......Page 14 1.4.3 Interval scale......Page 15 1.4.4 Ratio scale......Page 16 1.5 Role of the computer in statistics......Page 17 2.1 Sources of data: where to get the data......Page 22 2.2 Primary data sources......Page 23 2.2.2 Observations......Page 24 2.2.4 Survey by means of asking questions......Page 25 2.3.3 Types of questions we can ask......Page 27 2.4 Selecting a sample......Page 28 2.4.3 Sampling error......Page 29 2.5 Non-random or non-probability sampling methods......Page 30 2.5.4 Snowball sampling......Page 31 2.6.1 Simple random sampling......Page 32 2.6.4 Cluster sampling......Page 34 Unit 3: Summarising data using tables and graphs......Page 36 3.1.1 Frequency distributions......Page 37 3.1.2 Cross-tabulation......Page 39 3.1.3 Bar graph for a single data set......Page 40 3.1.4 Comparative bar graphs......Page 42 3.1.5 Pie chart......Page 46 3.1.6 Pictograms......Page 47 3.2.2 Dot plot......Page 48 3.2.3 Stem-and-leaf plot......Page 50 3.2.4 Frequency distribution tables......Page 53 3.3.1 The histogram and relative histogram......Page 59 3.3.2 Polygon and relative polygon......Page 62 3.3.3 Ogive (cumulative curve) and relative ogive......Page 63 3.4 Using software......Page 65 Unit 4: Summarising data using numberical descriptors......Page 72 4.1.1 Arithmetic mean......Page 73 4.1.2 Median......Page 77 4.1.3 Mode......Page 82 4.1.4 Choose between the mean, median or mode......Page 86 4.2.1 The range......Page 88 4.2.2 Mean absolute deviation (MAD)......Page 89 4.2.3 Standard deviation......Page 92 4.2.5 Coefficient of variation......Page 96 4.3 Measures of shape......Page 97 4.3.1 Skewness......Page 98 4.3.2 Measures of kurtosis......Page 100 4.4 Interpreting centre and variability......Page 101 4.5 Measures of relative standing......Page 105 4.6.1 Interfractile ranges......Page 110 4.6.2 Quartile deviation......Page 111 4.6.3 Five-number summary table......Page 112 4.6.4 Box-and-whisker plot......Page 113 Unit 5: Index numbers......Page 120 5.1 Construction of a simple index number......Page 122 5.2 Construction of composite (or aggregate) index numbers......Page 123 5.2.1 Unweighted index numbers......Page 124 5.2.2 Weighted composite index numbers......Page 125 5.3.1 The consumer price index......Page 127 5.3.2 Changing the base year......Page 128 5.3.3 Link (or chain) indexes......Page 129 5.3.4 Percentage points change......Page 130 5.3.5 Real value versus nominal value of money......Page 131 Unit 6: Summarising bivariate data: simple regression and correlation and analysis......Page 134 6.2 Scatter diagram......Page 135 6.3 Correlation analysis......Page 138 6.3.2 Interpreting a correlation coefficient......Page 139 6.3.3 The coefficient of determination......Page 140 6.4.1 Formulating the regression equation......Page 141 6.4.3 Plot the regression line on the scatter diagram......Page 142 6.5 Spearman rank correlation coefficient......Page 145 7.1 Components of a time series......Page 152 7.2 Historigram......Page 154 7.3.1 Trend analysis......Page 155 7.3.2 Seasonal variation......Page 163 Unit 8: Probability: basic concepts......Page 174 8.1 Language of probability......Page 175 8.2.1 Classical approach......Page 176 8.2.2 Empirical probability......Page 177 8.2.3 Subjective probability approach......Page 178 8.3 Properties of probabilities......Page 179 8.4.2 Intersection of two events......Page 181 8.4.3 Display events graphically......Page 182 8.5 Probability rules for compound events......Page 184 8.5.1 Addition rules......Page 185 8.5.2 Multiplication rules......Page 187 8.5.3 Calculating probabilities using a contingency table......Page 190 8.5.4 Tree diagrams......Page 192 8.6.1 Multiplication rule of counting......Page 194 8.6.3 Combination rule......Page 195 Unit 9: Probability distribution......Page 204 9.1 Discrete probability distributions......Page 205 9.1.1 The binomial distribution......Page 206 9.1.2 Poisson distribution......Page 208 9.2.1 The normal distribution......Page 210 9.2.2 Different areas under the normal curve......Page 212 10.1 Statistics and pa rameters......Page 222 10.2 Sampling distribution of the means......Page 223 10.3.1 Point estimation......Page 224 10.3.2 Confidence interval estimates......Page 225 10.3.3 Confidence interval estimate for the population mean (μ) fordata obtained from a population that is normally distributed or from large samples......Page 228 10.3.4 Confidence interval estimate for the population mean using small samples with σ unknown: t distribution......Page 229 10.3.5 Confidence interval estimate for the population proportion......Page 230 10.4 Sample size......Page 231 Unit 11: Hypothesis testing......Page 236 11.1.1 Stating the hypotheses......Page 237 11.1.2 Select a level of significance (α) to be used......Page 238 11.1.4 Determine the critical value(s) and identify the rejection region......Page 239 11.1.5 Conduct the statistical test......Page 241 11.1.7 Interpret the decision......Page 242 11.2 Hypothesis testing using the P value approach......Page 246 11.3 Testing the difference among means and proportions......Page 249 11.4.1 Test for independence......Page 253 11.4.2 Goodness-of-fit tests......Page 256 Part 2: Calculation skills......Page 266 12.1 The electronic calculator......Page 268 12.2.2 Real numbers and imaginary numbers......Page 270 12.2.3 Rational numbers and irrational numbers......Page 271 12.2.4 Whole numbers and fractions......Page 272 12.3 Common notation......Page 273 12.4.2 Adding and subtracting......Page 274 12.4.3 Multiplying and dividing......Page 275 12.5 Signed numbers......Page 277 12.7 Square roots......Page 278 12.9 Factorial notation......Page 279 12.10 Sigma notation......Page 280 12.11 Fractions......Page 281 12.12 Decimal numbers......Page 283 12.13 Scientific notation......Page 284 12.14 Rounding off decimals......Page 285 12.15 Significant digits......Page 287 12.16 The metric system......Page 290 13.1.1 Converting percentages to fractions and decimals......Page 292 13.1.2 Converting a fraction or decimal into a percentage......Page 293 13.1.4 Finding the rate......Page 294 13.1.6 Percentage rate increase or decrease......Page 295 13.1.7 Finding the amount......Page 296 13.2 Ratio (proportion) calculation......Page 297 13.3.1 Mark-up on cost price......Page 298 13.3.2 Mark-downs and discounts......Page 299 13.3.3 Value-added tax calculations......Page 300 14.1 Graph construction......Page 304 14.2.2 Linear cost function......Page 306 14.2.4 Linear profit function......Page 308 14.2.5 Break-even analysis......Page 309 15.1 Basic concepts......Page 312 15.2 Simple interest......Page 313 15.3 Compound interest......Page 314 15.5 Annuities......Page 317 15.5.1 Ordinary annuities certain......Page 318 15.5.2 Ordinary annuities due......Page 320 Appendix 1......Page 325 Appendix 2......Page 326 Appendix 3......Page 327 Appendix 4......Page 328