STATS 101 · Module 1

Data, samples and describing data

By the end of today you can say where data come from, what kind they are, and what they say.

Why statistics?

Statistics draws conclusions from data that vary

Image: everyday statistics: an opinion poll, a weather forecast, a clinical trial

Today

Three questions run through today's lecture

  1. Where do the data come from?

    Populations, samples and study design

  2. What kind of data are they?

    Types of variables

  3. What do the data say?

    Graphs, centre, spread and shape

London, 1854

A map of deaths pointed to one water pump

During a cholera outbreak in Soho, John Snow marked each death on a street map. The deaths clustered around one pump on Broad Street. The pump's handle was removed.

Image: John Snow's 1854 map of cholera deaths around the Broad Street pump

United States, 1936

2.4 million replies lost to 50,000 well-chosen people

Digest mailedphone books, car lists about 10 million Digest repliespredicted Landon about 2.4 million: wrong Gallup's samplepredicted Roosevelt about 50,000: right
Bars to scale. Roosevelt won about 61% of the popular vote and 46 of the 48 states.

The lesson of 1936

A huge biased sample is worse than a small, well-chosen one.

Where do the data come from?

We measure a sample to learn about a population

Population all students at the university Parameter: μ, σ usually unknown Sample 200 students who answered a survey Statistic: x̄, s the statistic estimates the parameter
Memory aid: Population goes with Parameter; Sample goes with Statistic.

What kind of data are they?

Every variable is categorical or numerical

Variable Categorical Numerical Nominalno order blood type, favouritecolour, country Ordinalnatural order satisfaction,year of study Discretecounts number of siblings,goals scored Continuousmeasurements height, time,temperature
Watch out: a postcode or a student ID is categorical; averaging them means nothing.

What kind of data are they?

20 kg is twice 10 kg, but 20 °C is not twice as hot as 10 °C

NominalOrdinalIntervalRatio
Order?noyesyesyes
Equal intervals?nonoyesyes
True zero?nononoyes
Exampleeye colourrace finishing positiontemperature in °Cweight, income, time

Where do the data come from?

Only a randomised experiment can show cause and effect

Observational study

Researchers observe and measure without assigning treatments, such as surveying students about sleep and grades. It can show an association, but not cause and effect.

Experiment

  • Researchers assign treatments and compare outcomes
  • A control group for comparison
  • Random assignment, so the groups are alike apart from the treatment
  • A placebo where possible, and blinding