STATS 150: Statistical Literacy and Communicating Statistics - Lecture 1

Core Philosophy: Statistical literacy is about making decisions under uncertainty. The course aims to teach students how to think statistically, evaluate reports, and construct sound statistical statements.
Key Quote: "There are three kinds of lies: lies, damn lies, and statistics," often attributed to Benjamin Disraeli. This highlights the potential for statistics to be used to mislead.
Modern Context: Unlike in $2004$ , where students were less engaged with news, today the challenge is the constant bombardment of headlines via smartphones and social media. This necessitates a "sixth sense" for detecting misleading information.
Data Ubiquity: Data is collected constantly via motorway sensors, CCTV, loyalty cards (supermarket shopping), and Hop cards (transport). However, a large volume of data does not guarantee usefulness if it is not representative (e.g., Netflix data cannot always predict the general population).
Expert Insight: Professor Thomas Lumley runs the "Stats Chat" blog, which critiques media reports and rugby predictions using statistical perspectives.

The Avocado and Breast Cancer Study:
- Headline: "Study finds avocado damaging to carriers of breast cancer gene."
- Reality: This was a laboratory study on cells treated with folate. No human women or actual avocados were part of the research. The headline was a massive leap from cell biology to a dietary warning.
The Chocolate Study:
- Headline: "Two chocolate bars a day keeps the doctor away."
- Reality: The study defined "two bars" as up to $100\,g$ of chocolate. However, $90\%$ of participants actually consumed less than $25\,g$ . The claim generalized an extreme consumption level that did not apply to most subjects.
The UK Immigration and Employment Crisis:
- Headline: " $27$ young foreign workers hired for everyone Brit as immigration fuels unemployment crisis."
- The Flaw: The claim was based on the increase in people on the payroll between $2020$ and late $2026$ , not the number of actual hires.
- The Numbers: Under- $25$ non-EU workers on payroll grew from $82,000$ to $370,000$ (an increase of $290,000$ ). Under- $25$ UK workers grew from $3,840,000$ to $3,850,000$ (an increase of $11,000$ ). While the ratio of the increase is approximately $27$ , the total number of UK workers still vastly outnumbered foreign workers. Dividing increases is a misleading way to represent hiring practices.

The Sheep Paradox: A photo of two sheep (a pregnant ewe and a lamb) illustrates how counting requires clear definitions. Depending on whether a "sheep" includes unborn lambs, the count could be $2$ or $3$ . Consensus requires an agreed-upon definition.
Poverty Definitions:
- Relative Poverty: Often defined in New Zealand and the OECD as households with income falling below $50\%$ of the median household income.
- Absolute Poverty: Lacking the basic resources required to sustain life.
- Measurement Difficulty: Comparing poverty across countries is difficult because definitions vary. You cannot compare "apples and oranges."
Homicide Statistics: To judge a claim like "a woman is killed every five weeks by a partner," one needs context. NZ has approx. $100$ homicides per year ( $2$ per week). In five weeks, there are approx. $10$ homicides. Knowing the baseline makes specific statistics easier to evaluate for believability.

Core Principle: Evidence beats anecdotes and self-proclaimed experts. "Belief is no substitute for arithmetic."
Perspectives:
- Bird’s Eye View: A broad survey of the whole population or dataset.
- Worm’s Eye View: A close-up view of personal experience. Both are legitimate, but individual experience (e.g., being on one busy bus) may not reflect the statistical average (e.g., overall falling bus occupancy).
Counterexamples in Stats vs. Math:
- In Mathematics, a single counterexample can disprove a proof.
- In Statistics, a counterexample (e.g., Dorothy, a $100$ -year-old smoker) does not disprove a general trend (smoking is bad for health). Statistics deals with averages and general tendencies, not absolute laws.
Specific Anecdote Examples:
- Leukemia and Power Lines: Despite powerful anecdotal stories from mothers, multiple case-control studies over eight years found no increased risk of leukemia from living near power lines.
- Spring Births and Height: There is a slight biological tendency for those born in spring to be taller on average, but the difference is statistically negligible for individuals.
- London Marathon: An individual suffering a heart attack at mile $25$ humanizes a story that contradicts the general statistical fact that exercise reduces heart attack risk.