Scientific Inquiry and Data Analysis
Scientific Inquiry and Data Analysis tests experimental design, variable identification, measurement quality, statistical reasoning, and interpretation of graphs and tables. Questions often present a scenario and ask what conclusion is justified, what control is missing, or whether a result is statistically significant.
Designing experiments
- The independent variable is manipulated; the dependent variable is measured; controlled variables are held constant.
- A control group provides a baseline; randomization reduces bias; replication increases reliability; blinding reduces expectancy effects.
- Correlation does not establish causation; a confounding variable can explain an association.
Measurement and uncertainty
- Accuracy is closeness to the true value; precision is consistency among repeated measurements.
- Standard deviation describes spread within a sample; standard error describes uncertainty in an estimate of the mean.
- Error bars may represent standard deviation, standard error, or confidence intervals; always identify which before interpreting overlap.
Statistical reasoning
- The null hypothesis usually states no difference or no association.
- A chi-square goodness-of-fit test compares observed and expected frequencies: χ² = Σ(O − E)²/E.
- A t-test compares means; a p-value is the probability of data at least as extreme as observed if the null hypothesis is true.
- Reject the null when p < 0.05 or when the test statistic exceeds the critical value.
Worked example
A chi-square test gives χ² = 6.2 with 2 degrees of freedom. The critical value at p = 0.05 is 5.99. Because 6.2 > 5.99, reject the null hypothesis: the observed frequencies differ significantly from the expected frequencies at the 5% level.
Traps that cost marks
- Calling a result "proven" when a hypothesis was not rejected.
- Interpreting p = 0.05 as a 5% chance the null is true.
- Confusing standard deviation with standard error.
- Using the wrong degrees of freedom in chi-square.
- Drawing conclusions beyond the range of the data, especially by extrapolation.