• Corpus ID: 124594430

Exact binomial confidence interval for proportions

@article{Morisette1998ExactBC,
  title={Exact binomial confidence interval for proportions},
  author={Jeffrey T. Morisette and Siamak Khorram},
  journal={Photogrammetric Engineering and Remote Sensing},
  year={1998},
  volume={64},
  pages={281-283}
}

• J. Morisette, S. Khorram
• Published 1998
• Mathematics
• Photogrammetric Engineering and Remote Sensing

Introduction In remote sensing accuracy assessment applications, the confidence interval is commonly used as a way to establish an appropriate sample size. However, confidence intervals are also informative when included in the accuracy assessment report. Many reports and papers give accuracy figures and leave out confidence intervals. In those cases where a confidence interval is constructed, the standard approach is to derive the interval through the use of a normal approximation of the binomial distribution or by referring to exact tables. This note briefly discusses the benefit of using confidence intervals. The main objective is to describe the calculation of an exact equal-tail confidence interval for the proportions of correctly classified pixels. The exact confidence interval is not based on a normal approximation but, instead, uses the relationship between the binomial and F distributions. While the derivation of the exact confidence interval relies on a somewhat involved mathematical relationship between the probability density functions, in practice the exact confidence interval is a relatively straightforward formula. With the percentiles of "F" Distributions now commonly available in hand calculators and spreadsheet (and other) programs, the exact confidence interval is easily calculated. After presenting the formula for the exact confidence interval, we will present an example using both the normal approximation and the exact confidence interval.