Table of contents

1 About statistics

1.1 Application of statistics in science

1.2 Statistics in everyday life

1.3 The Scope and limitations of statistics

3.1 Probability approaches

3.2 Random event

3.3 A priori and a posteriori probability

3.4 Cumulative probability, conditional probability and compound event probability

3.5 Combinatorics

3.5.1 Permutations

3.5.2 Variations

3.5.3 Combinations

3.6 Random variable

3.7 Probability distributions

3.7.1 Discrete random variable

3.7.1.1 Discrete uniform distribution

3.7.1.2 Bernoulli distribution

3.7.1.3 Geometric distribution

3.7.1.4 Binomial probability distribution

3.7.1.5 Poisson probability distribution

3.7.1.6 Hypergeometric probability distribution

3.7.2 A continuous random variable

3.7.2.1 Uniform distribution of a continuous random variable

3.7.2.2 Exponential probability distribution

3.7.2.3 Normal probability distribution

3.7.2.3.1 Standard normal distribution

3.7.2.3.2 Use of standard normal distribution tables

3.7.2.3.2.1 Calculating the probability of a particular result using statistical tables

3.7.2.3.2.1.1 An example of using a table containing the areas under the normal curve from µ to z to calculate the probability of a particular result

3.7.2.3.2.1.2 An example of using a table containing areas under the normal curve from -∞ to z to calculate the probability of a particular result

3.7.2.3.2.2 Calculating interval probabilities using statistical tables

3.7.2.3.2.2.1 An example of using a table containing the areas under the normal curve from µ to z to calculate within-range probabilities

3.7.2.3.2.2.2 Example of using a table containing the areas under the normal curve from -∞ to z to calculate interval probabilities

3.7.2.3.2.3 Finding a raw score from a given probability

3.7.2.3.2.3.1 An example of using a table containing the areas under the normal curve from µ to z to calculate a result for a certain probability

3.7.2.3.2.3.2 An example of using a table containing the areas under the normal curve from -∞ to z to calculate a result for a certain probability

3.8 Law of large numbers

3.9 Central limit theorem

4 Statistical inference

4.1 Population and sample

4.2 Statistical hypothesis testing

4.2.1 Statistical hypotheses

4.2.2 Statistical significance and critical values

4.2.3 One-way or two-way statistical hypothesis testing

4.2.4 General procedure for performing statistical tests

4.2.5 Errors in statistical hypothesis testing

4.2.6 Limitations of hypothesis testing

5 Correlation and regression analysis

5.1 Measures of association between variables

6 Statistical software

6.1 Trends in the development of statistical software

6.2 Characteristics of statistical software

6.3 Types of statistical software

6.4 Criteria for choosing statistical software

6.5 The use of spreadsheets in statistical data processing

6.6 Software packages for statistical data processing

6.7 Statistical software packages that require licensing

6.8 Open-source and free software packages for statistical data processing

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