Introducing Statistics

US$ 71.40

The publisher has enabled DRM protection, which means that you need to use the BookFusion iOS, Android or Web app to read this eBook. This eBook cannot be used outside of the BookFusion platform.

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

The book hasn't received reviews yet.