Computing confidence intervals for a proportion with raw data

This tutorial covers the steps for calculating confidence intervals for a single proportion in StatCrunch. To begin, load the 50 Coin Flips data set, which will be used throughout this tutorial. This data set contains a single column titled Coin flips. Each of the 50 values in this column represents the outcome of a single coin flip and is labeled either Heads or Tails. While this tutorial uses raw data, see Computing confidence intervals for a proportion with summary data to compute one-sample proportion results with summary data.

Calculating a confidence interval for the proportion

If the coin used is "fair", the proportion of heads the coin will produce over a very long run of flips should be 0.5. StatCrunch can create a confidence interval for the proportion of interest. For this example, choose Stat > Proportion Stats > One Sample > With Data menu option. Select the Coin Flips column. The Success input is used to define the label of the outcome of interest. In this case, set this value to Heads. Under Perform, choose Confidence interval for p. By default StatCrunch has a value of 0.95 for the Level input which will produce a 95% confidence level for the population proportion, p. Changing this value to 0.99 would produce a 99% confidence interval. Leave the Level at the default 0.95 and click Compute!. The results below show a 95% confidence interval for the long run proportion of Heads with "L. Limit" representing the lower limit of this confidence interval and "U. Limit" representing the upper limit of this confidence interval.

Changing the confidence interval method

By default the Standard-Wald normal approximation is used for calculating the above confidence interval. To instead use the alternative Agresti-Coull method, choose Options > Edit to reopen the one-sample proportion dialog window, and change Method to Agresti-Coull. The results below show a new confidence interval. The "L. Limit" and "U. Limit" values have changed because of the change in method of calculation.

Always Learning
Pearson