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AP Bio Unit 0.7

Aug 23, 2025

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Overview

This lecture introduces the chi-square (χ²) equation, how to use it in AP Biology for analyzing experimental data, and how to interpret results using critical values and p-values.

Chi-Square Equation Basics

  • The chi-square equation tests if differences between observed and expected results are due to chance or a tested variable.
  • Chi-square compares expected outcomes (what should happen) with observed data (what actually happened).
  • The formula: χ² = Σ((O - E)² / E), where O = observed, E = expected, and Σ = sum.

Understanding p-Values and Null Hypothesis

  • The p-value measures evidence against the null hypothesis (no significant difference between observed and expected results).
  • If p-value < 0.05, reject the null hypothesis; if p-value > 0.05, fail to reject it.
  • The 0.05 threshold comes from a 95% confidence interval.

Degrees of Freedom and Critical Values

  • Degrees of freedom = number of possible outcomes minus one (n - 1).
  • Use a chi-square chart to find the critical value for a given degree of freedom at p = 0.05.
  • If χ² value is greater than the critical value, reject the null hypothesis.

Practice Problems and Application

  • Example 1: Flipping a coin 50 times (2 outcomes, degrees of freedom = 1, critical value = 3.84).
    • If observed is 28 heads, 22 tails, χ² = 0.72, which is less than 3.84, so fail to reject the null hypothesis.
  • Example 2: Rolling a dice 36 times (6 outcomes, degrees of freedom = 5, critical value = 11.07).
    • If χ² = 18.3, which is greater than 11.07, so reject the null hypothesis.

Key Terms & Definitions

  • Chi-square (χ²) — a statistical test to compare observed and expected data.
  • Observed (O) — actual data collected from an experiment.
  • Expected (E) — predicted results based on hypothesis.
  • Null hypothesis — assumption that there is no significant difference between observed and expected.
  • p-value — probability that results are due to chance.
  • Degrees of freedom — number of possible outcomes minus one.
  • Critical value — threshold in chi-square chart to determine significance.

Action Items / Next Steps

  • Practice additional chi-square problems.
  • Review the chi-square chart and how to use it for different degrees of freedom.
  • Prepare for upcoming assessments on statistics in AP Biology.

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