Statistics 744, McMaster University

Information processing

• Image downloaded from defunct post This link no longer works ☹

• Some information from flowingdata

Scales

• The top of the hierarchy involves putting things on scales

• But what scale do we use?
  • Are our data anchored to zero?
    • If so, are we interested in differences or ratios?
  • Are they anchored somewhere else?

Anchors

Utter problem algae

Utter problem algae

Utter problem algae

Global temperature

Global temperature

Global temperature

• Data
• Code: clean; plot
• Dushoff craziness! shellpipes

Magazine circulation (advertisement)

Magazine circulation (absolute amount)

Magazine circulation (trend)

Magazine circulation (trend)

* Data * Code

Area and volume

From How to Lie with Statistics

Advertisement lessons

• Use area to indicate fair comparisons
  • On a physical scale
• Areas that can be compared linearly should be preferred
  • Depends on importance of feature
• Avoid using (or hinting at) volume

Ratio scaling

Physical quantities

• 1 is to 10 as 10 is to what?

• The log scale is often good for concrete quantities:
  • When zero means zero
  • When we are thinking about things that might be added together
    • But not when we actually want to add them together!

Provinces of Canada

Provinces of Canada

Provinces of Canada

Provinces of Canada

Provinces of Canada

Provinces of Canada

• Code: clean; plot
• Data

Coronavirus incidence

Coronavirus incidence

Coronavirus incidence

• Code: clean; plot
• Data

Odds-ratio scaling

Probabilities

• 1% is to 10% as 10% is to what?

• There is a simple, good answer
  • No single answer will always be best

Example

• 20% of the adult population is unvaccinated, but they account for 60% of clinical diagnoses

• How much greater is their risk?

Odds ratios

• The odds of an adult being unvaccinated is the ratio of the probabilities unvaccinated:vaccinated
  • 0.2/0.8 = 1/4
• The odds of a diagnosee being unvaccinated is
  • 0.6/0.4 = 1.5
  • The odds ratio is 6 – that’s the correct measure of relative risk
  • You can work this out the long way
• Odds are a natural basis for doing calculations with probabilities
  • These calculations are usually ratio-based
• Therefore: a good scale for many probability questions is the log-odds (or logit) scale

Probabilities

• 1% is to 10% as 10% is to …

• There is a simple, good answer
  • No single answer will always be best
• Odds scale: 1/99 is to 1/9 as 1/9 is to 11/9
  • Probability scale … 55%
  • Has a concrete meaning, for example screening tests:
  • if 1% prevalence implies 10% of positives are true, then:
  • Has a concrete meaning; if 10% prevalence implies 55% of positives are true

Coronavirus vaccination

Coronavirus vaccination

Coronavirus vaccination

• Code
• Data

Transformation lessons

• Transformations don’t make your data less real

• Different perspectives illuminate different questions

• Use visual clues to suggest whether your scales are additive