AP Biology Unit 0: Nature of Science - Quick Reference

Mean, Standard Deviation, Standard Error

• Interpretation:

  • SD = spread of the data around the mean

  • SE = precision of the estimated mean; smaller SE = more precise mean estimate

Analyzing Standard Deviation

• SD assesses data variability; compare SD across groups to judge consistency

• SE is often used in graphs to show how well the mean is known

Theory vs Hypothesis

• Theory: well-supported explanation of natural phenomena

• Hypothesis: testable, falsifiable statement derived from theory

Null vs Alternative Hypothesis

• Null hypothesis (H0): no effect or no difference

• Alternative hypothesis (Ha): there is an effect or a difference

• Decisions are based on data (p-values, confidence intervals) and pre-set significance level

Analyze data and draw conclusions

• Use statistical results to decide whether to reject H0

• Draw conclusions consistent with the data and the experimental design

Set up an experiment

• Define Independent Variable (IV): deliberately changed

• Define Dependent Variable (DV): measured outcome

• Controls: kept constant to ensure valid comparisons

• Include randomization and replication; document constants

Identify IV, DV, and Controls in an experiment

• IV: what you intentionally change

• DV: what you measure

• Controls: conditions kept the same across groups

Graphs and data sets: analysis and extrapolation

• Look for trends, direction, magnitude, and potential outliers

• Be cautious with extrapolation beyond data range

Statistical significance: error bars and p-values

• Error bars represent variability; can denote SD or SE (check legend)

• P-value: probability of obtaining data as extreme as observed under H0

• Compare p-value to significance level (e.g., \alpha = 0.05) to decide on rejecting H0

• Rule of thumb: non-overlapping error bars suggest a statistically significant difference (not guaranteed in all cases, but a common intuition)

Figure 1: Population trends and null-hypothesis refutation

• Figure shows urban vs rural population trends from 1900 to 2016

• Null hypothesis: animal biodiversity in rural and urban areas will be unaffected by human population trends shown in Figure 1

• Best refutation: "Urbanization causes habitat fragmentation." (directly links human trends to habitat change)

Experimental groups: controls vs. experiments

• Examples include controls vs. experimental groups and measured outcomes (e.g., Average Brood Size)

• Clear labeling of treatment vs. control is essential for interpretation

Quick calculation: standard deviation of the data set {4, 5, 6, 7}

• Mean: \bar{x} = \frac{4+5+6+7}{4} = \frac{22}{4} = 5.5

• Deviations: -1.5, -0.5, 0.5, 1.5

• Squared deviations: 2.25, 0.25, 0.25, 2.25

• Sum of squared deviations: 5.0

• Sample standard deviation: s = \sqrt{\frac{1}{n-1}\sum (x_i - \bar{x})^2} = \sqrt{\frac{5}{3}} \approx 1.29

• Population standard deviation: \sigma = \sqrt{\frac{1}{n}\sum (x_i - \bar{x})^2} = \sqrt{\frac{5}{4}} \approx 1.12