🛠️ Confidence interval for a proportion

💡 Use Case

• Six lines I have pasted into every analysis since 🎓 Lecture 6 - Confidence intervals: give it a count and a total, get back the proportion and a 95 percent interval.
• It is 📐 Confidence interval for a proportion in code and nothing cleverer.
• It exists so that I never again put a bare percentage on a slide. A percentage without its interval is an anecdote with a decimal point.

How I use it

What the six lines do, in order:

1. Take k successes and n trials.
2. p = k / n
3. Standard error: the square root of p * (1 - p) / n.
4. Margin: 1.96 times the standard error.
5. Lower and upper: p minus and plus the margin.
6. Print all three as percentages, to one decimal.

Worked once, on my own numbers. Issue 31 went to 1,196 people and 52 percent opened it: about 622 opens.

⚖️ Pros & Cons

Pros

• Six lines. I can read all of it and so can a reviewer.
• It prints the interval in the sentence form I am allowed to say, which is not the sentence I used to say (see 🔤 Confidence interval).

Cons

• It is the simple approximation. Near 0 or 100 percent, or with a few dozen cases, it is wrong, and it does not complain.
• It makes a number look more settled than the way the data was collected deserves.

🔄 Alternatives

• A statistics library's own function, with better small-sample behaviour and one more thing to install.
• Asking Bao Nguyen, who will also ask how the sample was drawn.