A-1
APPENDIX A
Statistical Reasoning in Everyday Life
- Describing Data
- Measures of Central Tendency
- Measures of Variation
- Correlation: A Measure of Relationships
- Significant Differences
- When Is an Observed Difference Reliable?
- close-up: Cross-Sectional and
Longitudinal Studies - When Is an Observed Difference
“Significant”?
In descriptive, correlational, and experimental research, statistics are tools that help us see and interpret what the unaided eye might miss. Sometimes the unaided eye misses badly, as it did when researchers asked 5522 Americans to estimate (as a percentage) the portion of the country’s wealth possessed by the richest 20 percent of the population (Norton & Ariely, 2011). The average person’s guess—58 percent—“dramatically underestimated” the actual figure. (The wealthiest 20 percent possess 84 percent of the wealth.)
Accurate statistical understanding benefits everyone. To be an educated person today is to be able to apply simple statistical principles to everyday reasoning. We needn’t memorize complicated formulas to think more clearly and critically about data.
Asked about the ideal wealth distribution in America, Democrats and Republicans were surprisingly similar. In the Democrats’ ideal world, the richest 20 percent would possess 30 percent of the wealth. Republicans preferred a similar 35 percent (Norton & Ariely, 2011).
Off-the-top-of-the-head estimates often misread reality and then mislead the public. Someone throws out a big, round number. Others echo it, and before long the big, round number becomes public misinformation. A few examples:
- Ten percent of people are lesbians or gay men. Or is it 2 to 3 percent, as suggested by various national surveys (Chapter 4)?
- We ordinarily use but 10 percent of our brain. Or is it closer to 100 percent (Chapter 2)?
- The human brain has 100 billion nerve cells. Or is it more like 40 billion, as suggested by one extrapolation from sample counts (Chapter 2)?
The point to remember: Doubt big, round, undocumented numbers.
Statistical illiteracy also feeds needless health scares (Gigerenzer et al., 2008, 2009, 2010). In the 1990s, the British press reported a study showing that women taking a particular contraceptive pill had a 100 percent increased risk of blood clots that could produce strokes. This caused thousands of women to stop taking the pill, leading to a wave of unwanted pregnancies and an estimated 13,000 additional abortions (which also are associated with increased blood clot risk). And what did the study find? A 100 percent increased risk, indeed—but only from 1 in 7000 to 2 in 7000. Such false alarms underscore the need to teach statistical reasoning and to present statistical information more transparently.