Intro Title Page Copyright Page Contents Preface Chapter 1 Dealing with data 1.1 The role of statistics in geography 1.1.1 Why do geographers need to use statistics? 1.2 About this book 1.3 Data and measurement error 1.3.1 Types of geographical data: nominal, ordinal, interval, and ratio 1.3.2 Spatial data types 1.3.3 Measurement error, accuracy and precision 1.3.4 Reporting data and uncertainties 1.3.5 Significant figures 1.3.6 Scientific notation (standard form) 1.3.7 Calculations in scientific notation Exercises Chapter 2 Collecting and summarizing data 2.1 Sampling methods 2.1.1 Research design 2.1.2 Random sampling 2.1.3 Systematic sampling 2.1.4 Stratified sampling 2.2 Graphical summaries 2.2.1 Frequency distributions and histograms 2.2.2 Time series plots 2.2.3 Scatter plots 2.3 Summarizing data numerically 2.3.1 Measures of central tendency: mean, median and mode 2.3.2 Mean 2.3.3 Median 2.3.4 Mode 2.3.5 Measures of dispersion 2.3.6 Variance 2.3.7 Standard deviation 2.3.8 Coefficient of variation 2.3.9 Skewness and kurtosis Exercises Chapter 3 Probability and sampling distributions 3.1 Probability 3.1.1 Probability, statistics and random variables 3.1.2 The properties of the normal distribution 3.2 Probability and the normal distribution: z-scores 3.3 Sampling distributions and the central limit theorem Exercises Chapter 4 Estimating parameters with confidence intervals 4.1 Confidence intervals on the mean of a normal distribution: the basics 4.2 Confidence intervals in practice: the t-distribution 4.3 Sample size 4.4 Confidence intervals for a proportion Exercises Chapter 5 Comparing datasets 5.1 Hypothesis testing with one sample: general principles. 5.1.1 Comparing means: one-sample z-test 5.1.2 p-values 5.1.3 General procedure for hypothesis testing 5.2 Comparing means from small samples: one-sample t-test 5.3 Comparing proportions for one sample 5.4 Comparing two samples 5.4.1 Independent samples 5.4.2 Comparing means: t-test with unknown population variances assumed equal 5.4.3 Comparing means: t-test with unknown population variances assumed unequal 5.4.4 t-test for use with paired samples (paired t-test) 5.4.5 Comparing variances: F-test 5.5 Non-parametric hypothesis testing 5.5.1 Parametric and non-parametric tests 5.5.2 Mann-whitney U-test Exercises Chapter 6 Comparing distributions: the Chi-squared test 6.1 Chi-squared test with one sample 6.2 Chi-squared test for two samples Exercises Chapter 7 Analysis of variance 7.1 One-way analysis of variance 7.2 Assumptions and diagnostics 7.3 Multiple comparison tests after analysis of variance 7.4 Non-parametric methods in the analysis of variance 7.5 Summary and further applications Exercises Chapter 8 Correlation 8.1 Correlation analysis 8.2 Pearson's product-moment correlation coefficient 8.3 Significance tests of correlation coefficient 8.4 Spearman's rank correlation coefficient 8.5 Correlation and causality Exercises Chapter 9 Linear regression 9.1 Least-squares linear regression 9.2 Scatter plots 9.3 Choosing the line of best fit: the 'least-squares' procedure 9.4 Analysis of residuals 9.5 Assumptions and caveats with regression 9.6 Is the regression significant? 9.7 Coefficient of determination 9.8 Confidence intervals and hypothesis tests concerning regression parameters 9.8.1 Standard error of the regression parameters 9.8.2 Tests on the regression parameters. 9.8.3 Confidence intervals on the regression parameters 9.8.4 Confidence interval about the regression line 9.9 Reduced major axis regression 9.10 Summary Exercises Chapter 10 Spatial Statistics 10.1 Spatial Data 10.1.1 Types of Spatial Data 10.1.2 Spatial Data Structures 10.1.3 Map Projections 10.2 Summarizing Spatial Data 10.2.1 Mean Centre 10.2.2 Weighted Mean Centre 10.2.3 Density Estimation 10.3 Identifying Clusters 10.3.1 Quadrat Test 10.3.2 Nearest Neighbour Statistics 10.4 Interpolation and Plotting Contour Maps 10.5 Spatial Relationships 10.5.1 Spatial Autocorrelation 10.5.2 Join Counts Exercises Chapter 11 Time series analysis 11.1 Time series in geographical research 11.2 Analysing time series 11.2.1 Describing time series: definitions 11.2.2 Plotting time series 11.2.3 Decomposing time series: trends, seasonality and irregular fluctuations 11.2.4 Analysing trends 11.2.5 Removing trends ('detrending' data) 11.2.6 Quantifying seasonal variation 11.2.7 Autocorrelation 11.3 Summary Exercises Appendix A: Introduction to the R package A.1 Obtaining R A.2 Simplecalculations A.3 Vectors A.4 Basicstatistics A.5 Plottingdata A.6 Multiplefigures A.7 Readingand writing data A.8 Summary Appendix B: Statistical tables References Index EULA.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Print version: Dadson, Simon James Statistical Analysis of Geographical Data