Mathematics and statistics in biology

Modern instruments, such as DNA sequencers and advanced microscopes, produce far more data than any notebook or spreadsheet can handle. So biologists need computing and statistics to make sense of it. But statistics only helps answer questions; it cannot replace asking good biological questions in the first place.

Correlation measures how closely two things change together. Regression fits a line showing how one changes as the other changes. In the book's example of ten patients' heart rate and blood pressure, a line is fitted through the points. Its R-squared value runs from 0 (no relationship) to 1 (a perfect fit: every point on the line); here it is high, showing a strong link.

Some key terms:

• Null hypothesis: the starting assumption that there is no relationship between the things being studied.
• p-value: the chance of getting your result (or a more extreme one) if the null hypothesis were true. A small p-value suggests a real effect.
• t-test: compares the means (averages) of two groups. ANOVA compares more than two.
• Multiple testing correction: an adjustment needed when many tests are run at once, since some will look significant by chance.

Good experimental design: enough replicates (biological and technical), independent repeats, random sampling to avoid bias, the right statistical test, and correction when many tests are run. Software like MATLAB and R helps with the analysis.

Be careful with the usual cut-off: a p-value below 0.05 is commonly called significant, but relying on it alone has produced many false positives. With small samples, show every data point, and do not force data into the wrong model (for example, wrongly assuming it follows a normal, bell-shaped distribution).