Lesson 4: Why Small Samples Fool Us

About 30 minutes — Discussion-based lesson

What You Will Learn

This lesson covers:

Small sample illusions: patterns that are not real
The hot hand fallacy in sports
Why medical studies need thousands of participants
How to recognize when a sample is too small to trust

Small sample illusions: patterns that are not real

This section covers the key ideas about small sample illusions: patterns that are not real. Discuss with your group or family and explore the concepts together.

The hot hand fallacy in sports

This section covers the key ideas about the hot hand fallacy in sports. Discuss with your group or family and explore the concepts together.

Why medical studies need thousands of participants

This section covers the key ideas about why medical studies need thousands of participants. Discuss with your group or family and explore the concepts together.

How to recognize when a sample is too small to trust

This section covers the key ideas about how to recognize when a sample is too small to trust. Discuss with your group or family and explore the concepts together.

Check Your Understanding

1. What is a small sample illusion?

Answer: When a small amount of data shows a dramatic pattern that would disappear with more data. 3 out of 5 people liking something is 60% — but it might be 45% if you asked 500.

2. What is the hot hand fallacy?

Answer: The belief that a basketball player who makes 3 shots in a row is 'hot' and more likely to make the next one. In reality, each shot has roughly the same probability. Short streaks happen by chance.

3. Why do medical studies need large samples?

Answer: Because small differences between treatment and placebo could be random variation. Large samples ensure that observed differences are real, not just noise.

4. How do you know if a sample is too small?

Answer: Ask: could the pattern I see be due to chance? Would I get similar results if I repeated the study? If the sample is under 30, be extra cautious about drawing conclusions.

Key Takeaways

Small sample illusions: patterns that are not real
The hot hand fallacy in sports
Why medical studies need thousands of participants
How to recognize when a sample is too small to trust

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Practice Activities

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