Study Design Slides Designing Your Study
Comparative Statistics Project: Phase I
What's the Difference?
"Is there a significant difference in [Variable] between [Population A] and [Population B]?"
Categorical vs. Quantitative
Does a student's grade level (9th vs 12th) affect their average hours of sleep (Quantitative)?
Independent vs. Paired
Are you comparing two distinct groups, or the same group under two different conditions?
Define Your Boundaries
Populations
The entire group you want to draw conclusions about.
Varsity Athletes
Commuter Students
Samples
The specific individuals you will collect data from.
Must be representative
Avoid convenience sampling!
How Will You Choose?
SRS
Simple Random Sample
Every individual has an equal chance. Random number generator is your best friend.
Stratified Sample
Divide into groups (e.g., GPA ranges) and sample randomly from each.
Cluster Sample
Sample entire existing groups (e.g., picking 3 random classrooms).
The Enemies of Accuracy
Selection Bias
Your sample doesn't represent the population (e.g., only surveying people in the gym about fitness).
Non-Response Bias
Certain types of people are more likely to ignore your survey, skewing the data.
Response Bias
The way questions are worded or who asks them changes the answers given.
Phase 1: The Proposal
In your teams, draft your Research Proposal. Define your populations, your variable, and your sampling strategy.
DEADLINE: End of Period. Approval required before collection.
Research Proposal Form Research Proposal
Comparative Statistics Project • Phase I
Applied Comparative Statistics
12th Grade Mathematics
Team Members
Date Submitted
1. The Research Question
State your research question clearly. It should compare two populations on a single quantitative or categorical variable.
2. Population A
Be specific (e.g., "All 12th grade athletes at Central High")
3. Population B
Must be distinct from Population A.
4. Variable & Measurement
What are you measuring?
Data Type
Quantitative
Categorical
5. Sampling Methodology
Explain exactly how you will select your subjects. Include how you will incorporate randomness to ensure independence.
Bias Check
Identify one potential source of bias in your plan and explain how you will attempt to minimize it (e.g., non-response, selection bias).
Instructor Use Only
Approved
Revise
Instructor Signature
Collection Ethics Slides Field Work & Ethics
Comparative Statistics Project: Phase II
The Researcher's Creed
Informed Consent
Subjects must know what the data is for and that participation is voluntary.
Anonymity
Data should not be traceable back to an individual. Never collect names or IDs if not necessary.
Integrity
Never "tweak" or omit data points just because they don't support your hypothesis.
Respect
If someone declines to participate, thank them and move on immediately.
The Problem with "No"
Non-response bias occurs when the people who don't respond are fundamentally different from those who do.
The Danger
If only the most "opinionated" or "available" people answer, your results are skewed toward extremes.
The Strategy
Follow-up with non-responders. Use different times of day. Maintain your random selection rigor!
Garbage In, Garbage Out
Your inferential test is only as good as your raw data. Pay attention to how you record values.
Consistency: Use the same units for everyone.Legibility: If hand-writing results, double-check your own notes.Outliers: Note any unusual circumstances during collection.
DB
Collection Log Ex.
Subject Variable Note #001 42 min Valid #002 -- Refused
Ready for Launch
You have your approved proposal. You have your ethics training. Go forth and collect!
Goal 1
Target Sample Size Reached
Goal 2
Zero Ethical Violations
Goal 3
Detailed Log Completed
Collection Log and Ethics Form Collection Log & Ethics
Comparative Statistics Project • Phase II
Status: FIELD COLLECTION
Team Name / Members
Target Sample Size (n)
Ethical Compliance Checklist
Informed Consent
Every subject was told that participation is voluntary and results are for a class project.
Privacy & Anonymity
No identifying information (names, ID numbers, birth dates) has been linked to individual data points.
Non-Coercion
No subjects were pressured, bribed, or penalized for refusing to participate.
Field Collection Log
Record every attempt, including refusals.
Date Population Status Notes / Obstacles Encountered
Non-Response Reflection
Describe any challenges you faced getting people to respond. Are you noticing a pattern in who is refusing? How might this affect your final analysis?
Applied Statistics • Field Protocol v2.0
EDA Slides Exploratory Data Analysis
Comparative Statistics Project: Phase III
Step 1: The Clean Up
Before you analyze, you must "scrub" your data. Raw field data is rarely perfect.
Incomplete Responses
If a subject skipped a critical question, you may need to exclude that record entirely.
Formatting Errors
Ensure all numbers are in the same units (e.g., convert minutes to hours if needed).
The Outlier Decision
Don't just delete high or low values! Use the \(1.5 \times \text{IQR}\) rule. Only remove data if it's a confirmed recording error.
\( [Q1 - 1.5\text{IQR}, Q3 + 1.5\text{IQR}] \)
Side-by-Side Comparisons
Parallel Boxplots
Best for comparing Medians, IQRs, and Spreads visually.
Back-to-Back Stemplots
9 8 7 |
1
| 2 4 5
Best for small datasets to see individual values and gaps.
The "S.O.C.S." Framework
S
Shape
Skewed? Symmetric? Unimodal vs. Bimodal?
O
Outliers
Any extreme values that pull the mean?
C
Center
Mean vs. Median. Which is better here?
S
Spread
Standard Deviation, IQR, or Range?
"The [Group A] distribution is slightly right-skewed with a median of 45, whereas [Group B] is symmetric with a median of 38..."
The "Smell Test"
EDA doesn't prove anything yet. It just tells you if your hypothesis is plausible.
Clean Your Data
Graph Everything
Calculate S.O.C.S.
Exploratory Analysis Worksheet Exploratory Analysis
Comparative Statistics Project • Phase III
Team Name
1
The Scrub: Data Cleaning
Original \(n\) vs. Final \(n\)
How many total subjects were attempted? How many valid records remain after cleaning?
Attempted
Valid
Exclusion Summary
Briefly list reasons for excluding any data (e.g., missing values, illogical answers).
2
The Sketch: Comparative Display
Choose between Parallel Boxplots or Back-to-Back Stemplots. Ensure axes are correctly scaled and groups are clearly labeled.
3
The Stats: Comparative Summary
Population Mean (\(\bar{x}\)) SD (\(s\)) Min / Q1 / Med / Q3 / Max A: B:
4
The Story: Comparative Description
Compare the Shape, Outliers, Center, and Spread of the two distributions. Use comparative language (e.g., "more variable than," "roughly symmetric compared to").
Inference Execution Slides Inference Execution
Comparative Statistics Project: Phase IV
Which Test?
2-Sample \(z\) Test
Categorical Data
Comparing proportions (e.g., % of students who drink coffee in Grade 11 vs. Grade 12).
2-Sample \(t\) Test
Quantitative Data
Comparing means of two independent groups (e.g., Avg. test scores of athletes vs. non-athletes).
Paired \(t\) Test
Quantitative Data
Comparing means of "Before/After" or matched subjects (e.g., Score before vs. after caffeine).
The "Conditions" Checklist
R
Random
Were your samples selected randomly from the population? (Crucial for generalization!)
10%
Independence
Is your sample size \(n \le 10\%\) of the total population? (Crucial if sampling without replacement.)
N
Normal / Large Sample
Are \(np \ge 10\) and \(n(1-p) \ge 10\)? Or is \(n \ge 30\) (CLT)? Or is the pop. distribution normal?
"The Moment of Truth"
P-Value \(\le \alpha\) (usually 0.05)
Reject \(H_0\)
Evidence of a significant difference! Your findings are unlikely to be due to chance alone.
Fail to Reject \(H_0\)
No significant evidence of a difference. The null hypothesis still stands.
Statistical vs. Practical
A p-value of 0.049 is statistically significant, but does it matter in the real world?
Always calculate a Confidence Interval!
The P-value tells you if there's a difference. The CI tells you how big it might be.
Inference Analysis Worksheet Inference Analysis
Comparative Statistics Project • Phase IV
SIGNIFICANCE LEVEL (\(\alpha\))
0.05
1
State: Hypotheses & Parameters
Null Hypothesis (\(H_0\))
Alternative Hypothesis (\(H_a\))
Define Parameters (\(\mu\) or \(p\))
1:
2:
2
Plan: Test & Conditions
Name of Procedure
Random
Verify random selection for both groups.
10% / Independent
Check population sizes.
Normal / Large
Large counts or CLT.
3
Do: Calculations
Test Statistic
P-Value
Confidence Interval
4
Conclude: Statistical Decision
Provide your conclusion in context. Does the evidence support your research question?
Communication Slides The Art of Evidence
Comparative Statistics Project: Final Phase
Speaking to Non-Statisticians
Avoid Jargon
Don't just say "p < 0.05". Explain that "the difference we saw is very unlikely to be just a lucky accident."
Lead with the Story
Start with your research question and your answer. The "math" is the proof, not the headline.
"Your job is to translate numbers into knowledge."
Visual Storytelling
Focus
Highlight the most important part of your graph. Use color to draw attention to the comparison.
Labels
Every axis needs a clear, descriptive title. No one should have to guess what "Variable X" means.
Simplicity
Don't clutter your poster with raw data tables. Show the summary stats and the graphs.
The Honest Statistician
No study is perfect. Your credibility depends on your honesty about what your study can't say.
Confounding Variables
Are there other reasons for the difference besides the groups you picked?
Sampling Error
Was your sample truly representative? Where might bias have crept in?
The Final Presentation
Question & Rationale
Methodology & Ethics
Visual Data Analysis
Inference Results & Limitations
Tell the school's story with science.
Presentation Guide Final Presentation Guide
"Translating Numbers into Knowledge"
PHASE V: FINAL
The Objective
Your goal is to communicate your findings to an audience that may not know statistics. Your presentation should be visually clear, logically structured, and scientifically honest. Use this guide to structure your final poster or slide deck.
Part 1: The Hook
Why did you choose this question? Why is it interesting to our community?
Notes for the intro...
Part 2: Methodology
Explain your sampling plan. How did you ensure it was random and ethical?
Part 3: Visual EDA
Show your comparative graphs. What was the "vibe" of the data before the test?
Include: Parallel boxplots or stemplots.
Part 4: Conclusion
The p-value result and its real-world meaning. Be sure to acknowledge limitations!
Visual Design Checklist
Text is legible from 3 feet away (for posters).
Graphs use high-contrast colors to show groups.
Axes are clearly labeled with units.
The P-value is present but explained in English.
Limitations (bias, confounding) are clearly stated.
Presentation flows logically (Question -> Data -> Answer).
Pre-Presentation Reflection
In 2-3 sentences, what is the single most surprising thing your data revealed about your populations?
Final Project Rubric Project Rubric
Applied Comparative Statistics • Grade 12
Total Points
100
Criteria Exemplary (4) Proficient (3) Developing (2-1) Research Design & Sampling Clearly defined populations and variables. Sampling plan effectively minimizes bias with clear random selection. Populations and variables are defined. Random selection is present but might have minor flaws or convenience bias. Vague population definitions. Sampling plan relies on convenience and lacks randomness. Data Ethics & Collection Full documentation of ethics. Comprehensive collection log showing all attempts and refusals. Ethics checklist completed. Collection log is present but lacks detail on refusals or obstacles. Incomplete ethical documentation. Missing or poorly kept collection log. Exploratory Analysis (EDA) Comparative graphs are perfect with labels. SOCS description uses precise comparative language. Comparative graphs are clear but may lack some labels. SOCS description is present but lacks depth. Graphs are missing or incorrect for the data type. Minimal descriptive analysis. Inferential Execution Appropriate test chosen. All conditions verified. Correct p-value, CI, and context-based conclusion. Correct test chosen. Conditions checked but minor errors in verify/do steps. Conclusion is in context. Wrong test chosen or major calculation errors. Conclusion lacks context or statistical logic. Communication & Limitations Professional visual design. Honest appraisal of confounding variables and sampling error. Clear presentation. Acknowledges some limitations but may miss key confounding factors. Unclear or cluttered presentation. Fails to acknowledge study limitations.
Instructor Comments
Final Score
____
/ 100
Comparative Statistics Project Rubric
2026 Academic Year
