One answer named you
This week1 of 1
100%
Visibility: 100%. You own this question.
One number wobbles. The 95% interval shows what's real.
Ask AI the same questions twice and you get a different number. Every Proofsource number comes with a range, so you can tell a real change from luck.
200 answers. 25 Prompts/Question. Top AI engines. 2 days. Free. No card.
The real rate is somewhere in here95% interval
43% to 62%
0%50%100%
That band is the 95% interval. One number wobbles. The band tells you what is real.
Same data, two reports. Which one would you act on?
A number without its range can be exactly right and still send you the wrong way. Switch between the two readings.
The drop that wasn't
Last week4 of 10
40%
This week2 of 10
20%
Visibility halved, 40% to 20%. Something broke.
The leaderboard that's too close
Your brand6 of 10
60%
Competitor4 of 10
40%
You lead, 60% to 40%.
The win that's real
Before the fix60 of 200
30%
After the fix100 of 200
50%
Visibility up from 30% to 50%.
Every headline above is arithmetically correct, and three of the four would send you the wrong way. Switch to see why.
A smaller number you can trust beats a bigger one that isn't real. That is the whole reason the range is there.
The one-line answer
53 of 100 answers named Tesla, so its mention rate is 53%, with a 95% interval of 43% to 62%. Ask the same buyer questions again and the 53% comes out a little different each time; the interval is a range drawn so that, 19 times in 20, it contains the rate you would get if you could ask forever.
The dot is the rate we measured, 53.0%. The bar is the 95% interval, 43.3% to 62.5%. Read it as: Tesla is named in somewhere between about 43% and 62% of answers to these questions, most likely near 53%.
Watch it: ask the same questions again and again
Nothing changes between these reports: the true rate is fixed. Only chance changes which answers come back. Press the button and watch where each report lands.
True rate (what you would get asking forever)
Answers per report
10 reports, each from 25 answers. The headline number ran from 24.0% to 52.0%, though nothing changed: the true rate stayed at 40%.
10 of 10 ranges (100%) contain the true rate, marked by the dashed line. Keep asking and it settles at 93.6% for this setting, close to 19 in 20: answers come in whole numbers, so the exact figure moves a little around 95%. No misses yet; keep asking and the odd orange one appears.
Try your own numbers
The same calculation the product runs on every number: the Wilson score interval at 95%.
53.0% mention rate
95% interval: 43.3% to 62.5%, about 9.6 points either way.
Move answers up and watch the range tighten: four times the answers, roughly half the width.
Why AI answers need a range at all
AI engines don't give the same answer twice. Ask the same question tomorrow, or word it a little differently, and the brands named change.
In our own tracking, 47% of day-to-day changes in AI answers reversed the next day (40 buyer questions, four engines, up to nine days). A brand named on one phrasing of a question was named on a reworded one only 55% of the time (13,994 answers).
So a single answer, or a single day, is one draw from a moving target. The interval turns many draws into an honest statement: the rate, and how sure we can be of it.
More answers, a tighter range
The width depends mostly on how many answers sit behind the number. Drag along the curve.
| Answers | Named (at 30%) | 95% Wilson interval | Plus or minus |
|---|---|---|---|
| 10 | 3 of 10 | 10.8% to 60.3% | about 24.8 points |
| 25 | 8 of 25 | 17.2% to 51.6% | about 17.2 points |
| 50 | 15 of 50 | 19.1% to 43.8% | about 12.3 points |
| 100 | 30 of 100 | 21.9% to 39.6% | about 8.8 points |
| 200 | 60 of 200 | 24.1% to 36.7% | about 6.3 points |
| 400 | 120 of 400 | 25.7% to 34.7% | about 4.5 points |
| 1,000 | 300 of 1,000 | 27.2% to 32.9% | about 2.8 points |
Is a change real, or noise?
The question every weekly report raises. Three rules cover it.
- The ranges don't touch: the change is real. Act on it.
- The ranges touch: that does not prove nothing changed. Two 95% ranges from identical samples overlap more than 99% of the time, so overlap is a very strict test (why overlapping error bars are not the test). Compare the questions that flipped from named to not named, and back, instead.
- Our alerts are deliberately strict: they fire only when the ranges separate and the move clears the threshold you set, so an alert you get is one you can trust.
What the Wilson interval is
The method behind every range we show, published by the statistician Edwin B. Wilson in 1927 and the one the statistics literature recommends for a rate from a modest number of yes-or-no results.
Each AI answer either names your brand or it doesn't, so a mention rate is a share of yes-or-no results: what statisticians call a binomial proportion. Wilson's method draws the range around that share in two steps. It nudges the centre slightly toward 50%, more when there are few answers, and then draws a range around that centre whose width depends on the rate and the number of answers. With p the share of answers that named you, n the number of answers and z = 1.96 for 95%:
centre = (p + z^2/(2n)) / (1 + z^2/n) half-width = z / (1 + z^2/n) × √( p(1 - p)/n + z^2/(4n^2) ) 95% range = centre - half-width to centre + half-width
The simpler formula from most textbooks, the rate plus or minus 1.96 standard errors (the Wald interval), breaks exactly where AI visibility lives: small samples and rates near 0% or 100%. The same answers, both ways:
| Answers | Rate | Simple plus-or-minus | Wilson 95% |
|---|---|---|---|
| 53 of 100 | 53.0% | 43.2% to 62.8% | 43.3% to 62.5% |
| 2 of 25 | 8.0% | -2.6% to 18.6%, below zero | 2.2% to 25.0% |
| 0 of 25 | 0.0% | 0.0% to 0.0%, no range at all | 0.0% to 13.3% |
| 25 of 25 | 100.0% | 100.0% to 100.0%, no range at all | 86.7% to 100.0% |
That is why Brown, Cai and DasGupta's review of the common methods in Statistical Science (2001) recommends Wilson for samples of 40 or fewer, why Agresti and Coull (1998) found it covers the true rate more reliably than the textbook formula, and why Newcombe's comparison of seven methods in Statistics in Medicine (1998) favoured it. Dashboard, reports, exports and the API all compute the same Wilson interval, so a number means the same thing wherever you read it. The worked formula is also on What is a Wilson interval?, and every number we compute is described on Methodology.
References
The papers behind the method, so you can check the maths yourself.
- Journal of the American Statistical Association1927
Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209-212.
The original paper: the score interval for a proportion that our ranges use.
Open on doi.org - Statistical Science2001
Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101-133.
The standard review of the methods. Shows the textbook plus-or-minus interval misbehaves and recommends Wilson for small samples.
Open on doi.org - The American Statistician1998
Agresti, A., & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52(2), 119-126.
Finds the Wilson (score) interval covers the true rate more reliably than the textbook formula.
Open on doi.org - Statistics in Medicine1998
Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine, 17(8), 857-872.
Compares seven methods on the same cases and favours the Wilson score interval.
Open on doi.org - NIST e-Handbook of Statistical MethodsNIST
NIST/SEMATECH e-Handbook of Statistical Methods, section 7.2.4.1: Confidence intervals for a proportion.
The US National Institute of Standards and Technology's handbook presents the Wilson method, noting it is recommended by Brown, Cai and DasGupta and by Agresti and Coull.
Open on itl.nist.govFree to read - Journal of Insect Science, on PubMed Central2003
Payton, M. E., Greenstone, M. H., & Schenker, N. (2003). Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance? Journal of Insect Science, 3(1), 34.
Why two overlapping 95% ranges do not mean nothing changed: overlap behaves like a test at about 1%, not 5%.
Open on pmc.ncbi.nlm.nih.govFree to read - Psychometrika1947
McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153-157.
The test for comparing the same questions asked twice, by the questions that flipped.
Open on doi.org - Evan MillerEssay
Miller, E. How not to sort by average rating.
A widely read plain-language case for the Wilson interval when ranking items by a share of yes-or-no votes.
Open on evanmiller.orgFree to read
Common questions about the 95% interval
Does 95% mean we are 95% sure our number is right?
Not quite. It means the method that drew the range catches the true rate 19 times in 20. Any one range either contains the true rate or it doesn't; the 95% is how often the method gets it right over many measurements.
Why not just show the percentage?
Because a percentage from a small number of AI answers can move a lot by chance. Without the range, a drop from 53% to 45% looks like news when it may be noise. The range tells you how much a number can wobble before it means anything.
Why is the range lopsided near 0% and 100%?
Rates can't go below 0% or above 100%, so the Wilson method bends the range away from the edge. 2 of 25 answers gives about 2% to 25%, not a symmetric 8% plus or minus 11%, which would dip below zero.
How do I make the range narrower?
Ask more answers: more buyer questions, more engines, or more days of tracking. The width shrinks with the square root of the answers, so four times the answers roughly halves it.
Does the range cover everything that could be wrong?
No. It covers chance in which answers we happened to get. It doesn't cover which questions were asked, engine changes between days, or answers we judged wrong. Those are handled by choosing questions buyers really ask, re-asking on a schedule, and keeping the answers so you can check them.
Two of my bars overlap. Did nothing change?
Not necessarily. Two 95% ranges from identical samples overlap over 99% of the time, so overlap is a very strict test that misses real moves. When the bars don't touch, the change is real. When they touch, compare the questions that changed answer instead.
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