Does a small cohort need fewer replies?
A margin of five points on a cohort of 180 needs 123 replies, not the 385 the standard formula gives. Sampling most of a small population is the one case where the correction rescues you, and 123 out of 180 is still a response-rate problem.
Words on this sheet
- Cohort: One group who start together and are counted together: an intake of students, a class year, or the customers who joined in the same month.
School Starter Sample Size (General) free
After you install, this is the model to open.
How Many Responses for a Course Survey?
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
- Responses needed
- 123 ±5 points at 95% confidence, cohort of 180
- Without the correction
- 385 more responses than students on the course
- The finite pool saves
- 262 responses off the textbook number
A cohort of 180 students and a course survey that has to land within five points at 95% confidence. Click Run with the goal set to estimating a percentage and the population set to 180: the answer is 123 replies. Now clear the Population box and run it again: 385, which is more than twice the number of students on the course. That is the finite-population correction doing its work, and this is the one situation where it changes the answer rather than nudging it.
The standard formula assumes you are drawing from an effectively unlimited pool, so each new response tells you something genuinely new. When you are sampling most of a small group, each response also removes a student from the pool of people who could still disagree with you, and past a certain point the survey stops being a sample and becomes a census.
Read the table before you set a target. A five-point result needs 68% of the cohort to reply. A seven-point result needs 95 replies, 53% of them. A three-point result needs 86%, which no course survey has ever achieved. The sheet also records that last term produced 71 replies, which on this arithmetic bought about nine points, so the honest way to report last term was around 74%, give or take nine, and not 74%.
The practical consequence is that this is a chasing problem rather than a statistics problem: the difference between a usable result and an unusable one is about fifty more replies, and the tools for that are a reminder in the last session and a two-minute form rather than anything on this sheet. One caution about the 50% best guess. It is the worst case and therefore safe, but on a course where past cohorts have run near 85% recommending, entering 85 drops the requirement from 123 to 95.
That is legitimate if the history is real and it is wishful thinking if it is not, and getting it wrong widens the margin you promised rather than the one you report. To use your own cohort, change the cohort size and the margin, put the population into the panel, and rerun.
The model
It arrives on a tab called Template: How Many Responses for a Course Survey, carrying these columns:
- What we are estimating
- The share of the cohort who would recommend the course
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
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Every model like this one, and the method behind them: Statistics in Google Sheets.