Analysis of Delphi study 7-point linear scale data by parametric methods: Use of the mean and standard deviation
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.079 | 0.188 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".