Introducing Statistics
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Description
Contents
Reviews
Language
English
ISBN
9781382018180
Front Cover
IFC
Imprint
Contents
Preface to the Second Edition
Preface to the First Edition
Glossary of Notation
1 Summary diagrams and tables
1.1 The purpose of Statistics
1.2 Variables and observations
1.3 Types of data
1.4 Tally charts and frequency distributions
1.5 Stem-and-leaf diagrams
1.6 Bar charts
1.7 Multiple bar charts
1.8 Compound bars for proportions
1.9 Pie charts
1.10 Grouped frequency tables
1.11 Difficulties with grouped frequencies
1.12 Histograms
1.13 Frequency polygons
1.14 Cumulative frequency diagrams
Step diagrams
1.15 Cumulative proportion diagrams
1.16 Time series
1.17 Scatter diagrams
1.18 Choosing which display to use
1.19 Dirty Data
Chapter summary
2 Summary statistics
2.1 The purpose of summary statistics
2.2 The mode
Modal class
2.3 The median
2.4 The mean
2.5 Advantages and disadvantages of the mode, mean and median
Advantages
Disadvantages
2.6 Sigma (Σ) notation
Applications of sigma notation
2.7 The mean of a frequency distribution
2.8 The mean of grouped data
2.9 Using coded values to simplify calculations
2.10 The median of grouped data
2.11 Quartiles, deciles and percentiles
Grouped data
Ungrouped data
2.12 Range, inter-quartile range and midrange
2.13 Box-whisker diagrams
Refined boxplots
2.14 Deviations from the mean
2.15 The variance
Using the divisor n
Using the divisor (n - 1)
2.16 Calculating the variance
2.17 The sample standard deviation
Approximate properties of the standard deviation
2.18 Variance and standard deviation for frequency distributions
2.19 Variance calculations using coded values
2.20 Symmetric and skewed data
2.21 The weighted mean and index numbers
Chapter summary
3 Data collection
3.1 Data collection by observation
3.2 The purpose of sampling
3.3 Methods for sampling a population
The simple random sample
Cluster sampling
Stratified sampling
Systematic sampling
Quota sampling
Self-selection
A national survey
3.4 Random numbers
Pseudo-random numbers
Tables of random numbers
3.5 Methods of data collection by questionnaire (or survey)
The face-to-face interview
The postal questionnaire
The telephone interview
3.6 Questionnaire design
Some poor questions
Some good questions
The order of questions
Question order and bias
Filtered questions
Open and closed questions
The order of answers for closed questions
The pilot study
3.7 Primary anf secondary data
Chapter summary
4 Probability
4.1 Relative frequency
4.2 Preliminary definitions
4.3 The probability scale
4.4 Probability with equal likely outcomes
4.5 The complementary event, E
4.6 Venn diagrams
4.7 unions and intersections of events
4.8 Mutually exclusive events
The additional rule
4.9 Exhaustive events
4.10 Probability trees
4.11 Sample proportions and and probability
4.12 Unequally likely possibilitie
4.13 Physical independence
The multiplication rule
4.14 Orderings
Orderings of similar objects
4.15 Permutations and combinations
4.16 Sampling with replacement
4.17 Sampling without replacement
4.18 Conditional probability
The generalised multiplication rule
4.19 Statistical independence
4.20 The total probability theorem
4.21 Bayes theorem
Chapter summary
5 Probability distrubutions and expectations
5.1 Notation
5.2 Probability distributions
The probability function
Illustrating probability disctributions
Estimating probability distributions
The cumulative distribution function
5.3 Some special discrete probability distributions
The discrete uniform distribution
The Bernoulli distribution
5.4 The geomatric distribution
Notation
Cumulative probabilities
A paradox!
5.5 Expectations
Expected value or expected number
Expectation of X²
5.6 The variance
5.7 The standard deviation
5.8 Greek notation
Chapter summary
6 Expectation algebra
6.1 E(X + a) and Var(X + a)
6.2 E(aX) and Var(aX)
6.3 E(aX + b) and Var(aX + b)
6.4 Expectations involving more than one variable
Var(X + Y)
E(X₁ + X₂) and Var (X₁ + X₂2)
The difference between 2X and X₁ + X₂
6.5 The expectation and variance of the sample mean
6.6 The unbiased estimate of the population variance
Chapter summary
7 The binomial distribution
7.1 Derivation
7.2 Notation
7.3 Successes and failures
7.4 The shape of the distribution
7.5 Tables of binomial distributions
7.6 The expectation and variance of a binomial random variable
Chapter summary
8 The Poisson distribution
8.1 The Poisson process
8.2 The form of the distribution
8.3 The shape of a Poisson distribution
8.4 Tables for Poisson distributions
8.5 The Poisson approximation to the binomial
8.6 Sums of independant Poisson random variables
Chapter summary
9 Continuous random variables
9.1 Histograms and sample size
9.2 The probability density function, f
Properties of the pdf
9.3 The cumulative distribution function F
The median, m
9.4 Expectation and variance
9.5 Obtaining f from F
9.6 Distribution of a function of a random variable
9.7 The uniform (rectangular) distributions
Chapter summary
10 The normal distribution
10.1 The standard normal distribution
10.2 Tables of Φ (z)
10.3 Probabilities for other normal distributions
10.4 Finer detail in the tables of Φ (z)
10.5 Tables of percentage points
10.6 Using calculators
10.7 Applications of the normal distribution
10.8 General properties
10.9 Linear combinations of independant normal random variables
Extension to more than two variables
Distribution of the mean of normal random variables
10.10 The Central Limit Theorem
The distribution of the sample mean, X
10.11 The normal approximation to a binomial distribution
Inequalities
Choosing between the normal and Poisson approximations to a binomial distribution
10.12 The normal approximation to a Poisson distribution
Chapter summary
11 Point and internal estimation
11.1 Point estimates
11.2 Confidence intervals
11.3 Confidence interval for a population mean
Normal distribution with known variance
Unknown population distribution, known population variance, large sample
Unknown population distribution, unknown population variance, large scale
Poisson distribution, large mean
11.4 Confidence interval for a population proportion
11.5 The t-distribution
Tables of the t-distribution
11.6 Confidence interval for a population mean using the t-distribution
Chapter summary
12 Hypothesis tests
12.1 The null and alternative hypotheses
12.2 Critical regions and significance levels
12.3 The general test procedure
12.4 Test for mean, known variance, normal distribution or large sample
12.5 Identifying the two hypotheses
The null hypothesis
The alternative hypothesis
12.6 Test for mean, large sample, variance unknown
12.7 Test for large Poisson mean
12.8 Test for proportion, large sample
12.9 Test for mean, small sample, variance unknown
12.10 The p-value approach
12.11 Hypothesis tests and confidence internvals
12.12 Type I and Type II errors
The general procedure
12.13 Hypothesis tests for a proportion based on a small sample
12.14 Hypothesis tests for a Poisson mean based on a small sample
12.15 Comparison of two means
12.16 Comparison of two means - known population variances
Confidence interval for the common mean
12.17 Comparison of two means - common unknown population variance
Large sample sizes
Small sample sizes
Chapter summary
13 Goodness of fit
13.1 The chi-squared distribution
Properties of the chi-squared distribution
Tables of the chi-squared distribution
13.2 Goodness of fit to prescribe probabilities
13.3 Small expected frequencies
13.4 Goodness of fit to prescribe distribution type
13.5 Contingency tables
The Yates correction
Chapter summary
14 Regression and correlation
14.1 The equation of a straight line
Determining the equation
14.2 The estimated regression line
14.3 The method of least squares
14.4 Dependant random variable Y
14.5 Transformations, extrapolation and outliners
14.6 Confidence intervals and significance tests for the population regression coefficient β
Mean and variance of the estimator of β
Significance test for the regression coefficient
14.7 Confidence intervals and significance tests for the intercept x and for the expected value of Y, with known σ²
14.8 Distinguishing x and Y
14.9 Deducing x from a Y-value
14.10 Two regression lines
14.11 Correlation
Nonsense correlation
14.12 The product-moment correlation coefficient
The population product-moment correlation coefficient, p
Testing the significance of r
14.13 Spearmans rank correlation coefficient
Testing the significance
Alternative table formats
14.14 Using r for non-linear relationships
Chapter summary
Appendices
Cumulative probabilities for the binomial distribution
Cumulative probabilities for the Poisson distribution
The normal distribution function
Upper-tail percentage points for the standard normal distribution
Percentage points for the t-distribution
Percentage points for the x² distribution
Critical values for the product-moment correlation coefficient
Critical values for Spearmans rank correlation coefficient
Random number
Answers
Index
IBC
Back Cover
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