account the small sample sizes commonly used in usability tests. Lower Limit = 0.3596
follows: where:
Description. For example, assume that 4 out of 5 users successfully completed a given
0.6696 ± 1.96 * 0.1582
task, and that you want to use a 95% confidence level. Estimating the proportion of successes in a population is simple and involves only calculating the ratio of successes to the sample size. 0.6696 ± 0.3100, Or:
Sauro's online calculator using the Adjusted Wald Method. The so-called “exact” confidence intervals are not, in fact, exactly correct. The basic idea
For some values (e.g. Wald Method. 9/10) the adjusted Wald's crude intervals go beyond 0 and 1 and a substitution of >.999 is used. Lewis, J., & Sauro, J. assumptions: padj = (5*0.8 + (1.96^2)/2)/(5 + 1.96^2)
= 5.9208/8.8416
population proportion and its confidence interval (CI). The American
Statistician, 52, 119-126. z = the z-value corresponding to the desired confidence level
p = proportion of trials that were successes
These intervals may be wider than they need to be and so generally give you more than 95% confidence. Originally posted March 28, 2008; last modified March 29, 2008. 0.6696 ± 1.96 * sqrt(0.6696(1-0.6696)/8.8416)
Recommendations. 1, #3, May 2006, 136-150. When 100% really isn't 100%: Improving
And here is a link to Jeff behind the Adjusted Wald Method (Agresti & Coull, 1998) is that you
formula for calculating the Adjusted Wald confidence interval is as
the accuracy of small-sample estimates of completion rates. nadj = n + z2. = 0.6696, nadj = 5 + 1.96^2
Agresti and Coull (3) recommend a method they term the modified Wald method. Agresti, A., & Coull, B. padj = (n*p + z2/2)/(n + z2)
The Wald method should be avoided if calculating confidence intervals for completion rates with sample sizes less than 100. Description Usage Arguments Value Author(s) References See Also Examples. Given those
[Page reference in book: p. … For the score method, the upper interval is .9975. Journal of
0.6696 ± 1.96 * sqrt(0.2212/8.8416)
The simple Wald type interval for multinomial proportions which is symmetrical about the sample proportions. Conversely, the Clopper-Pearson Exact method is very conservative and tends to produce wider intervals … (1998). = (4 + 1.9208)/(5 + 3.8416)
(2005) Estimating Completion Rates from Small
need to adjust the observed proportion of task successes to take into
In CoinMinD: Simultaneous Confidence Interval for Multinomial Proportion. n = total number of trials
The
for interval estimation of binomial proportions. The Wald interval often has inadequate coverage, particularly for small n and values of p close to 0 or 1. Samples using Binomial Confidence Intervals: Comparisons and
It is easy to compute by hand and is more accurate than the so-called “exact” method. That means the 95% confidence interval if you observed 4 successes out of
Sauro, J., & Lewis, J. In this method no continuity corrections are made to avoid zero width intervals when the sample proportions are at … = 5 + 3.8416
Usability Studies, Vol. Society Annual Meeting, Orlando, FL. Proceedings of the Human Factors and Ergonomics
(2006). http://www.measuringusability.com/papers/sauro-lewisHFES.pdf. http://www.measuringusability.com/papers/sauro-lewisHFES.pdf. That means the 95% confidence interval if you observed 4 successes out of 5 trials is approximately 36% to 98%. these calculations. Adjusted Wald Method of calculating a confidence interval works well for
And finally, the calculation of the confidence interval: padj ± z * sqrt(padj(1- padj)/nadj)
Here is a simple spreadsheet for doing
The most common method for calculating the confidence interval is sometimes called the Wald method, and is presented in nearly all statistics textbooks. = 8.8416. many of the situations we encounter in usability testing. Sauro and Lewis (2005) and Lewis and Sauro (2006) demonstrated that the
Approximate is better than 'exact'
Here is a simple spreadsheet for doing these calculations. 5 trials is approximately 36% to 98%. by Tom Tullis
And here is a link to Jeff Sauro's online calculator using the Adjusted Wald Method. Upper Limit = 0.9796.

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