Did the course work or do the students just differ?
For a teacher or trainer with one class assessed twice: put in each student's score before and after the course, one row per student, and get back whether the class really improved or the gain could be luck. The sample is fourteen students on a two-day course: the average rises 6.8 points and the paired test calls it real, even though two students went backwards.
In plain words: this sheet answers one question, did the course move the scores, by comparing each student with themselves. Type your own before and after marks over the sample and run it.
Words on this sheet
- Pre-course score: The mark each student got before the course started, on the scale in the header (here out of 100).
- Post-course score: The mark the same student got after the course, on the same scale, so the two columns can be compared row by row.
- Paired: Each row is one student measured twice, so the test looks at every student's own change rather than at two separate class averages.
School Starter Statistics free
After you install, this is the model to open.
Did the Course Move the Scores?
- 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
- The gain
- 6.8 points: 60.6 in, 67.4 out
- Paired t
- -4.61 on 13 degrees of freedom
- p (two-tail)
- 0.0005 five in ten thousand by chance
- Same data, unpaired
- p = 0.19 the pairing is what makes 14 students enough
Plain answer: scores rose by about 7 points on average after the course, and that gain is real, not a fluke of who happened to be in the room, because the chance of seeing a gain this size by luck alone is under 1 in 1,000. Fourteen students, assessed on the way into a two-day course and on the way out. The class mean goes from 60.64 to 67.43, a gain of 6.79 points.
Click Run: the paired test returns t of -4.61 on 13 degrees of freedom with a two-tail p-value of 0.00049, so a gain this size across these fourteen students would happen by chance about five times in ten thousand. That is a result you can put in front of whoever paid for the course. Two things stop it being a victory lap. First, read the change column: Ines dropped three points and Kara dropped two, so twelve improved and two did not, and a course that works on average still fails individual people.
Neither of those two is a rounding artifact and both deserve a conversation the average will never prompt. Second, run the same two ranges through t-Test: Equal Variances, which treats the two columns as unrelated groups of scores, and it returns a p-value of 0.1949 and no verdict at all. Nothing about the data changed. The students simply differ from each other far more than the course changed any of them, from 35 to 88 on the way in, so the unpaired test never sees past the class while the paired test never looks at it.
Matching each student to themselves is exactly what makes fourteen people enough, and it is the whole reason to design the assessment this way rather than testing one cohort against another. If your assessment is a rank rather than a mark, or your scores bunch up at the top of the scale, run Wilcoxon Signed-Rank on the same two ranges instead: it asks the same question without assuming the differences are bell-shaped.
What no test here can tell you is whether the gain lasts, because a post-test on the last afternoon measures recall and not much else; if that is the claim you need, assess again in six weeks and run this template on those two columns. To use your own class, put pre-course scores under the first score heading and post-course scores under the second, one row per student in the same order, and widen both ranges to match.
The model
It arrives on a tab called Template: Did the Course Move the Scores, carrying these columns:
- Student
- Pre-course score (/100)
- Post-course score (/100)
- Change (points)
with the model computed beside the data:
| Students who improved | 12 |
| Students who went backwards | 2 |
| Biggest single gain | 14 |
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
- Would more places actually fix the shortfall?Will the Programme Cover Its Costs?
- Is the cheapest fix on your risk list the best one?What Could Go Wrong This Term?
- Which class should go to the hired hall?Fit the Timetable Without a Clash
- Did the workshop actually move anyone?Did the Training Change Each Person's Score?
- How many teachers will next summer actually need?How Many Students Next Term?
- Build the course yourself or license one?Is the New Course Worth Building?
Every model like this one, and the method behind them: Statistics in Google Sheets.