Scientific Reasoning and Data Interpretation: Variables, Graphs, and Evidence
Designing an experiment
A testable hypothesis predicts a relationship between an independent variable (what the researcher manipulates) and a dependent variable (what is measured). The control group receives no treatment or a placebo, while controlled variables are held constant for all groups. Only by changing one variable at a time can a cause-and-effect claim be supported.
Judging data
Accuracy describes how close a measurement is to the true value; precision describes how closely repeated measurements agree. Large samples and repeated trials improve reliability. Correlation does not establish causation, and observational studies cannot prove cause. Watch for bias: selection bias, small samples, missing control groups, and results that are statistically significant but practically trivial.
Reading graphs and numbers
Identify the axes and units before reading values, and note whether an axis starts at zero, since a truncated axis exaggerates change. Slope of a line equals change in y divided by change in x. Distinguish percent change from percentage points: going from 10% to 15% is a 5-percentage-point rise but a 50% relative increase.
Traps
The control group is easily confused with controlled variables. Accuracy and precision are frequently swapped. An outlier is not automatically an error - it may be real.
Worked example
A line graph plots plant height (cm, y-axis) against weeks (x-axis) and passes through (2 weeks, 6 cm) and (6 weeks, 18 cm). Slope = (18 − 6) ÷ (6 − 2) = 12 ÷ 4 = 3 cm per week. Rule of thumb: before answering any data question, state what is on each axis and in what units, then calculate.