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
- Descriptive statistics summarise the data we have: tables, graphs, averages. Most of today.
- Inferential statistics use a sample to draw conclusions about a larger population, with a measure of uncertainty. Later modules.
Image: everyday statistics: an opinion poll, a weather forecast, a clinical trial
Today
Three questions run through today's lecture
Where do the data come from?
Populations, samples and study design
What kind of data are they?
Types of variables
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
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
What kind of data are they?
Every variable is categorical or numerical
What kind of data are they?
20 kg is twice 10 kg, but 20 °C is not twice as hot as 10 °C
| Nominal | Ordinal | Interval | Ratio | |
|---|---|---|---|---|
| Order? | no | yes | yes | yes |
| Equal intervals? | no | no | yes | yes |
| True zero? | no | no | no | yes |
| Example | eye colour | race finishing position | temperature in °C | weight, 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