Statistics

From this page I will soon be uploading statistical exercises and cases with worked step-by-step solutions that will be linking to their respective theory pages in ‘My notes on statistics’.

Below, you will find the directory for ‘My notes on statistics’. Each page has a comments module – thanks for your feedback. 

My notes on statistics

Probability

• Sample space, events and probabilities
• Complement of an event
• Independent events
• Dependent events
• Mutually exclusive events
• Mutually inclusive events
• Permutations
• Combinations
• Conditional probability
• Law of total probability
• Bayes’ Theorem

Summarizing quantitative data

• Mean, median and mode
• Interquartile range (IQR)
• Variance and standard deviation of a population
• Variance and standard deviation of a sample

Discrete Probability Distribution

• Discrete vs. continuous random variables
• Discrete probability distributions
• Mean, variance and standard deviation
• Mean of sum & difference
• The binomial distribution
• Poisson distribution
• The geometric distribution
• Hypergeometric distribution

Modelling data distributions

• Continuous vs. discrete data
• Density curves
• Significance level
• Critical value
• Z-score
• The p-value
• The Central Limit Theorem
• Skewness and kurtosis

The Normal Distribution

• The normal distribution
• The Empirical Rule
• Z-table for proportions
• Student’s t-distribution

Study design

• Statistical questions
• Census and sampling
• Non-probability sampling
• Probability sampling
• Bias

Confidence intervals

• Confidence intervals
• Confidence interval for a population
• Confidence interval for a mean

Hypothesis Testing

• Hypothesis testing
• One-tailed tests
• Two-tailed tests
• Proportion hypothesis testing
• Hypothesis test for a mean
• Statistical power
• Power of test calculation
• Chi-square Goodness of Fit Test

Simple linear regression, fundamentals

• Scatter plots
• Correlation coefficient
• Regression line
• Squared errors of line
• Coefficient of determination, r2

Simple linear regression, Inference

• Inference about regression
• The LINER model
• Residual plots
• Standard error of the slope
• Confidence interval for the slope
• Hypothesis test for the slope
• Mean and single response intervals
• Influential points
• Precautions in simple linear regression
• Transformation of data

Two-sample inference for the dif. between groups

• Comparing two proportions
• Comparing two means
• Pooled variance t-procedure

ANOVA and the F-distribution

• One-way ANOVA
• Multiple comparison testing in ANOVA
• Two-way ANOVA

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