Incorporating Statistics into Biology: Chi-square, Sampling, Estimation, and Interpretation
Lesson Plan by Lynn Waterhouse and Joanne Johnson

This is a 4 part unit meant to be spread throughout the year. The units introduce and then incorporate statistical skills into the biology curriculum. The students will collect data, develop hypotheses, analyze the data, and learn all the skills required for the AP Biology exam, and learn some additional ecological sampling techniques. There are 4 primary lessons and numerous handouts that can be used as quizzes or as homework assignments. Topics covered include hypotheses, sampling, chi-square analysis, density, mean, total abundance, standard deviation, and balancing systems, quadrat sampling and additional ecological techniques.
  • Students will be able to develop and formulate hypotheses.
  • Students will be able to conduct a chi-square analysis testing the assumption of statistical equal numbers in different categories.
  • Students will understand the difference between sampling and conducting a census.
  • Students will also be able to explain the pros and cons of doing either option.
  • Students will be able to explain the difference between a biased and unbiased sample.
  • Students will be able to give an example of sampling that would be biased.
  • Students will understand random sampling. They will also understand convenience sampling and be able to provide examples of each type of sampling method.
  • Students will be able to use quadrat sampling to estimate total abundance.
  • Students will be able to list various methods for estimating total populations and indicate in which scenarios certain methods are more appropriate.
  • Students will be able to calculate means, standard deviation of the mean, and to compare different groups using the standard deviation of the mean.
  • Students will be able to use basic mark-recapture methods to estimate total abundance.
  • Students will be able to describe a tagging study appropriate for studying organisms at the individual scale and at the population scale.
  • Part 1: Introduction to Chi-Square Analysis.
  • Part 2: Introduction to Assessing Populations through Sampling.
  • Part 3: Population Estimation: Nassau Grouper & Tagging Studies.
  • Part 4: Balancing Cycles & Flow Diagrams.
  • The first PowerPoint (Introduction to Hypotheses PowerPoint) introduces hypotheses and the statistical testing framework. Students are asked to try formulating hypotheses. Topics covered include: Null hypothesis, alternative hypothesis, statistical result, biological result, and significance level (alpha).
  • The second PowerPoint (Introduction to Chi-Square PowerPoint) introduces the chi-square analysis test for equality (simply referred to as chi-square). As a class an example will be worked through.
  • The M&M lab (M&M Lab Activity Worksheet) is meant to be the main activity for students to learn chi-square analysis.
  • Students learn what a statistical hypothesis is, chi-square analysis, and a variety of applications within the biological framework.
  • Chi-square analysis is required by the AP Biology test and the handouts are meant to be used throughout the school year to ensure students have learned how to conduct a chi-square analysis.
  • The zebrafish handout (Zebrafish Example) requires familiarity with the terms genotype and phenotype.
  • The wetland bird handout (Wetland Bird Example) requires familiarity with basic species distribution concepts.
  • Part 1 will take multiple classes to do all the materials. The introduction to hypothesis and introduction to chi-square PowerPoints will take up most of a 40 minute class. The M&M lab activity will take a full class, and the advanced activity can be given as homework or take up a partial class.
  • The optional handouts (zebrafish example, dizziness example, wetland bird example, and census data example) should only take students around ten minutes to complete once they have mastered chi-square analysis, but until they have mastered the concepts more time should be allotted.
  • The PowerPoint (PowerPoint Introduction to Quadrat Sampling) introduces the concepts of sampling, random sampling, and using quadrats.
  • The mini-activity (Teacher Guide Sampling Mini Activity) can be done prior to doing the PowerPoint introduction to quadrat sampling, during the PowerPoint (the teaching notes indicate after which slide), or afterwards.
  • The concepts of biodiversity, species richness, and species evenness are discussed in the mini-activity (Teacher Guide Sampling Mini Activity).
  • The quadrat sampling activity (Quadrat Sampling Activity Worksheets) is meant to be done in groups. Every student needs a worksheet. Every group will need the three base sheets (provided in the Quadrat Sampling Base Sheets Files, Quadrat Sampling Base Sheets) and some quadrats. If you the teacher cannot make quadrats out of coffee stirrers (or popsicle sticks), a template that can be printed and cutout of paper is provided, at least three will need to be made per group. All sheets are provided to be printed in black and white. Note: students answers will vary based on individual quadrat placement. An example answer key is provided.
  • The advanced quadrat sampling activity (Advanced Quadrat Sampling Activity Sheet) requires open space. This activity is optional, and is just a more active version of the other activity. It requires some additional materials. They are all found in the Teacher’s instructions (Advanced Quadrat Sampling Teacher Instructions).
  • Part 2: Introduction to Assessing Populations: Quadrat Study will require at least 3 40 minute classes to complete everything. The mini-activity and introductory PowerPoint can be completed in one 40-minute class. The quadrat sampling activity will take another class and the chi-square extension can be given as homework or take a partial class. The advanced quadrat sampling activity will also take a full 40 minute class period. For both quadrat activities the students will most likely have computations to do for homework.
  • This lesson should begin by having students review the Tagging Studies PowerPoint (Tagging Studies PowerPoint) and the teacher should go over it in class. Concepts covered include: population estimation, tagging studies, and satellite tracking studies. Students will learn the math skills required for mark recapture studies and calculating mean, standard deviation, and standard error.
  • It is up to the discretion of the teacher to assign any activity for a grade. Example answer keys have been provided for all worksheets. The individual students’ answers will vary from the answer key as they require experimental data for the marking beans and advanced marking beans activity.
  • The marking beans (Marking Beans Activity) and advanced marking beans activity (Marking Beans Advanced Activity) requires bags of white beans, and black beans. Alternatively you can use orange goldfish crackers and pretzel goldfish crackers, or different colored beads. The material used does not matter, just ensure you have enough of them and that you have two colors. There should be well over 100 white beans per bag. This activity also requires cups for sampling. Every group will need a bag of white beans, some black beans, and a cup.
  • The Changing Seas (Changing Seas Student Sheet) activity requires playing video for the entire class to see. It is a video, produce by PBS, which gives a larger picture of the Nassau Grouper in the Caribbean.
  • There is a short introductory PowerPoint on Estimating Nassau Grouper Populations (Estimating Nassau Grouper Populations PowerPoint) that can either be done before or after the Changing Seas Activity (Changing Seas Student Sheet). The PowerPoint (Estimating Nassau Grouper Populations PowerPoint) and Changing Seas (Changing Seas Student Sheet) video should be followed by the activity in which students design their own research study for Nassau Grouper (Design A Study for Nassau Grouper Handout). This is a fairly open ended assignment, but students should be applying what they have learned thus far about sampling, scientific hypotheses, and the process of observation and hypothesis testing.
  • Part 3: Population Estimation will require 3 class periods. The introduction PowerPoint and marking beans tagging activity will require a full class. The marking beans advanced activity will take an additional class. The Nassau grouper video tagging activity can take a full class, or just part of one (depending on which videos are shown).
  • This lesson should begin by having students review the Flow Diagram and Cycles Introduction PowerPoint (Flow Diagram and Cycles Introduction PowerPoint) and then having the teacher review it in class. Concepts covered include: exponents, flow cycles, and flow diagrams. Students should be able to do all math by hand, but should be allowed a calculator if necessary.
  • Two cycle diagrams (Hydrological Cycle Worksheet and Flow Chart Worksheet) are provided, one is the hydrological cycle worksheet (Hydrological Cycle Worksheet) and the other is the flow chart worksheet (Flow Chart Worksheet). It is up to the discretion of the teacher to actually assign these for a grade.
  • The create your own flow diagram activity (Create Your Own Flow Diagram and Cycle) can be given as a homework assignment on an individual basis or as a group activity. The activity can be modified for a variety of skills and grade levels and also for various time constraints.
  • Part 4: Balancing Cycles & Flow Diagrams is intended to last for two partial segments of class-days (two twenty to thirty minute sections) for the introduction PowerPoint the first day along with one of the worksheets in class or for homework followed by the create your own flow diagram in a following class (or classes if you make it a more advanced assignment).
  • This activity was designed for an 11th grade AP Biology class, and would also be appropriate for a high school biology or advanced biology class. Some work is indicated as “Extra” and this is intended for the more advanced students. Work that is indicated as “Extra” is also beyond the standards that the AP Biology exam requires.
  • The chi-square activity handout on zebrafish requires knowledge of genetics (phenotypes and genotypes).
  • The chi-square activity handout on birds and wetlands requires knowledge on basics of animal distribution.
  • The quadrat sampling activity requires knowledge of animal distribution.
  • All activities require basic mathematical knowledge including addition, subtraction, division, power functions, and order of operations.
  • These activities introduce statistical concepts, but could also be used to reinforce them for any students that have already been introduced to statistics.
  • We assigned appropriate readings (review of PowerPoints and other course website provided materials) and completing the lab reports (including graphs) discussed and started in class that day. Additional handouts, review sheets, and quizzes are provided. These can be used as in class exercises or for graded assignment. Deciding on an appropriate homework assignment, if any, is left up to the instructor.
  • Some activities in this unit have questions with no right or wrong answer. They are designed to get the students thinking, observing, and applying concepts.
  • Some of the handouts are best in color, however care was taken to ensure that the activities would work in black and white.
  • Some activities require watching online video. Most video resources do not require audio, additional videos for reference may require audio but are optional. The Changing Seas video activity requires audio.
  • Next Generation Science Standards HS-LS3-3. Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.
  • Next Generation Science Standards HS-LS2-2. Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales.
  • Next Generation Science Standards HS-LS2-4. Use mathematical representations to support claims for the cycling of matter and flow of energy among organisms in an ecosystem.
  • Common Core State Standards for Mathematics MP.2. Reason abstractly and quantitatively.
  • Common Core State Standards for Mathematics MP.4. Model with mathematics.
  • Common Core State Standards for Mathematics MP.5. Use appropriate tools strategically.

Scuba diver in Kelp Forest in La Jolla, CA (Photocredit: Noah Ben-Ardent)


Rocky Intertidal in Scripps Coastal Reserve (Photocredit: Lynn Waterhouse)


Rockfish, Urchins, Algae spp. off La Jolla Cove, CA (Photocredit: Lynn Waterhouse)
Lesson Specifics
  • Grade Level: Specifically designed for 11th grade AP Biology Class. Can be used for advanced 9th or 10th grade
  • Time Frame: 4 full days, 4 partial days for follow up (spread out over the course of the year)

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