AP Biology Scientific Method and Quantitative Analysis Review

Quantitative Data: Measured using instruments (e.g., a height of $6\,ft$ ).
Qualitative Data: Observations gathered using the senses (e.g., blonde hair).
Deductive Reasoning: Derives specific results from general premises (e.g., determining work departure times based on traffic patterns).
Inductive Reasoning: Derives generalizations from a large number of specific observations (e.g., designing a floor plan to maximize sales).

Law: Statement of fact usually expressed as a mathematical formula; describes an observation without explaining "how or why", is generally accepted as true, and serves as the basis for the scientific method.
Theory: Summarizes a group of hypotheses; broader in scope, supported by a massive body of evidence, generates new hypotheses, and NEVER becomes a law.
Hypothesis: An explanation to a question tested by experiment or continued observation; can be disproven, but cannot be proven true.

Independent Variable: The factor changed or manipulated by the experimenter.
Dependent Variable: The factor measured in the experiment, whose value depends on how the independent variable is manipulated.
Positive Controls: Groups not exposed to the experimental treatment, but exposed to a treatment known to produce an expected effect to ensure there is an effect when expected.
Negative Controls: Groups not exposed to any treatment or exposed to a treatment known to have no effect, ensuring there is no effect when expected.
Constants: All factors that remain the same throughout an experiment.

Null Hypothesis ( $H_0$ ): Asserts that there is no difference between groups of data and experimental observations are due to chance; researchers attempt to disprove, reject, or nullify this hypothesis.
Alternate Hypothesis ( $H_1$ , $H_2$ ): A hypothesis that the experiment aims to support.

Mean: The average of a data set, calculated by summing all data points and dividing by the count.
Median: The middle value in an ordered range of data points (or the average of the two middle numbers).
Mode: The value that appears most frequently in a data set.
Variability: Measure of how far a data set diverges from central tendencies, measured by range and standard deviation.
Standard Deviation: A measure of how spread out data is from the mean.
- Low Standard Deviation: Data points are closer to the mean; changes are likely caused by the independent variable.
- High Standard Deviation: Data points are farther from the mean; factors other than the independent variable are likely causing changes.
Standard Error of the Mean & Error Bars: Standard error determines the precision of and confidence in the mean value, represented graphically by error bars.
- Overlapping Error Bars: Indicate that the difference between data groups is not significant.
- Non-Overlapping Error Bars: Indicate that the difference between data groups may be significant.