Overlap indices for single-case data

The overlap function provides the most common overlap indices for single-case data and some additional statistics.

Usage

overlap(data, dvar, pvar, mvar, decreasing = FALSE, phases = c(1, 2))

Arguments

data: A single-case data frame. See scdf() to learn about this format.
dvar: Character string with the name of the dependent variable. Defaults to the attributes in the scdf file.
pvar: Character string with the name of the phase variable. Defaults to the attributes in the scdf file.
mvar: Character string with the name of the measurement time variable. Defaults to the attributes in the scdf file.
decreasing: If you expect data to be lower in the B phase, set decreasing = TRUE. Default is decreasing = FALSE.
phases: A vector of two characters or numbers indicating the two phases that should be compared. E.g., phases = c("A","C") or phases = c(2,4) for comparing the second to the fourth phase. Phases could be combined by providing a list with two elements. E.g., phases = list(A = c(1,3), B = c(2,4)) will compare phases 1 and 3 (as A) against 2 and 4 (as B). Default is phases = c(1,2).

Value


`overlap`	A data frame consisting of the following indices for each single-case for all cases: PND, PEM, PET, NAP, PAND, IRD, Tau-U (A vs. B - Trend A), Diff_mean, Diff_trend, SMD, Hedges-g.
`phases.A`	Selection for A phase.
`phases.B`	Selection for B phase.
`design`	Phase design.

Details

See corresponding functions of PND, PEM, PET, NAP, PAND for calculation. Tau_U(A) reports "A vs. B - Trend A" whereas Tau_U(BA) reports "A vs. B + Trend B - Trend A". Base_Tau is baseline corrected tau (correction applied when autocorrelation in phase A is significant). Diff_mean is the mean difference. Diff_trend is the difference in the regression estimation of the dependent variable on measurement-time (x ~ mt) for each phase. SMD is the mean difference divided by the standard deviation of phase A. Hedges_g is the mean difference divided by the pooled standard deviation: \(\sqrt{ (n_A - 1)sd_A^2 + (n_B - 1)sd_B^2 \over n_A + n_B - 2 }\) with a hedges correction applied: \(Hedges_g * (1 - \frac{3}{4n - 9} ) )\).

Author

Juergen Wilbert

Examples


## Display overlap indices for one single-case
overlap(Huitema2000, decreasing = TRUE)
#> Overlap Indices
#> 
#> Comparing phase 1 against phase 2 
#> 
#>               Case1
#> Design          A-B
#> PND              40
#> PEM              70
#> PET             100
#> NAP              70
#> NAP rescaled     40
#> PAND             60
#> IRD             0.4
#> Tau_U(A)      -0.51
#> Tau_U(BA)     -0.69
#> Base_Tau      -0.73
#> Diff_mean     -20.4
#> Diff_trend   -17.87
#> SMD            -0.9
#> Hedges_g      -0.71
#> 
#> The following variables were used in this analysis:
#> 'score' as dependent variable, 'phase' as phase variable, and 'mt' as measurement-time variable.

## Display overlap indices for six single-cases
overlap(GruenkeWilbert2014)
#> Overlap Indices
#> 
#> Comparing phase 1 against phase 2 
#> 
#>              Anton   Bob  Paul Robert   Sam   Tim
#> Design         A-B   A-B   A-B    A-B   A-B   A-B
#> PND            100   100   100    100   100   100
#> PEM            100   100   100    100   100   100
#> PET            100   100   100    100   100   100
#> NAP            100   100   100    100   100   100
#> NAP rescaled   100   100   100    100   100   100
#> PAND           100   100   100    100   100   100
#> IRD              1     1     1      1     1     1
#> Tau_U(A)      0.67  0.66  0.75   0.68  0.65  0.68
#> Tau_U(BA)     0.48  0.57  0.60   0.49  0.51  0.35
#> Base_Tau      0.67  0.77  0.75   0.77  0.72  0.66
#> Diff_mean     4.14  5.82  5.00   4.78  4.48  6.00
#> Diff_trend    0.43  0.00  0.28  -0.08 -0.07  0.60
#> SMD           5.07  7.13  6.64   5.72  8.17  7.35
#> Hedges_g      5.06  6.50  6.53   4.90  5.36  6.11
#> 
#> The following variables were used in this analysis:
#> 'score' as dependent variable, 'phase' as phase variable, and 'mt' as measurement-time variable.

## Combining phases for analyszing designs with more than two phases
overlap(exampleA1B1A2B2, phases = list(c("A1","A2"), c("B1","B2")))
#> Overlap Indices
#> 
#> Comparing phases A1 + A2 against phases B1 + B2 
#> 
#>                    Pawel      Moritz      Jannis
#> Design       A1-B1-A2-B2 A1-B1-A2-B2 A1-B1-A2-B2
#> PND                   55          78          71
#> PEM                  100         100         100
#> PET                  100         100         100
#> NAP                   94          97          98
#> NAP rescaled          89          94          97
#> PAND                  85          85          90
#> IRD                 0.75        0.80        0.89
#> Tau_U(A)            0.54        0.44        0.43
#> Tau_U(BA)           0.45        0.46        0.38
#> Base_Tau            0.65        0.68        0.68
#> Diff_mean          12.25       13.58       15.27
#> Diff_trend         -0.05        0.00       -0.54
#> SMD                 2.68        3.27        3.62
#> Hedges_g            2.07        2.72        2.98