Statistics and Data Science

The aim of this module is to equip the learner with the tools and methods to find structure and to give deeper insight into data and to analyse and quantify uncertainty.   Learners will understand how data science can help organisations to reduce costs, make more informed decisions and develop new products and services.

Statistics and Data Science

Introduction

• Study types: observational studies and experiments; causation
• Gathering data: primary & secondary sources; questionnaires; experimental design
• Population and sample; parameters and statistics; sampling methods
• Variables and observations
• Bias
• Descriptive vs. inferential statistics

Exploratory data analysis (EDA):

• Types of variables: categorial, numerical
• Measurement scales: nominal, ordinal, discrete, continuous
• Types of graphs: bar charts, histograms, boxplots, time series plots, scatterplots, etc.
• Summarising distributions: measures of centre (mean, median and mode); measures of variance (range, interquartile range, standard deviation); measures of skewness
• Descriptions of a distribution: shape; modality; outliers
• Contextualising EDA using industry software: examples using Python

Probability

• Random experiments; outcomes; sample spaces; (simple & compound) events
• Classical, relative frequency, and subjective probability approaches
• Calculating simple probabilities; marginal and conditional probabilities
• Mutually exclusive events; dependent and independent events; multiplication rule; addition rule; Bayes’ theorem
• Central limit theorem
• Contextualising probability using industry software: examples using Python

Discrete Distributions

• Probability mass functions (PMFs)
• Bernoulli random variables
• Binomial distribution
• Poisson distribution
• Contextualising distributions using industry software: examples using Python

Continuous Distributions

• Cumulative distribution functions (CDFs) and probability density functions (pdfs)
• Exponential distribution
• Normal distribution: properties, z-scores, normal tables
• Contextualising distributions using industry software: examples using Python

Statistical Inference

• Point estimates; standard error
• Confidence intervals
• Testing theories; Introduction to hypothesis testing
• Testing a mean or proportion (one-sample tests)
• Testing the difference between two means or two proportions (two-sample tests)
• Chi-squared tests
• Sample size and power
• Contextualising hypothesis tests using industry software: examples using Python

Making predictions

• Correlation
• Regression line; regression analysis; least squares fit; producing predictions
• Multiple regression and non-linear regression
• Model validation; outliers; influential observations
• Contextualising predictions using industry software: examples using Python

Data science in context

• Report writing
• Statistics in business: legal issues, ethics, GDPR, privacy
• Introduction to advanced topics, such as: data warehouses, machine learning, data mining, big data