By the end of the hour you can tell a sample from a population, choose a graph for any variable, and read the centre, spread and shape of a set of numbers.
STATS 101Introductory · no prior statisticsPrerequisite: high-school algebra
The three questions
How the hour is built
Where do the data come from? ~15 min
What kind of data are they? ~10 min
What do the data say? ~25 min
Why statistics?
Statistics is the science of collecting, describing and drawing conclusions from data — in the presence of variation and uncertainty.
Two branches, found everywhere
Descriptive
Summarise the data we already have: tables, graphs, averages. Most of this module.
Inferential
Use a sample to draw conclusions about a larger population, with a measure of uncertainty. Later modules.
In everyday life
Opinion polls
Clinical trials
Sports analytics
Weather forecasts
Website A/B tests
Question one
1
Where do the data come from?
Two stories, then population, sample, and how data are collected.
Story one · London, 1854
John Snow maps cholera
During a cholera outbreak in Soho, Snow marked each death on a street map. The deaths clustered around one water pump on Broad Street. The pump's handle was removed.
Image placeholder: John Snow's 1854 cholera map of Soho — deaths marked as X's, clustered around the Broad Street pump.
Story two · US election, 1936
The Literary Digest poll
The huge poll
About 10 million ballots mailed
About 2.4 million returned
Drawn from phone books & car lists
Predicted: Alf Landon wins
The small poll
George Gallup, about 50,000 people
A better-chosen sample
Predicted: F. D. Roosevelt wins
Roosevelt won ~61% of the vote, 46 of 48 states
A huge biased sample is worse than a small, well-chosen one.
How data are collected matters more than how much there is.
Population, sample, parameter, statistic
From the whole group to one number
Click 1: the two boxes and the chosen few. Click 2: the arrows. Click 3: the numbers they produce.
Parameter vs statistic
Parameter
A number describing the population — usually unknown. Notation: the mean μ and standard deviation σ.
Statistic
A number computed from the sample, used to estimate the parameter. Notation: the mean x̄ and standard deviation s.
Two families of variables
Categorical
Nominal — no order: blood type, favourite colour, country
Ordinal — a natural order: satisfaction (low / med / high), year of study
Continuous — measured on a scale: height, time, temperature
Watch out
Numbers aren't always numerical data. A postcode or a student ID is categorical — averaging them means nothing.
Question two · what kind of data
Levels of measurement
Order?
Equal intervals?
True zero?
Example
Nominal
No
No
No
eye colour
Ordinal
Yes
No
No
race finishing position
Interval
Yes
Yes
No
temperature in °C
Ratio
Yes
Yes
Yes
weight, income, time
Collecting the data
2
How is the data collected?
Observation or experiment, sampling methods, and the biases that mislead.
Observation vs experiment
Observational study
Observe and measure without assigning treatments — e.g. surveying students about sleep and grades. It can show an association, but not cause and effect.
Experiment
A control group for comparison
Random assignment — groups alike apart from the treatment
A placebo where possible, and blinding (double-blind)
Only a randomised experiment shows cause and effect
Five ways to sample
Method
How it works
Example
Simple random
Every group of n has the same chance
draw 100 student IDs at random
Stratified
Split into groups (strata), sample each
25 students from each year of study
Cluster
Split into groups, choose whole groups
pick 5 lecture sections, survey all in them
Systematic
Every k-th from a list, after a random start
every 20th name on the class list
Convenience
Whoever is easiest to reach — not random, avoid
asking friends in the cafeteria
Bias: when a sample misleads
Selection bias — the way you choose the sample leaves out part of the population (the Digest's phone and car lists).
Non-response bias — the people who don't respond differ from those who do.
Response bias — the wording or setting pushes an answer ("Don't you agree that…?").
Voluntary response bias — only people with strong opinions take part (online polls, call-in shows).
A bigger sample does not fix bias — it only makes a biased answer look more precise.
Question three
3
What do the data say?
Graphs, shape, centre, spread, outliers, z-scores and correlation.
Choosing the right graph
Data
Graph
What it shows
One categorical
Bar chart (or pie)
counts or percentages per category
One numerical
Histogram
shape of the distribution
One numerical
Box plot
five-number summary & outliers
Two numerical
Scatter plot
relationship: direction, form, strength
A variable over time
Line graph
trends
Always plot the data first
Four pictures, the same numbers
Anscombe's quartet (1973): four sets of 11 points each, x̄ ≈ 9, ȳ ≈ 7.50, r ≈ 0.816, line y = 3 + 0.5x — yet four different pictures.