Making Sense of Statistics

Chapter summary

• Statistics help interpret data, and mathematics is an integral part of biological science.
• Statistics cannot show causation. They can only show correlation. Good experimental design is needed to explore causes.
• Statistics cannot make a silk purse out of a sow’s ear: poor data gives poor conclusions.

Why use statistics?

• Biological systems are diverse. Statistics make sense of numbers and test whether relationships are significant.
• The choice of method can change the conclusion. This is the root of the old line, often attributed to Disraeli or Mark Twain, about “lies, damned lies, and statistics”.
• Most people misunderstand randomness.
• Example: a study finds more soft-drink drinkers have diabetes. Statistics show the link, but not whether the drinks caused it.
• Researchers cannot run the ideal trial (1,000 people assigned to zero, one, two or three cans for ten years) because it would be unethical. They return to animal studies to ask why.

The bell curve problem

• Grading on a curve assumes a normal (Gaussian) distribution: in a class of 100, about two get an A and 14 a B.
• The normal distribution assumes randomness and a very large universe to sample from.
• In biology, distributions are often lopsided, samples are small and many populations do not fit the bell curve.
• Even large cohorts, such as 35,000 US nurses, may not represent everyone.

Where views differ

• Sceptics: Given the right statistics, one can prove anything. Misused, statistics compound the lies.
• Defenders: Properly used, statistics isolate patterns, reduce bias and tell us whether a measured difference is real. Without them, opinion rules.
• The author’s position: Statistics are tools. Their value depends on the design and honesty of the study behind them.

Questions to ask

• Is the difference between groups meaningful, not just statistically significant?
• What are the average and the spread of the population?
• The “average person” does not exist. In the 2011 US population by age and sex, the distribution is not bell-shaped, and age strongly shapes medical issues.
• Populations change over time, so older results may not apply today.

Take-away points

• Correlation is not causation.
• Look at the study design before the p-value.

References

• University of Kansas Medical Center. Normal distribution (bell curve) teaching material, as cited in the book.
• US Census Bureau (2011) Population by age and sex, as cited in the book.
• Disraeli, B. and Twain, M. Attributed quotation on “lies, damned lies, and statistics”.