1. Non-Overlap Methods in Single Case Research Methodology Erin E. Barton, PhD, BCBA-D

2. Non-overlap Methods 1.PND 2.PEM (ECL) 3.PEM-T 4.PAND 5.R-IRD 6. NAP 7. Tau-U

3. Rationale: Non-overlap Methods 1.Need to aggregate across studies to determine evidence for practice Meta-analysis is a well established practice for group experiments –Magnitude –Aggregate findings –Moderator analyses

4. Rationale: Non-overlap Methods 1.Need to aggregate across studies to determine evidence for practice –Many have argued if SCRD will not be included in reviews of evidence-based practices unless an effect size estimator is used –They are often left out of reviews in disciplines outside of special education

5. Rationale: Non-overlap Methods 2.Emphasis on “effect sizes” in education research to quantify the magnitude –Standardized effect sizes are particularly valued –Reviewers compare results across studies having different outcome measures that otherwise could not be easily compared

6. Rationale: Non-overlap Methods 3.Meta-analytic techniques are compromised when data are serially dependent –On a single individual –Using the same definitions –Using the same data collection procedures –In the same context –Under the same procedures –Often with short intervals between observations

7. Rationale: Non-overlap Methods 4.Current meta-analytic techniques are inappropriate for aggregating SCR data  The data patterns must shift consistently in the predicted (therapeutic) direction with each change in experimental condition  Replication logic is used to make judgments about functional relations  The design needs an adequate number of replications of the experimental conditions (internal validity)

8. Rationale: Non-overlap Methods 5.Non-parametric techniques needed Short data sets or few data points Non-normal or unknown distributions Unknown parameters

9. PND: Percent of Non- overlapping Data

10. One of the oldest of the overlap methods (Scruggs, & Mastropieri, 1998; Scruggs, Mastropieri, & Casto, 1987) Used extensively Easily calculated Does not assume data are independent

11. Calculating PND 1.Identify the intended change 2.Drawing a straight line from the highest (or lowest) point in Phase A and counting the number of data point in Phase B above the line 3.Quotient = # above the line / total number in Phase B X 100

12. Interpreting PND  70% is effective, 50% to 70% is questionable effectiveness, and <50% is no observed effect  (Scruggs & Mastropieri, 1998)

15. Practice: Calculating PND Schilling (2004), David In Seat A1 to B1: B1 to A2: A2 to B2: Engaged A1 to B1: B1 to A2: A2 to B2:

16. A1 to B1: 22% B1 to A2: 100% A2 to B2: 100% AVERAGE: 74% Practice: Calculating PND Schilling (2004), David In SeatEngaged A1 to B1: 100% B1 to A2: 100% A2 to B2: 100% AVERAGE: 100%

19. Practice: Calculating PND Vaughn (2002) Disruptive Behavior Arrival: 100% Mealtime: 75% Departure: 100% AVERAGE: 92% Engaged Arrival: 100% Mealtime: 75% Departure: 100% AVERAGE: 92%

20. Outliers PND = 0% Functional Relation?

21. Trends PND = 0% Functional Relation?

22. Magnitude PND = 100% Functional Relation?

23. Outliers PND = 0% Functional Relation?

24. BUT NO ONE USES A-B-A-B….. You might be thinking….

25. Functional Relation? PND = 68% PND = 43% PND = 86% Social Initiations to Peers

26. PND = 68% PND = 43% PND = 86% PND = 66% TREND?

27. Functional Relation? PND = 0% Social Initiations to Peers

28. PND = 0% MAGNITUDE?

29. Functional Relation? PND = 100% Social Initiations to Peers

30. WHAT DOES THAT MEAN? You SHOULD be thinking….

31. PND Flaws Compared with consensus visual analysis, PND resulted in an error in about 1 of 5 condition changes—high rate of errors (Wolery, Busick, Reichow, & Barton, 2010) Compromised by: –Longer data sets, # of data points –Variability –Outliers –Trends Should not be used (Brossart et al., 2013; Kratochwill et al., 2010; Parker & Vannest, 2009)

32. PND Flaws Is it an Effect Size? Replication Magnitude Can it supplement visual analysis? 1.Level 2.Trend 3.Variability 4.Immediacy 5.Overlap 6.Consistency  Vertical analysis

33. PAND: Percent of All Non- overlapping Data

34. Not compromised by serial dependency or other data assumptions Percentage of data remaining after determining the fewest data points that must be removed to eliminate all between-phase overlap

35. Calculating PAND 1.Count the total number of data points in comparison 2.Identify how many need data points need to be removed to eliminate overlap 3.Count the number of remaining data points 4.Divide count in step 3 by count in step 1 5.X by 100

36. Practice: Calculating PAND Schilling (2004), David In Seat A1 to B1: 94% B1 to A2: 100% A2 to B2: 100% AVERAGE: 98% (PND Average was 74%) Engaged A1 to B1: 100% B1 to A2: 100% A2 to B2: 100% AVERAGE: 100% (PND Average was 100%)

37. Practice: Calculating PAND Vaughn (2002) Disruptive Behavior Arrival: 100% Mealtime: 85% Departure: 100% AVERAGE: 95% PND was 92% Engaged Arrival: 100% Mealtime: 85% Departure: 100% AVERAGE: 95% PND was 92% Adding more data points Extinction burst Variability

38. PAND = 96% PAND = 93% Social Initiations to Peers

39. PAND = 96% PAND = 93% PAND = 94% MAGNITUDE?

40. PAND = 100% Social Initiations to Peers

41. PAND Flaws Is it an Effect Size? Replication Magnitude Can it supplement visual analysis? 1.Level 2.Trend 3.Variability 4.Immediacy 5.Overlap 6.Consistency  Vertical analysis Should not be used (Brossart et al., 2013; Manolov et al., 2010)

42. PEM: Percent Exceeding the Median (Ma, 2006)

43. Not compromised by serial dependency and other data assumptions Designed to eliminate problem with baseline datum point being at floor or ceiling –Designed to not rely on the most extreme datum point –Less influenced by variability in baseline

44. Calculating PEM 1.Drawing a line at the median of Phase A data through Phase B data 2.Count the number of data points in Phase B above (or below) the line and divide by the total number of data points in Phase B

45. PEM Flaws Compared with consensus visual analysis, PEM resulted in an error in about 1 of 6 condition changes—high rate of errors (Wolery et al., 2010) Should not be used (Parker, Vannest, & Davis, 2011)

46. PEM Flaws Is it an Effect Size? Replication Magnitude Can it supplement visual analysis? 1.Level 2.Immediacy 3.Overlap 4.Consistency  Vertical analysis

47. PEM-T: Percent Exceeding the Median Trend Line ECL: Extended Celeration Line

48. PEM-T: Percent Exceeding the Median Trend Line (Wolery et al., 2010) Not compromised by serial dependency and other data assumptions Designed to eliminate problem with baseline datum point being at floor or ceiling –Designed to not rely on the most extreme datum point –Less influenced by variability in baseline –Less influenced by trends in data

49. Calculating PEM-T 1.Graph data on semi-logarithmic chart 2.Calculate and draw a split middle line of trend estimation for Phase A data and extend it through Phase B 3.Count # of Phase B data points above/below the split middle line of trend estimation 4.Divide count from Step 4 by # data points in Condition 2 and multiply quotient by 100

50. PEM-T Flaws Compared with consensus visual analysis, PEM-T resulted in an error in about 1 of 8 condition changes—high rate of errors (Wolery et al., 2010)

51. PEM-T Flaws Is it an Effect Size? Replication Magnitude Can it supplement visual analysis? 1.Level 2.Trend 3.Variability 4.Immediacy 5.Overlap 6.Consistency  Vertical analysis

52. So what, right?

53. Social Stories for Children with ASD 20 studies met design standards with or without reservation, which exceeded the minimum number of five studies set by the WWC as needed to be represented across studies. Across 3 research groups Qi & Barton, under review

54. Social Stories for Children with ASD Using Non-overlap indices: –28 participants (51%) had a PND score higher than 70; 41 (75%) had a PEM score higher than 70; 40 (73%) had a PEM-T score higher than 70; and 50 (91%) had a PDO 2 score higher than 70. Using visual analyses: –only 13 participants were included across the one study that provided strong evidence and in the six studies that provided moderate evidence. Qi & Barton, under review

55. Social Stories for Children with ASD Based on visual analysis, social stories interventions were not considered an EBP according to WWC criteria. Based on non-overlap indices, social stories interventions were considered an EBP according to WWC criteria. Qi & Barton, under review

56. R-IRD: Robust Improvement Rate Difference

57. Not compromised by serial dependency and other data assumptions Not about rate IRD calculation begins as PAND, but in a second step converts the results to two improvement rates (IR), for phase A and B respectively. The two IR values are finally subtracted to obtain the “Improvement Rate Difference” (IRD) R-IRD requires rebalancing (by hand) of a 2 x 2 matrix

58. R-IRD: Robust Improvement Rate Difference The original IRD article recommended that in the first step, data point ‘removal’ “should be balanced across the contrasted phases” (Parker et al., 2009, p. 141) for more robust results. A better robust IRD solution was later described and formalized as “Robust IRD” (R-IRD). R-IRD requires rebalancing (by hand) of a 2 x 2 matrix IRD is interpreted as the difference in the proportion of high or “improved” scores between phases B and A.

59. R-IRD: Robust Improvement Rate Difference The superior robust version of IRD (R- IRD) requires that quadrants be balanced. –Balancing when a large number of data points are be removed arbitrarily from one side and a few from the other… –Does not allow bias in removal of data points from A versus B, as some datasets provide two or more equally good removal solutions.

60. Calculating R-IRD 1.Determine the fewest data points that must be removed to eliminate overlap 2.Balance quadrant W and Z 3.Then balance Y = A –Phase A: W / (W + Y) 4.Then balance X = B –Phase B: X / (X + Z) 5.R - IRD = B – A

61. Calculating R-IRD http://www.singlecaseresearch.org/calculat ors/ird Flaws: Length of data can impact (Brossart et al., 2013; Manolov et al., 2011)

62. NAP: Non-overlap of All Pairs

63. The percentage of data that improve from A to B or operationally, the percentage of all pairwise comparisons from Phase A to B which show improvement or growth (Parker & Vannest, 2009)

64. Calculating NAP 1.NAP begins with all pairwise comparisons (#Pairs = n A × n B ) between phases. 2.Each paired comparison has one of three outcomes: improvement over time (Pos), deterioration (Neg), or no change over time (Tie). 3.NAP is calculated as (Pos +.5 × Tie) / #Pairs.

65. Practice: Calculating NAP Phase A: 0 4 3 0 0 Phase B: 5 2 3 5 3 5 6 7

66. # of Pairs = 5*8 = 40 #Pos = 34, #Neg = 4, #Tie = 2 NAP = (#Pos +.5*#Ties)/#Pairs NAP = (34 +.5*2)/40 NAP =.875 N=5 N=8

67. NAP Flaws Is it an Effect Size? Replication Magnitude Can it supplement visual analysis? 1.Level 2.Trend 3.Variability 4.Immediacy 5.Consistency 6.Overlap  Vertical analysis

68. Tau-U Extension of NAP – but can control for trend.

69. Tau-U: (Kendall’s Tau + Mann-Whitney U) NAP’s major limitation of insensitivity to data trend led to development of a new index that integrates non- overlap and trend: TauU (Parker, Vannest, Davis, & Sauber, 2011). Melding KRC and MW-U are transformations of one another and share the same S sampling distribution The Tau-U score is not affected by the ceiling effect present in other non-overlap methods, and performs well in the presence of autocorrelation. NAP is percent of non-overlapping data, whereas TauU is percent of non-overlapping minus overlapping data. Can control for baseline trends

70. Calculating Tau-U Simplest Tau (non-overlap only) Conduct the same pairwise comparisons (n A × n B = #Pairs) across phases as is NAP, resulting in a Pos, Neg, or Tie for each pair The Tau simple non-overlap form (not considering trend) is Tau = (Pos - Neg) / Pairs Tau-U can control for baseline trend

71. Practice: Calculating TauU Phase A: 0 4 3 0 0 Phase B: 5 2 3 5 3 5 6 7

72. # of Pairs = 5*8 = 40 #Pos = 34, #Neg = 4, #Tie = 2 Tau-U = (#Pos - #Neg)/#Pairs Tau-U = (34 - 4)/40 Tau-U =.75 N=5 N=8

73. Practice Tau-U = -.82 Tau-U =.79 Tau-U = -.81 7 8 6 7 56 pairs, 2+, 6=, 48- 48 pairs, 40+, 6=, 2- 42 pairs, 1+, 6=, 35-

74. Calculating Tau-U www.singlecaseresearch.org

76. Calculating Tau-U Schilling (2004), David In Seat A1 to B1: 1 (0.54, 1.46) B1 to A2: -1 (-1.59, -.41) A2 to B2: 1 (.36, 1.64) PAND Average: 98% (PND Average was 74%) Engaged A1 to B1:.83 (.37, 1.29) B1 to A2: -1 (-1.59, -.41) A2 to B2: 1 (.36, 1.64) PAND Average: 100% (PND Average was 100%)

77. Calculating Tau-U Vaughn (2002) Disruptive Behavior Arrival: -1 (-1.708, -0.23) Mealtime: -.67 (-1.44,.11) Departure: -1 (-1.78, -.23) PAND was 95% PND was 92% Engaged Arrival: 1 (.292, 1.71) Mealtime:.83 (.06, 1.61) Departure: 1 (.23, 1.76) PAND was 95% PND was 92%

78. Tau-U = 1.0 Social Initiations to Peers Tau-U = 1.0

79. Social Initiations to Peers Tau-U = 1.0

80. Tau-U Flaws Is it an Effect Size? Replication Magnitude Can it supplement visual analysis? 1.Trend 2.Level 3.Variability 4.Overlap 5.Immediacy 6.Consistency  Vertical analysis Tau-U is the recommended non- overlap index

81. Summary Complete non-overlap measures offer the most robust option (NAP, Tau-U) –Complete measures equally emphasize all scores –Incomplete measures emphasize particular scores (e.g., median)

82. Summary Determination of evidence-based practice does not need to involve summary statistic Dynamic, flexible nature of SCRD allow for ongoing decision making while maintaining experimental control Replication logic can not be ignored

83. Summary Visual Analysis is complex and involves more than overlap –Graphing is important! Effect sizes, non-overlap measures should not take the place of visual analysis

84. Continue to: 1.Determine if the design supports the demonstration of a functional relation and meets design standards 2.Use systematic visual analysis to determine if data support a functional relational –Not just behavioral change or effect –Report protocol used and perhaps training of VAs –Include predicted data pattern in RQ 3.Consider magnitude and social validity 4.If using an effect size estimator, test and report assumptions

85. Develop: Effect sizes that are: Is consistent with single case research design logic Synthesis of SC studies with similar IVs and DVs Synthesis rigorous, experimental studies using SCR and RCTs

86. References Broissart, D. F., Vannest, K. J., Davis, J. L., & Patience, M. A. (2014). Incorporating nonoverlap indices with visual analysis for quantifying intervention effectiveness in single-case experimental designs. Neuropsychological Rehabilitation: An International Journal, 24, 464- 491. Ma, H. H. (2006).An alternative method for quantitative synthesis of single-subject research: Percentage of datapoints exceeding the median. Behavior Modification, 30, 598–617. Parker, R., & Vannest, K. J. (2008). An improved effect size for single case research: Non- overlap of all pairs (NAP). Behavior Therapy, 40, 357-67. Parker, R. I., Vannest, K. J., & Brown, L. (2009). The improvement rate difference for single case research. Exceptional Children, 75, 135–150. Parker, R. I., Vannest, K. J., & Davis, J. L. (2011). Effect size in single-case research: A review of nine nonoverlap techniques. Behavior Modification, 35, 303-322. Wolery, M., Busick, M., Reichow, B., & Barton, E. (2010). Comparison of overlap methods for quantitatively synthesizing single-subject data. Journal of Special Education, 44, 18-28.