Interactive school project using a chi-square test of independence.
Research question: Is preferred study environment associated with students' self-reported level of focus?
Student & Peer Team Information
Complete this section before beginning. Because you will work in pairs, both students are responsible for the data, calculations, discussion, and final conclusion.
Peer Roles
Assign a primary role to each person, but both students must understand every part of the investigation.
Peer-work expectation: Do not split the assignment into isolated halves. Discuss each decision together, cross-check all calculations, and make sure both students can explain the final chi-square conclusion independently.
Detailed Student Instructions
Follow these steps in order. Do not move directly to the chi-square calculation before completing the research question, hypotheses, ethics check, and observed-data table.
Form your pair. Complete the Student & Peer Team Information section and assign roles. Both partners must participate in every stage.
Read the case study carefully. Make sure you understand the two categorical variables: preferred study environment and self-reported focus level.
Complete the background research. Explain why the question is relevant, why both variables are categorical, why chi-square is appropriate, and why association does not prove causation.
Write the research question in your own words. It must clearly identify both variables and ask whether they are associated.
Write both hypotheses before collecting or analysing the data. Your null hypothesis should state that the variables are independent. Your alternative hypothesis should state that an association exists.
Review the ethical requirements. Survey participation must be voluntary and anonymous. Do not record names of surveyed students. Do not pressure anyone to participate.
Collect survey data. Ask each participant the same two survey questions. Record only one response for study environment and one response for focus level per participant.
Avoid duplicate responses. Your pair should have a simple method for ensuring that the same student is not counted twice, without writing student names in the project.
Enter the observed frequencies. Place every response into exactly one of the four cells in the 2 × 2 table. Confirm that the row totals, column totals, and grand total match your raw tally.
Check sample size. Aim for at least 40 responses if practical. Larger samples generally provide more stable estimates than very small samples.
Calculate the expected frequencies. Use the formula shown in the worksheet. Show at least one complete expected-value calculation in the written-work box.
Check the expected-count condition. Before interpreting the chi-square test, confirm that expected frequencies are sufficiently large. If an expected value is below 5, discuss this limitation with your teacher before drawing a firm conclusion.
Complete the chi-square analysis. Check each contribution and the total χ² value. Both partners should independently verify the calculation.
Use the correct degrees of freedom. For this 2 × 2 table, df = 1. At p = 0.05, the critical value is 3.84.
Make the statistical decision. Compare your calculated χ² value with 3.84. If χ² is greater than 3.84, reject H₀. If χ² is less than 3.84, fail to reject H₀.
Do not claim causation. Even a statistically significant association does not show that music causes focus or distraction. Consider alternative explanations and confounding variables.
Evaluate the investigation. Identify at least three limitations, explain how each could affect the results, and propose a realistic improvement.
Write the final evidence-based conclusion. Include χ², df, p, the critical value, your statistical decision, and a clear interpretation in the context of the school survey.
Peer check before submission. Each student should read the entire project, verify the numbers, and be able to explain the result orally without relying on the other partner.
Submit one final project per pair unless your teacher gives different instructions. Both student names must appear on the final submission.
Academic integrity: You may discuss the work with your partner, but the pair must collect, analyse, and explain its own data. Do not copy another group's dataset or conclusion.
1. Background Research
2. Research Question
3. Null Hypothesis (H₀)
4. Alternative Hypothesis (Hₐ)
5. Ethical Survey Design
6. Survey Questions
Q1. Which study environment do you generally prefer? • Quiet • Background music
Q2. Which best describes you during independent work? • Highly focused • Easily distracted
7. Enter Observed Data
Study Environment
Highly Focused
Easily Distracted
Row Total
Quiet
0
Background Music
0
Column Total
0
0
0
8. Expected Frequencies
Expected = (row total × column total) ÷ grand total
Category
Observed
Expected
Quiet + Highly Focused
0
0.00
Quiet + Easily Distracted
0
0.00
Music + Highly Focused
0
0.00
Music + Easily Distracted
0
0.00
Enter observed data to check expected-frequency conditions.
9. Chi-Square Analysis
χ² = Σ ((O − E)² / E)
Category
O
E
(O−E)²/E
Quiet + Highly Focused
0
0.00
0.000
Quiet + Easily Distracted
0
0.00
0.000
Music + Highly Focused
0
0.00
0.000
Music + Easily Distracted
0
0.00
0.000
χ² = 0.000 | df = 1 | Critical value at p = 0.05 = 3.84
10. Statistical Decision
11. Association Is Not Causation
12. Evaluation and Limitations
13. Peer Collaboration Reflection
Complete this together before writing the final conclusion.
14. Final Evidence-Based Conclusion
Save Progress downloads a reusable .json file. Load Progress restores that file, even on another device. Keep the file private because it contains student responses.