• Course philosophy
• Software
• Contents

• Definition
• Types of statistician
• Variability
• Probability
• Die roll outcomes
• Why is knowledge of statistics important?
• Descriptive vs inferential statistics
• Inferring population parameters
• Quantitative data
• Qualitative data
• R statistical software
• RStudio
• Interactive exercise manual demo

• What is exploratory data analysis (EDA)
• Histograms and bar charts
• Bar chart vs histogram
• Central tendency and spread
• Bin width is crucial
• Right-skewed data
• Outliers
• Left-skewed data
• Bimodal data
• Separate subpopulations for analysis
• Individual value plot
• Subpopulation individual value plots
• Benefits of boxplots
• Boxplot
• Boxplot vs histogram
• Left-skewed boxplot
• Compare subpopulations using boxplots
• Swedish salaries by level of education
• Measures of central tendency
• Mean vs median
• Mean vs median for skewed data
• Mode
• Measures of spread
• Range and IQR
• Standard deviation
• Six figure summary
• Central tendency and spread equations
• Quantiles

• Numbers are mostly reckless estimates
• Random variables
• Male life expectancy in UK distribution
• What’s the probability that a US man is 6’ or more?
• What is a probability distribution?
• Populations vs samples
• Sampling the heights of 10 random American men
• Sampling the heights of 100,000 random American men
• Discrete probability distributions
• Roll two dice and histogram the results
• Poisson distribution
• Binary probability distributions
• Probability distribution for cars/household in the UK
• Binomial distribution
• Geometric distribution
• Negative Binomial distribution
• Continuous probability distributions
• Uniform distribution
• Triangular distribution
• Normal distribution
• Properties of the normal distribution
• Distribution of IQ scores
• Different means (same standard deviation)
• Different standard deviations (same mean)
• z-distribution
• 68–95–99.7 (empirical) rule
• Quantile-Quantile (Q-Q) plot
• Q-Q plot of non-normal data
• Common probability distributions “family tree”

Transforming data with Relational Operators

• Samples are proxies for the population of interest
• Unfortunately, samples vary
• Larger samples exhibition less variation
• Statistics vs parameters
• Distributions involved in statistical inference
• Sampling distribution of mean IQ
• Collecting more IQ samples
• Sampling distribution of mean die roll
• Sampling distribution of mean project duration
• Create a sampling distribution
• Central limit theorem
• Implications of the central limit theorem
• Standard error of the mean (SEM)
• Impact of sample size on SEM
• What is a confidence interval?
• 95% confidence interval
• Bigger samples give greater precision
• Smaller confidence levels result in tighter intervals
• How should we interpret the confidence interval?
• Random sampling
• Simple random sampling
• Stratified sampling
• Cluster sampling
• What is bootstrapping?
• Estimating median life expectancy

• What is statistical inference?
• Why must we use samples?
• Why do we need to conduct hypothesis tests?
• What is hypothesis testing?
• Null hypothesis
• Alternative hypothesis
• Rejecting the null hypothesis
• One- vs Two-tailed hypothesis tests
• Choosing between one- and two-tailed tests
• What are p-values?
• Significance level (?)
• Types of errors
• Confidence levels vs significance levels
• Performing hypothesis tests
• p-value controversy
• When to use a t-test
• t-value
• t-distribution
• t-distributions
• Slot machine observed ”Return to Player”
• Are slot machine payouts within tolerance?
• Preform a t-test on RTP data using R
• Two-sample t-test
• When to use a z-test
• Conducting hypothesis tests using z-scores
• When to use a 2 test
• Education and Brexit vote
• Brexit vote breakdown
• 2 value
• 2 distributions
• Are education and Brexit vote related?
• When to use a F-test
• Conducting hypothesis tests using F-values
• F-distributions
• Height distribution by sex
• Does height variation differ by sex?
• When to use analysis of variance (ANOVA)
• Determining the F-value
• Are all diets the same?
• All diets are apparently not the same
• Normality hypothesis tests
• Statistically significant treatments?
• What is statistical power?
• Calculating statistical power
• Statistical power curve
• Improving statistical power of hypothesis tests