Contents
1 Introduction
1.1 Discrete Data
1.2 Continuous Data
1.2.1 Choice Of Class Interval
1.2.2 How many classes? The \(2^k\) rule and Sturges’ formula
1.3 Histogram With Unequal Class Intervals
1.3.1 Stem-and-Leaf Plots
1.4 Data Collection
1.5 Measures Of Central Tendencies
1.5.1 Mean
1.5.2 Median and Interquartile Range
1.5.3 Median from a frequency table for discrete data
1.5.4 Median of a Continuous Data
1.5.5 Median for grouped data
1.5.6 Quartiles for grouped data
1.5.7 Mode
1.5.8 Mode for grouped data
1.6 Measure Of Dispersion
1.7 Range
1.8 Standard Deviation
1.8.1 Population and sample: why the divisor changes
1.9 Mean Deviation
1.10 Quartiles
1.10.1 Interquartile Range
1.10.2 Interquartile Range for grouped data
1.11 Percentiles
1.11.1 The five working forms of the variance
1.12 Properties of \(E(X)\)
1.13 Properties of Variance
1.14 Properties of Covariance (Cov\((X,Y)\))
1.15 Moments
1.15.1 Raw moments (about the origin)
1.15.2 Central moments (about the mean)
1.15.3 Converting between them
1.15.4 Making them comparable
1.15.5 Moment Ratios
1.15.6 Skewness
1.16 Practice problems
2 Estimation and Sampling Distributions
2.1 The Four Distributions You Will Need
2.1.1 The normal distribution
2.1.2 Why the sample mean is normal: the Central Limit Theorem
2.1.3 The \(t\)-distribution
2.1.4 The chi-square distribution
2.1.5 The \(F\)-distribution
2.1.6 Choosing between them
2.1.7 Properties of Estimation
2.1.8 Estimating the population variance
2.1.9 An Unbiased Estimation of Population Proportion
2.1.10 Expected Values And Variances of Some Common Point Estimators
2.1.11 Confidence Interval
2.1.12 Properties of Confidence Intervals
2.2 Practice problems
3 Statistical Hypothesis Testing
3.1 The \(P\)-value
3.1.1 What the \(P\)-value does not mean
3.1.2 Directed Hypothesis Test
3.2 Test for the Variance and Standard Deviation
3.2.1 Chi-Square Tests
3.3 Type I and Type II Errors
3.4 Test of Independence and Goodness of Fit Test
3.5 Practice problems
4 Analysis of Variance
4.1 Contingency Table
4.1.1 Design of Experiments
4.2 Completely Randomised Design
4.3 Randomised Block Design
4.4 Latin Square Design
4.5 Practice problems
5 Linear Regression and Correlation Analysis
5.1 Correlation
5.2 Scatter diagram
5.3 Calculation of Correlation Coefficient
5.3.1 Pearson Product-Moment Correlation Coefficient
5.3.2 Spearman’s Rank Correlation Coefficient
5.4 Linear Regression
5.4.1 The Method of Least Squares
5.5 Inference for the Regression Line
5.5.1 Partitioning the variation
5.5.2 The coefficient of determination
5.5.3 The ANOVA table for regression
5.5.4 Testing and estimating the slope
5.5.5 Estimating A Value for \(\sigma ^2_{Y/X}\)
5.5.6 Confidence Limit For \(\beta \)
References
5.6 Practice problems
1.1 Discrete Data
1.2 Continuous Data
1.2.1 Choice Of Class Interval
1.2.2 How many classes? The \(2^k\) rule and Sturges’ formula
1.3 Histogram With Unequal Class Intervals
1.3.1 Stem-and-Leaf Plots
1.4 Data Collection
1.5 Measures Of Central Tendencies
1.5.1 Mean
1.5.2 Median and Interquartile Range
1.5.3 Median from a frequency table for discrete data
1.5.4 Median of a Continuous Data
1.5.5 Median for grouped data
1.5.6 Quartiles for grouped data
1.5.7 Mode
1.5.8 Mode for grouped data
1.6 Measure Of Dispersion
1.7 Range
1.8 Standard Deviation
1.8.1 Population and sample: why the divisor changes
1.9 Mean Deviation
1.10 Quartiles
1.10.1 Interquartile Range
1.10.2 Interquartile Range for grouped data
1.11 Percentiles
1.11.1 The five working forms of the variance
1.12 Properties of \(E(X)\)
1.13 Properties of Variance
1.14 Properties of Covariance (Cov\((X,Y)\))
1.15 Moments
1.15.1 Raw moments (about the origin)
1.15.2 Central moments (about the mean)
1.15.3 Converting between them
1.15.4 Making them comparable
1.15.5 Moment Ratios
1.15.6 Skewness
1.16 Practice problems
2 Estimation and Sampling Distributions
2.1 The Four Distributions You Will Need
2.1.1 The normal distribution
2.1.2 Why the sample mean is normal: the Central Limit Theorem
2.1.3 The \(t\)-distribution
2.1.4 The chi-square distribution
2.1.5 The \(F\)-distribution
2.1.6 Choosing between them
2.1.7 Properties of Estimation
2.1.8 Estimating the population variance
2.1.9 An Unbiased Estimation of Population Proportion
2.1.10 Expected Values And Variances of Some Common Point Estimators
2.1.11 Confidence Interval
2.1.12 Properties of Confidence Intervals
2.2 Practice problems
3 Statistical Hypothesis Testing
3.1 The \(P\)-value
3.1.1 What the \(P\)-value does not mean
3.1.2 Directed Hypothesis Test
3.2 Test for the Variance and Standard Deviation
3.2.1 Chi-Square Tests
3.3 Type I and Type II Errors
3.4 Test of Independence and Goodness of Fit Test
3.5 Practice problems
4 Analysis of Variance
4.1 Contingency Table
4.1.1 Design of Experiments
4.2 Completely Randomised Design
4.3 Randomised Block Design
4.4 Latin Square Design
4.5 Practice problems
5 Linear Regression and Correlation Analysis
5.1 Correlation
5.2 Scatter diagram
5.3 Calculation of Correlation Coefficient
5.3.1 Pearson Product-Moment Correlation Coefficient
5.3.2 Spearman’s Rank Correlation Coefficient
5.4 Linear Regression
5.4.1 The Method of Least Squares
5.5 Inference for the Regression Line
5.5.1 Partitioning the variation
5.5.2 The coefficient of determination
5.5.3 The ANOVA table for regression
5.5.4 Testing and estimating the slope
5.5.5 Estimating A Value for \(\sigma ^2_{Y/X}\)
5.5.6 Confidence Limit For \(\beta \)
References
5.6 Practice problems