Analysis of Delphi study 7-point linear scale data by parametric methods: Use of the mean and standard deviation

Abstract

The Delphi technique is a unique survey method that involves an iterative process to gain consensus when consensus is challenging to establish. Survey participants typically rate a variety of statements using a specified rating scale. The survey is repeated for several rounds, and at each round statements that do not reach a predefined level of consensus are advanced to the next round while giving the participants information about the responses of other participants for their comparison. The final statements are then ranked in order of the average rating. The statistical methods to analyze Delphi studies are not well described. This study investigates the use of a 1–7 linear rating scale along with parametric summary statistics for assessment of consensus and ranking of statements. A study set of 9297 individual ratings on the 1–7 scale were obtained from previously performed Delphi studies and used to create 490,000 simulated Delphi ratings with various numbers of participants. While the overall distribution of ratings was strongly left skewed the sampling distribution was near normally distributed for studies with five or more participants. The average difference between the standard deviation and interquartile range was −0.26/7. The overall risk of falsely concluding consensus using the standard deviation as a summary statistic was 7.3% when compared to using the interquartile range. The average difference between mean and median was −0.20/7. The risk of falsely ranking the statements by a value of 0.5 or more was near zero for all sample sizes when the mean was compared to the median. This study suggests that the use of the 1–7 linear rating scale in combination with the parametric summary statistics of standard deviation and mean is a valid method to analyze ratings from Delphi studies.