1. Single-case designs: Methodology and data analysis
Analyses via web-based applications

2. Outline Visual analysis: 6 aspects [15] Level Trend Overlap
Variability
Immediacy of effects
Consistency of data patterns

3. Outline Visual aids [18] Trend stability envelope
Standard deviation bands
Projecting split-middle trend with limits
Conservative Dual Criterion

4. Outline Mean difference: [24] Within-case standardized mean difference
Log Response Ratio
Percentage change (all data or last three per phase)
(Percentage Zero Data)
Slope and Level Change
Mean Phase Difference (projected vs. actual)

5. Outline Nonoverlap indices: [37] Percentage of Nonoverlapping Data
Percentage of data points Exceeding the Median
Nonoverlap of All Pairs
Improvement Rate Difference
Tau: without and with trend correction
Baseline corrected Tau: conditional correction
PEM-Trend
PNCorrectedD

6. Outline Regression analyses (taking trend into account) [51]
Overall: Ordinary least squares
Overall + taking autocorrelation into account: Generalized least squares
Immediate effect + change in trend: Piecewise regression

7. Outline Several comparisons beyond AB [56] Slope and level change
Mean phase difference
Two-level models:
(HLM / Multilevel / Mixed effects)
Between-cases standardized mean difference
Multiple-baseline design
Reversal design

8. Outline Alternating treatments design [80] Mean difference
Quantifications of variability
Nonoverlap of All Pairs
PND according to Wolery et al. (2010)
Average Difference between Successive Observations
Comparing Actual and Linearly Interpolated Values

9. Outline: R-Cmdr plug-in
Randomization tests [96]
Using R, R-Commander, plug-ins
AB design
Multiple-baseline design
Alternating treatments design

12. Example: Baldwin & Powell (2015)
Protocol design
Multiple baseline across behaviors (not staggered) preferred over ABAB due to ethical reasons
Baseline (A) compared with Google Calendar text alerts delivered to a mobile phone as a memory aid
1 patients with traumatic brain injury + severe problems in memory and executive functioning
Outcome: number of events forgotten + a subjective measure (Everyday Memory Questionnaire)
Original analysis: Nonoverlap of all pairs

13. Example: Baldwin & Powell (2015)

15. Web-based Visual aids: Loading & summarizing the data

16. Web-based Visual aids: WWC Standards

17. Web-based Visual aids: WWC Standards consistency

18. Web-based Visual aids: Trend stability envelope

19. Web-based Visual aids: Standard deviation bands

20. Web-based Visual aids: Split-middle trend & Md-envelope

21. Web-based Visual aids: Split-middle trend & IQR-interval

22. Web-based Visual aids: (Conservative) Dual Criterion

24. Web-based Within-case SMD (/SA)

25. Web-based Within-case SMD (/Spooled)

27. Web-based Log response ratio

29. Web-based Percentage change: Loading & summarizing the data

30. Web-based Percentage change: Percentage change index

31. Web-based Percentage change: Percentage zero data

33. Web-based Slope & Level Change

34. Web-based Slope & Level Change

35. Web-based Mean phase difference

37. Web-based Nonoverlap indices : Percentage of nonoverlapping data

38. Web-based Nonoverlap indices : Percentage of nonoverlapping data

39. Web-based Nonoverlap indices : % data points exceeding the Md

40. Web-based Nonoverlap indices : Nonoverlap of all pairs

41. Web-based Nonoverlap indices : Improvement rate difference

43. Web-based Nonoverlap indices : Tau without trend correction

44. Web-based Nonoverlap indices : Tau-U with trend correction

45. Web-based Nonoverlap indices : Baseline corrected Tau

46. Web-based Nonoverlap indices: Loading & summarizing the data

47. Web-based Nonoverlap indices: Baseline corrected Tau

48. Web-based Nonoverlap indices: % data points exceeding median trend

49. Web-based Nonoverlap indices: PNCorrectedD

51. Web-based Regression-based ES: Loading & summarizing the data
Web-based Regression-based ES: Loading & summarizing the data

52. Web-based Regression-based ES: Ordinary least squares
Web-based Regression-based ES: Ordinary least squares
𝑑= 𝛽 0𝐵 − 𝛽 0𝐴 + 𝛽 1𝐵 − 𝛽 1𝐴 2 𝑛 𝐴 + 𝑛 𝐵 +1 /2, 𝑛 𝐴 −1 𝑠 2 𝑒𝑟𝑟𝑜𝑟𝐴 + 𝑛 𝐵 −1 𝑠 2 𝑒𝑟𝑟𝑜𝑟𝐵 ( 𝑛 𝐴 + 𝑛 𝐵 −2)

53. Web-based Regression-based ES: Generalized least squares (“directly”)
Web-based Regression-based ES: Generalized least squares (“directly”)
𝑑= 𝛽 0𝐵 − 𝛽 0𝐴 + 𝛽 1𝐵 − 𝛽 1𝐴 2 𝑛 𝐴 + 𝑛 𝐵 +1 /2, 𝑛 𝐴 −1 𝑠 2 𝑒𝑟𝑟𝑜𝑟𝐴 + 𝑛 𝐵 −1 𝑠 2 𝑒𝑟𝑟𝑜𝑟𝐵 ( 𝑛 𝐴 + 𝑛 𝐵 −2)

54. Web-based Regression-based ES: Piecewise regression
Web-based Regression-based ES: Piecewise regression

56. Example:
Baldwin & Powell (2014)

57.
Web-based SLC & MPD for multiple baseline: Loading & summarizing the data

58. Web-based SLC for multiple baseline: Graphing the data
Web-based SLC for multiple baseline: Graphing the data

59. Web-based SLC for multiple baseline: Graphing the differences
Web-based SLC for multiple baseline: Graphing the differences

60. Web-based SLC for multiple baseline: Numerical results
Web-based SLC for multiple baseline: Numerical results

61. Web-based MPD for multiple baseline: Graphing the differences
Web-based MPD for multiple baseline: Graphing the differences

62. Web-based MPD for multiple baseline: Numerical results
Web-based MPD for multiple baseline: Numerical results

64. Web-based Two-level HLM: Loading & summarizing the data
Web-based Two-level HLM: Loading & summarizing the data

65. Web-based Two-level HLM: Graphical results
Web-based Two-level HLM: Graphical results

66. Web-based Two-level HLM: Numerical results
Web-based Two-level HLM: Numerical results

68. Web-based Between-cases SMD

69. Web-based Between-cases SMD

70. Web-based Between-cases SMD

73. Example: Coker et al. (2009) Protocol design ABAB design
Intervention: mCIMT (1 hour /day)
Participant: One child aged 5 months in the beginning; 9 months at B1; 18 months at follow up
Outcome measures: video analysis of affected limb use for:
Reaching an object
Stabilizing weight
Approaching midline

74. Example: Coker et al. (2009) What did the authors do?
Reported graphically observed affected limb use from videotapes.
No visual aids provided. No statistics.
Simple description of graphs in results section.
Peabody developmental motor scale: percentile & age normative groups - comparison
Is it appropriate? Yes, but insufficient.
Only 2 A1 points, due to “no improvement” (ethics, clinical)
Great variability in each phase
Difficult to conclude whether the intervention is effective

75. Example: Coker et al. (2009)
What are we doing? Apply the d-statistic by Hedges, Pustejovsky, and Shadish (2012).
Why? Obtain a summary quantification; SCED-specific; applicable to ABAB designs replicated across participants or behaviors; get an overall summary, given that visual inspection is unclear.
What more can be done? Not much, too short baseline data. Maybe, nonoverlap indices.

76. Web-based Between-cases SMD
Web-based Between-cases SMD

77. Web-based Between-cases SMD

78. Web-based Between-cases SMD

81. Example: Kirsch et al. (2004)
Protocol design
ABA design (Study 1); Alternating treatments design (Study 2)
Intervention: Assistive technology for cognition
Participants: Study 1: 19-year-old man, with topographical disorientation after traumatic brain injury (TBI). Study 2: 71-year-old woman with cognitive declines associated with TBI and a pre-injury history of chronic ischemic changes.
Outcome measures: recorded
Navigation task: average number of errors per route (Study 1)
Setting an alarm clock: Average number of errors per task substep (Study 2)
Setting an alarm clock: number of substeps attempted (Study 2)

82. Example: Kirsch et al. (2004)
Specific characteristics of the Alternating treatments design
Referred to as “modified ABAB” by Kirsch et al. (2004)
«One or two trials were conducted each day, depending on the participant’s availability. However, time of day and order of conditions within and across days were counterbalanced.»
Other possibilities for designs in which frequent alternation of conditions is possible:
Completely randomized sequence of conditions (limiting nA=nB)
Randomized block design: for each pair of measurement occasions, decide at random whether A or B is taking place
«ATD»: random sequence of conditions with a restriction of a maximum of two consecutive administrations of the same conditions.

83. Web-based ATD data analysis: Basic quantifications

84. Web-based ATD data analysis: PND as a quantification of superiority

85. Web-based ATD data analysis: Regression analyses

86. Web-based ATD data analysis: Regression analyses

87. Web-based ATD data analysis: Regression analyses

88. Web-based ATD data analysis: Average DIfference between Successive Observations

89. Web-based ATD data analysis: Actual and Linearly Interpolated Values: Difference

91. References for the examples
Baldwin, V. N., & Powell, T. (2015): Google Calendar: A single case experimental design study of a man with severe memory problems. Neuropsychological Rehabilitation, 25, Coker, P., Lebkicher, C., Harris, L., & Snape, J. (2009). The effects of constraint-induced movement therapy for a child less than one year of age. NeuroRehabilitation, 24, 199–208. Kirsch, N. L., Shenton, M., Spirl, E., Rowan, J., Simpson, R., Schreckenghost, D., & LoPresti, E. F. (2004). Web-Based assistive technology interventions for cognitive impairments after traumatic brain injury: A selective review and two case studies. Rehabilitation Psychology, 49,

92. References for the analyses
Nonoverlap indices
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,
Tarlow, K. (2016, November 8). An improved rank correlation effect size statistic for single-case designs: Baseline corrected Tau. Behavior Modification. Advance online publication. doi: /
Tarlow, K. R., & Penland, A. (2016, September 26). Outcome assessment and inference with the Percentage of Nonoverlapping Data (PND) single-case statistic. Practice Innovations. Advance online publication. doi: /pri
Vannest, K. J., & Ninci, J. (2015). Evaluating intervention effects in single-case research designs. Journal of Counseling & Development, 93,

93. References for the analyses
Within-case standardized mean difference (SMD)
Beretvas, S. N., & Chung, H. (2008). A review of meta-analyses of single-subject experimental designs: Methodological issues and practice. Evidence-Based Communication Assessment and Intervention, 2,
Between-cases standardized mean difference (SMD)
Shadish, W. R., Hedges, L. V., Horner, R. H., & Odom, S. L. (2015). The role of between-case effect size in conducting, interpreting, and summarizing single-case research (NCER ). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved on October 12, 2016 from
Slope and level change (SLC) and Mean phase difference (MPD)
Manolov, R., & Rochat, L. (2015). Further developments in summarising and meta-analysing single-case data: An illustration with neurobehavioural interventions in acquired brain injury. Neuropsychological Rehabilitation, 25,

94. References for the analyses
Alternating treatments designs
Jacoby, W. G. (2000). Loess: A nonparametric, graphical tool for depicting relationships between variables. Electoral Studies, 19, 577–613.
Manolov, R., & Onghena, P. (in press). Analyzing data from single-case alternating treatments designs. Psychological Methods.
Moeyaert, M., Ugille, M., Ferron, J., Beretvas, S. N., & Van Den Noortgate, W. (2014). The influence of the design matrix on treatment effect estimates in the quantitative analyses of single-case experimental designs research. Behavior Modification, 38, 665–704.
Solmi, F., Onghena, P., Salmaso, L., & Bulté, I. (2014). A permutation solution to test for treatment effects in alternation design single-case experiments. Communications in Statistics - Simulation and Computation, 43, 1094–1111.
Wolery, M., Gast, D. L., & Hammond, D. (2010). Comparative intervention designs. In D. L. Gast (Ed.), Single subject research methodology in behavioral sciences (pp. 329–381). London, UK: Routledge.

97. Example: Winkens et al. (2014)
Protocol design
AB design. The moment of change in phase determined at random
Baseline (A) compared with the ABC method: a simplified form of behavioural modification therapy especially designed for nursing staff (B)
1 patients with acquired brain injury: olivo-pontocerebellar ataxia
Outcome: daily score on verbal aggressiveness (2x 0: not at all to 2x 4: continuous yelling, screaming, cursing, or threatening)
Original analysis: Randomization test + NAP

98. Example: Winkens et al. (2014)

99. R-Commander data analysis: Websites

100. R-Commander data analysis: Installing the package once

101. R-Commander data analysis: Loading the package every time

102. R-Commander data analysis: Using the package for design

103. R-Commander data analysis: Using the package for design

104. R-Commander data analysis: Using the package for analysis

105. R-Commander data analysis: Using the package for analysis

106. R-Commander data analysis: Using the package for analysis

107. R-Commander data analysis: Using the package for analysis

109. Example: Fictitious

110. R-Commander data analysis: Using the package for analysis

111. R-Commander data analysis: Using the package for analysis

112. R-Commander data analysis: Using the package for analysis

114. Example: Sil et al. (2013)

115. Example: Sil et al. (2013) Protocol design
Several Alternating treatments designs with initial baseline. Alternation determined at random with a maximum of 2 consecutive per condition (restricted randomization; semi-random)
Baseline (A) compared with passive distraction (B) and interactive distraction (C)
4-year-old girl receiving repeated burn dressing changes
Outcome: child cooperation (to increase) and distress (to reduce) as reported by a parent and a nurse
Original analysis: Randomization test

116. Example: Sil et al. (2013)

117. R-Commander data analysis: Using the package for analysis

118. R-Commander data analysis: Using the package for analysis

119. R-Commander data analysis: Using the package for analysis

120. R-Commander data analysis: Using the package for analysis

121. Additional references
Heyvaert, M., & Onghena, P. (2014). Analysis of single-case data: Randomisation tests for measures of effect size. Neuropsychological Rehabilitation, 24, Heyvaert, M., & Onghena, P. (2014). Randomization tests for single-case experiments: State of the art, state of the science, and state of the application. Journal of Contextual Behavioral Science, 3, 51–64. Levin, J. R., Ferron, J. M., & Gafurov, B. S. (2016, July 1). Comparison of randomization-test procedures for single-case multiple-baseline designs. Developmental Neurorehabilitation. Advance online publication. doi: / Sil, S., Dahlquist, L. M., & Burns, A. J. (2013). Case study: videogame distraction reduces behavioral distress in a preschool-aged child undergoing repeated burn dressing changes: A single-subject design. Journal of Pediatric Psychology, 38, 330–341. Winkens, I., Ponds, R., Pouwels-van den Nieuwenhof, C., Eilander, H., & van Heugten, C. (2014). Using single-case experimental design methodology to evaluate the effects of the ABC method for nursing staff on verbal aggressive behaviour after acquired brain injury. Neuropsychological Rehabilitation, 24,