Simulated Results Teacher Guide Chance or Choice
Teacher Facilitation Guide | Tier 2 Intervention
Standard
CO HS.S-IC.B.5
Instructional Goal
Students will determine if the difference in means between two treatment groups in a randomized experiment is statistically significant by creating and analyzing a randomization distribution via simulation.
Key Vocabulary
Randomized Experiment: Assigning subjects to treatments by chance to ensure groups are similar.
Observed Difference: The actual gap between the means of Group A and Group B.
Simulation: Re-running the experiment many times assuming the treatment has no effect .
Statistically Significant: When an outcome is very unlikely to happen by pure chance.
Materials Needed
Deck of index cards (or "Data Cards")
Calculators
Dot plot stickers or markers
Chance or Choice Slides
Data Detective Worksheets
Intervention Pacing
15m
The "What If?" Logic (Direct Instruction)
Use the Slides to present the reaction time experiment. Focus on the core question: "Did the energy drink cause the speed, or was this person just fast anyway?"
Scaffolding Tip: Use the "Card Shuffling" metaphor. If the drink does nothing, the numbers on the cards are fixed—only the labels (Drink vs. Water) change.
25m
Hands-On Simulation (Guided Practice)
Students use the Data Detective Worksheet . They perform 10 manual shuffles.
Check for Understanding: Ask, "Why are we shuffling? What does shuffling represent?" (Answer: It represents pure chance).
10m
Analysis & Wrap-Up
Combine class data on a large dot plot. Locate the Observed Difference .
Common Misconceptions
"More is always better": Students may think any difference is significant. Remind them that small differences happen by chance all the time.Directionality: Students might only look at one side of the dot plot. Remind them to look at "this difference or more extreme."The Simulation Goal: Clarify that we simulate the Null (no effect) to see if our real result looks like an accident. Chance or Choice Slides Chance or Choice?
Using simulations to find out if results are real or just lucky.
The Experiment
10 students are randomly split into two groups:
1 Group A: Energy Drink
2 Group B: Plain Water
We measure their reaction time on a simple computer test (in milliseconds).
The Results
Drink Group
240 ms
Water Group
285 ms
Difference in Means
45 ms
The Million Dollar Question
Is the 45 ms difference because of the drink, or did the "fast" students just happen to end up in Group A?
Treatment Effect
Pure Luck
The Simulation Strategy
01
Assume NO Effect
Pretend the drink does absolutely nothing. The times would be the same no matter which group students were in.
02
Shuffle the Labels
Mix all 10 scores in a hat. Randomly deal them into two new "fake" groups. Calculate the "fake" difference.
03
Repeat 1,000 Times
See how often a "fake" difference is 45 ms or larger just by shuffling. This is our Dot Plot.
What does it mean?
0 ms
20 ms
45 ms (Ours!)
Significant
If our result almost never happens by chance, the treatment likely worked!
Not Significant
If our result happens often by chance, the difference might just be luck.
Data Detective Worksheet Data Detective Investigation
STATISTICS INTERVENTION | LAB JOURNAL
Name:
Date:
Case File: The Plant Power Experiment
A gardener wants to know if "GrowFast" fertilizer works better than regular water. She takes 8 identical plants and randomly gives 4 of them GrowFast. After two weeks, she measures their height in inches.
Treatment A: GrowFast
12 15 14 17
Mean Height:
14.5 in
Treatment B: Water
10 11 12 11
Mean Height:
11.0 in
Step 1: The Observed Difference
GrowFast Mean
14.5
−
Water Mean
11.0
=
OBSERVED DIFF
Step 2: Simulation (By Chance)
ASSUMPTION: TREATMENT HAS NO EFFECT
If the fertilizer does nothing, the 8 heights (10, 11, 11, 12, 12, 14, 15, 17) were fixed. Any difference we saw was just "luck of the draw" during group assignment. Let's re-shuffle the plants into two new random groups and calculate the new difference.
Trial "Fake" Group A Mean "Fake" Group B Mean Simulated Difference (A - B) 1 2 3
*Use your 8 data cards to shuffle and calculate 3 trials. Then, look at the class dot plot for 100 trials.
Step 3: Visual Analysis
Randomization Distribution (100 Trials)
FREQUENCY
-2.0
-1.0
0.0
1.0
2.0
3.0
3.5
1. Identify Your Result
How many dots are at 3.5 or higher?
Out of 100 trials, what is the percentage?
2. Draw a Conclusion
Is this difference likely to happen by pure chance? Why or why not?
Final Verdict:
Does the GrowFast fertilizer actually work better, or was the gardener just lucky? Use the data above to justify your answer.
Significance Check Exit Ticket Significance Check
EXIT TICKET | END-OF-LESSON ASSESSMENT
Student Name
Date
1 Why do we use simulation to analyze an experiment?
To make the data look more impressive to others.
To see how often the result happens by pure chance.
To change the original data so it fits our theory.
2 Analyze the Simulation Plot
In a simulation of 100 trials, an observed difference of 10 grams occurred only 2 times . Is this result statistically significant?
Yes
No
Explain your reasoning:
Confidence Level
STILL CONFUSED
GOT IT!
