Biology | Genetics Data Analysis (Chi-square) Tutor Prep Guide

Biology | Genetics Data Analysis (Chi-square) Tutor Prep Guide | Testing 3:1 and 1:2:1

2026-11-06

Tutor lesson-prep guides · Secondary Biology

Students can recite 3:1, but the paper hands them 290:110. This lesson gives them a statistical sentence for whether that gap is sampling noise or a broken ratio.

Objectives — Students will be able to: (1) turn a genetic ratio and a sample size into expected numbers that add back to the sample; (2) compute chi-square as the sum of (O-E)^2/E and set degrees of freedom from the number of classes; (3) compare against 3.841 or 5.991 and write a full conclusion instead of the word close.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Genetic ratio	What ratio does Aa x Aa give	3 dominant to 1 recessive
Expected numbers	Split 400 flies in 3:1	300 and 100, and they must total 400
Significance level	What does the 0.05 line mean	A gap this large happens under 5% of the time, so the ratio is rejected

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Prerequisite check	Ask for the 3:1 ratio and the expected-number method, repair on the spot	Three oral answers
8-20 min	Set the hypotheses	Write H0 as fits 3:1 and H1 as does not, then list observed and expected rows	Fill the table
20-35 min	Compute chi-square	Square each gap, divide by its expected value, then total	Students compute 290:110
35-45 min	Set df	df equals classes minus one: two classes give 1, three give 2	Read the critical table
45-53 min	Write the conclusion	Compare the value with the critical value and state reject or do not reject	Two sentences
53-60 min	Exit check	Three oral questions, wrong answers sent back to the matching act	Work independently

03 Teaching script (read it out)

Scene 1: Act one: pin the expected numbers on the table first

Write H0 as the observed numbers fit 3:1, not as they follow Mendel, which cannot be tested. Without a stated ratio there is nothing to compare against.
Expected numbers come from ratio times sample: 400 x 3/4 = 300 and 400 x 1/4 = 100, and the row must total 400. If it does not, the arithmetic is wrong.
For 1:2:1 the same step gives 240 x 1/4 = 60, 240 x 2/4 = 120 and 60, totalling 240.

Ask the student: does this expected row add back to the sample size?

Scene 2: Act two: chi-square is each gap squared, divided, then summed

There is one formula: chi-square equals the sum of (O-E)^2/E. The common error is adding the gaps before squaring; square each cell first, divide, and only then add.
For 290:110 both gaps are 10, so 100/300 = 0.333 and 100/100 = 1.000, giving 1.333.
For 55:130:55 against 60:120:60 the cells give 0.417 + 0.833 + 0.417 = 1.667. Keep three cells separate and never merge them.

Ask the student: did you square each cell, or add the gaps first?

Scene 3: Act three: degrees of freedom and the conclusion sentence

Degrees of freedom equals classes minus one, not sample size minus one. Two classes give df 1 with a critical value of 3.841; three classes give df 2 with 5.991 at the 5% level.
Below the critical value, write that H0 is not rejected at the 5% level and the observed ratio does not differ significantly from 3:1. Above it, write that H0 is rejected.
The sentence needs a direction and the term: close or nearly is not an answer and scores nothing.

Ask the student: what is the df, and what critical value goes with it?

04 Question types and worked steps

Type	Example	Steps	Answer
Single factor 3:1	400 flies at 290:110	H0, expected 300 and 100, chi-square 1.333, df 1, compare 3.841	Conclusion: do not reject H0
Codominance 1:2:1	240 plants at 55:130:55	Expected 60/120/60, chi-square 1.667, df 2, compare 5.991	Conclusion: do not reject H0
Dihybrid 9:3:3:1	160 plants in four classes	Expected 90/30/30/30, df 3, critical value 7.815	df follows classes, never fixed at 1
Reverse question	Given chi-square 9.2 with df 1	Compare with 3.841, reject H0, then name the largest contribution	Point at the cell driving the value

Sanity check (teach this): Sanity check: 290 plus 110 is 400 and the expected row also totals 400. A chi-square of 1.333 is below 3.841 at df 1, so H0 stands. The second set totals 240 observed and 240 expected, with 1.667 below 5.991 at df 2, so H0 stands again. The observed percentages are 72.5 and 27.5 against an expected 75 and 25, a gap of 2.5 points that sits inside sampling error, which is exactly what close but not equal looks like.

05 Independent practice (3 questions)

Question	Answer	What to watch
Work three data sets	One each for 3:1, 1:2:1 and 9:3:3:1	Does the expected row add back to the sample
Write the conclusion only	Given a value and df, two minutes	Is reject or do not reject stated with a reason
Find the error	Prepare a solution that added gaps first	Can they name the wrong step

06 Common mistakes and what to say

Mistake	Student writes	Say this
Adding gaps before squaring	Writing (10+10)^2/400	Square and divide each cell first, total last. Wrong order means zero marks however tidy the number.
Using sample size minus one for df	Writing df as 399	df counts classes only: two classes give 1, three give 2. Sample size never enters.
A conclusion that only says close	It is very close to 3:1	Write that H0 is not rejected at the 5% level. Close is not statistical language and earns nothing.
Expected numbers that no longer total	Rounding to 300.4 and 100.4	Expected numbers must add back to the sample. Decimals mean the ratio or the sample was misread, so check the question again.

07 Homework (paper, section and question numbers)

Biology chapter index — Compare with the other genetics chapters
Prep guide master index — Find the matching data-handling chapter
Redo this chapter — Items 1 and 2, one run each

08 Exit check (last 5 minutes)

Question	Answer	Decision
How is df set	Classes minus one: two classes give 1, three give 2	Sample size minus one means act two was missed
Chi-square 1.333 at df 1 means what	Below 3.841, so H0 is not rejected and the ratio does not differ from 3:1	Saying close means act three is unfinished
What must the expected row satisfy	It must add up to the sample size	Not knowing this means the act-one check was skipped

09 Tutor FAQ

Can I teach the formula only, without statistics?

Yes, but keep the five steps: state H0, compute expected, compute chi-square, compare the critical value, write the conclusion. The formula is only step three.

Must students memorise the critical table?

The paper usually supplies it. They need the df rule and the two common values: 3.841 at df 1 and 5.991 at df 2.

What if expected numbers are tiny?

Merge classes until every expected value reaches 5, otherwise the test is unreliable. Say this explicitly or students will compute on tiny cells.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.