The width of the confidence interval equals two margins of error, thus the width of the CI is affected by the margin of error. The three variables affecting the margin of error and thus determine the width of the confidence interval are:

The standard deviation is used to measure the variability of the data in the sample. Given the same confidence level, the more variable the sample or population is, the wider the CI will be. For binary data, the standard deviation is equal to the square root of the proportion (p) multiplied by one minus the proportion (1-p). While for Continuous data (i.e. Time, SUS score, Likert scale responses) the standard deviation is equal to the square root of the variance, where variance is the sum of the squared distance each data point has from the mean, divided by the total number of the data points minus one.

The confidence level (CL) indicates how certain we would like to be in our assessment. Some common values for the CL are 95% and 90% but lower and higher values are also used. Given that the sample size and variability remain the same, the higher the confidence level is, the wider the CI will be.

The sample size has an inverse square root relationship with the CI. This tells us that to reduce the CI by half, we almost have to quadruple our sample size. Given that the confidence level remains the same, smaller samples generate wider CI while larger samples tend to generate narrower CI, thus a better estimate of the population parameter.