# Terminating Sequential Delphi Survey Data Collection

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4 Practical Assessment, Research & Evaluation, Vol 17, No 5 Page 4 found that three iterations of the rounds of the Delphi survey data collection are enough to reach a consensus among the panel of experts (Kalaian & Shah, 2006; Yang, 2003). The next sections cover a list of possible statistical methods (Parametric and non-parametric) that one can use to make decisions about terminating the Delphi survey administration rounds. It is important to realize that at this point we are not promoting a choice of one method over the others. Rather, we think that a good practice is to collect evidences from as many statistical methods as possible based on valid assumptions in support of the timing for the termination of sequential rounds of administering the Delphisurvey. PARAMETRIC METHODS FOR ANALYZING DELPHI DATA The following is an overview and presentation of four parametric statistical methods to be used in Delphi studies for setting stopping criteria for further rounds of survey administration and data collection (Shah & Kalaian, 2009; Yang, 2003). These parametric statistical methods require that the Delphi survey study to have at least 30 experts. Nonparametric statistical methods need to be used if the number of experts in the panel is less than 30 (Kalaian & Shah, 2006; Shah & Kalaian, 2009; Yang, 2003). 1. Coefficient of Variation (CV) difference for an item from two consecutive rounds. Coefficient of Variation (CV) is the ratio of the standard deviation of the responses of the panel of experts on a specific item to its corresponding mean (average). Therefore, the responses of the experts for each of the items in the survey from each of the rounds of the Delphi survey data collection will yield one coefficient of variation. For example, a Delphi survey with 25 items will yield 25 coefficients of variation for each of the rounds of the Delphi survey administration. The Coefficient of Variation (CV) is calculated using: A large value of the coefficient of variation (CV) for an item in the Delphi survey (larger than 1) indicates that the responses of the experts are scattered compared to the mean of the responses for the item. In other words, the amount of the variation among the opinions (responses) of the expert panelists compared to the mean (average) of the item is large. In contrast, a small value of CV indicates that the amount of variation among the responses of the expert panelists is small compared to the mean of the responses to the item. Next, to measure the stability of the responses for an item an absolute CV difference for each item needs to be calculated by subtracting CV obtained for each item in the Delphi survey from any two consecutive rounds (Dajani, Sincoff, & Talley, 1979; Kalaian & Shah, 2006; Shah & Kalaian, 2009; Yang, 2003). For example, a Delphi survey study with two rounds (x and y) will have the following CV difference between the coefficients of variation for each of the items in the structured Delphi survey CV Difference (Rounds x & y) = CV (Round y) CV (Round x). A small value and close to zero of absolute CV difference for each item in the Delphi survey indicates that the stability of responses and consensus among the experts on a specific item from the two rounds is reached and there is no need for further rounds of survey administration and data collection. In contrast, a large value of absolute CV difference indicates that a consensus or agreement among the expert panelists for a specific item is not reached and there is a need to further rounds of data collection from the same experts after dropping the items that have an absolute CV difference value of zero or close to zero. 2. F-ratio for comparing the variances of an item from two consecutive rounds. An F-ratio is performed to determine the ratio of two variances of an item (question) for any two consecutive rounds of a Delphi survey administration. In other words, an F-ratio is used to

6 Practical Assessment, Research & Evaluation, Vol 17, No 5 Page 6 Delphi survey item from two consecutive rounds of administering the survey. Paired t-test statistical procedure is used to analyze this data using the SPSS software. The t-value of the test equals with a p = 0.18 (see Table 1) suggest that the difference in the ratings of the responses to the item from the two rounds of the Delphi survey is not significantly different from zero. This result indicates that there is little change in the responses from the two consecutive rounds (Round 1 and Round 2) and this specific item should be removed from the Delphi survey in the third round of the survey administration. Table 1: Ratings of the panel members on a specific item from the two consecutive rounds of the Delphi survey administrations Experts Round 1 (R1) Round 2 (R2) Expert Expert Expert Expert Expert Expert Expert Expert Expert Expert Expert Item Mean Item S.D R1-R2 Mean R1-R2 S.E t-value p-value 0.18 NONPARAMETRIC METHODS FOR ANALYZING DELPHI DATA The following are the nonparametric statistical methods that are suggested in the literature (Yang, 2003; Kalaian & Shah, 2006) that can be used to analyze categorical and ordinal Delphi survey data. These methods are recommended to be used instead of the parametric methods when the number of experts in the panel is less than 30 and/or the distribution of the responses for each of the items are skewed (non-normal distribution). 1. McNemar Change Test of the responses of the experts on an item from two consecutive rounds. McNemar Change Test is used in the Delphi survey studies when the responses to the Delphi questions are dichotomous (e.g., yes-no or agreedisagree responses). A hypothetical example showing the structure of the dichotomous Delphi question is presented in Table 2. The A and D diagonal cells are those indicating a change in response from the previous round to the current round (in this example, a change in response from Round 2 to Round 3). The B and C diagonal cells are those indicating no change between the responses of the panel of experts from the two consecutive rounds of the Delphi survey administrations (Yang, 2003). Table 2. The structure of dichotomous data from two rounds of a Delphi study Delphi Survey Round 2 Rounds Disagree Agree Agree A B Round 3 Disagree C D In the above example, the interest is only in the cells that reflect a change of opinion about the question, which are cells A and D. The null hypothesis in this case is: There are an equal number of changes in responses of the panel of experts in both directions (in this example, changes from Agree to Disagree and changes from Disagree to Agree). Hence, we are testing that the expected frequencies in cell A will be equal to the expected frequencies in cell D. Using McNemar Chi-Square test statistic that is computed as

7 Practical Assessment, Research & Evaluation, Vol 17, No 5 Page 7 A continuity correction is applied to the above equation to make the approximate sampling distribution of Chi-square calculated from the above equation more precise (Siegel & Castellan, 1988; Yang, 2003), which can be represented as: 1 In this example, there is one degree of freedom associated with McNemar change statistic because there are two rows and two columns in the above table. Degrees of freedom equal (number of rows 1) x (number of columns 1) and in this example equal (2-1) x (2-1) = 1. Looking up for the critical value of a Chi-square distribution with one degree of freedom at α = 0.05 (Chi-square Distribution Table can be found in any statistics textbook or online), we get If the computed McNemar Chi-square value is smaller than the critical Chisquare value, which is 3.841, the null hypothesis is not rejected. Hence, for this example, it can be concluded that the experts opinions about the specific issue have not significantly changed from one direction to the other from the two consecutive Delphi survey administrations (from Round 2 to Round 3). Therefore, this specific item should be dropped from the Delphi survey and not be included in the subsequent round of the Delphi survey administration (in this example, Round 4). 2. Spearman s Rank Correlation Coefficient between the ratings of the experts on an item from two consecutive rounds. Spearman s rank correlation, r s represents the correlation between the ranks of the ratings or responses of the experts for each of the items in the Delphi survey. It is calculated by using 2 6 r s d = 1 - i 2 nn ( 1) where, d i is the difference between the ranks of the responses or the ratings on the i th item of the Delphi survey, for example, from rounds 1 and 2. The number of experts in a panel is represented by n. The value of r s always falls between -1 and +1, with +1 indicating perfect positive correlation between the responses on an item from two consecutive rounds. The closer r s falls to +1, the greater the correlation between the ranks from the two consecutive rounds. The closer r s is to 0, the less the relationship indicating no correlation between rankings from the two consecutive rounds. The closer r is to -1 the greater the correlation between the responses (e.g., ratings) of the item in an opposite direction indicating a disagreement in the responses of the experts on the item from the two consecutive rounds. For example, in a hypothetical Delphi study two rounds of a survey questionnaire are administered. The six panel members rate the items on a Likert-scale of 1 to 5 as shown in Table 3. Table 3. Ratings of the panel members on a specific item from the two rounds of Delphi survey administrations Round 1 Round 2 Difference between Ratings (d i ) Experts (i) Expert Expert Expert Expert Expert Expert di 8 Calculating r s for the above data using the above formula for the Spearman Rank Order Correlation we get r s = 1-6(8) 6(6 2 1) = The value of shows a positive correlation between the ratings of the same experts on the specific item from the two consecutive rounds of the Delphi survey administration (in this example, Round 1 and Round 2). Looking at the table for the critical values of the Spearman s rank correlation coefficient, at α = 0.05, we get the value Since the calculated r s = is smaller than the critical d i 2

8 Practical Assessment, Research & Evaluation, Vol 17, No 5 Page 8 value of 0.829, we conclude that the association between the ratings of the panel members on this particular item from the two rounds of the Delphi survey administration is not significantly different from zero. Since the test result of the relationship between the two ratings on an item from the two consecutive rounds is not significantly strong, this specific item should be included in the next round of the Delphi survey administration (in this example, Round 3). 3. Wilcoxon Paired Signed-Ranks T Test. Wilcoxon paired signed-ranks T test assesses whether or not the ranks of the difference in responses to an item on the survey from two rounds is equal to a zero. In other words, there is no difference between ranks of the responses of the experts from the two rounds (Privitera, 2012). The test is used as the nonparametric alternative to the parametric paired t-test (see the parametric section of this article). The test provides the sum of each of the positive and negative ranks of the differences between any consecutive rounds of Delphi survey responses (e.g., ratings) with a Z statistic and its asymptotic p-value. A hypothetical data of the ratings of 8 experts on items of a Delphi survey is listed in Table 4. We used SPSS to perform the Wilcoxon paired signed ranks T test to analyze the data. The SPSS results show (see Table 4) that 3 ranks of the difference between Round 3 and Round 2 are negative with a mean sum negative ranks of The results also show (see Table 4) that 4 ranks of the difference between Round 3 and Round 2 are positive with a mean sum positive of The Z- value of the test is with a p-value of These results suggest that the differences in ranks of the responses to the item from the two rounds of the Delphi survey (Round 2 and Round 3) are not significantly different from zero. This result indicates that there is little change in the responses from the two consecutive rounds (in this case, Rounds 2 and Round 3) and the item should be removed from the survey. Table 4. Wilcoxon Paired Signed-Rank T Test for the ratings of the panelists on a specific item from two rounds of Delphi survey administrations Experts Round 2 (R2) Round 3 (R3) Expert Expert Expert Expert Expert Expert Expert Expert Mean Sum Negative Ranks 4.83 (3) of R3-R2 (#) Mean Sum Positive Ranks of 3.38 (4) R3-R2 (#) # Tied Ranks of R3-R2 1 Z-value p-value 0.93 CONCLUSIONS The Delphi survey is a sequential and iterative mail or electronic ( or web-based) survey data collection method to investigate and gain informed anonymous consensus among a panel of experts on a particular complex issue or problem in a specific field of study. It is used as an alternative method to conventional face-to-face meetings to anonymously gain consensus for differing and alternative ratings of positions and opinions between the expert panelists regarding an issue or problem. The ultimate goal is to make informed decision about a specific issue or problem. In this paper we presented four parametric and three nonparametric analytical methods that can be used to analyze a collected Delphi survey data to make decisions about terminating further Delphi data collection rounds. The use of these statistical methods are needed to ensure that (a) all expert opinions are represented in the data set; and (b) terminating the Delphi survey rounds is based on sound statistical results, which helps the Delphi survey researchers to conclude that there is no

9 Practical Assessment, Research & Evaluation, Vol 17, No 5 Page 9 significant variation existing among the opinions of the experts. These parametric and non-parametric statistical methods are easy to calculate and the calculations can be done with the help of any available spreadsheet (e.g., EXCEL), statistical software (e.g., SPSS), or a calculator. It is important to note that the parametric statistical methods require that the Delphi survey study involves 30 or more experts and/or the distribution of the responses for each item is normal. Otherwise, nonparametric statistical methods such as the McNemar Change Test should be used. In other words, the choice of any of the four parametric and the three nonparametric methods presented in this article should be based on (a) number of the expert panelists; and (b) meeting the assumptions of the statistical method. For example, it is recommended that nonparametric methods should be used if the number of the experts in the Delphi study is less than 30 or the distributions of the responses to the Delphi survey questions are skewed (not normal). Shah and Kalaian (2009) compared the three parametric method presented above and found that the three methods yielded similar conclusions for terminating the Delphi data collection process. They recommended using the Coefficient of Variation (CV) method for termination decisions. To avoid the problems associated with using the traditional simple means and percentages of the responses on each item in the Delphi survey and comparing these means and percentages across the rounds of the Delphi survey, which are suggested in the literature, Delphi survey researchers need to use one of the four parametric or one of the three nonparametric statistical methods presented in this paper to make valid, objective, and informed conclusions about the results of the Delphi study. Therefore, analyzing the collected data from a Delphi study using the appropriate statistical methods is a necessary step and should be taken into consideration when planning and designing a Delphi study to have successful findings and conclusions for policy making purposes. REFERENCES Blair, S., & Uhl, N.P. (1993). Using the Delphi method to improve the curriculum. The Canadian Journal of Higher Education, 23(3). Dajani, J. S., Sincoff, M. Z., & Talley, W. K. (1979). Stability and Agreement Criteria for the Termination of Delphi Studies. Technological Forecasting and Social Change, 13, Delbecq, A.L., Van de Ven, A.H., & Gustafson, D.H. (1975). Group techniques for program planning: A guide to nominal group and Delphi processes. Scott Foresman and Company: Glenview, IL. Hsu, Chia-Chien & Sandford, Brian A. (2007). The Delphi Technique: Making Sense of Consensus. Practical Assessment Research & Evaluation, 12(10). [Available online: Kalaian, S. A., & Shah, H. (2006, October). Overview of Parametric and Non-parametric Statistical Methods for Analyzing Delphi Data. Paper presented at the Annual Meeting of the Mid-Western Educational Research Association. Columbus, Ohio. Linstone, H. A., & Turoff, M. (1975). The Delphi method: Techniques and applications. Addison-Wesley: MA. Privitera, G. J. (2012). Statistics for the Behavioral Sciences. California: Sage Publications, Inc. Shah, H., & Kalaian, S. A. (2009). Which Parametric Statistical Method to Use For Analyzing Delphi Data? Journal of Modern Applied Statistical Method (JMASM). 8(1), Siegel, S. & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. New York: McGraw Hill. Yang, Y. N. (2003). Testing the Stability of Experts Opinion between Successive Rounds of Delphi Studies. Paper presented at the Annual Meeting of the American Educational Research Association. Chicago, Illinois. Yousuf, Muhammad Imran (2007). Using Experts Opinions through Delphi Technique. Practical Assessment Research & Evaluation, 12(4). Available online:

10 Practical Assessment, Research & Evaluation, Vol 17, No 5 Page 10 Citation: Kalaian, Sema & Rafa M. Kasim, (2012). Terminating Sequential Delphi Survey Data Collection. Practical Assessment, Research & Evaluation, 17(5). Available online: Corresponding Author: Sema Kalaian, Ph.D. Professor of Statistics and Research Design College of Technology School of Technology Studies 161 Sill Hall Eastern Michigan University Ypsilanti, MI

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