| Title: | A Calculator for Single-Case Effect Sizes |
|---|---|
| Description: | Provides R functions for calculating basic effect size indices for single-case designs, including several non-overlap measures and parametric effect size measures, and for estimating the gradual effects model developed by Swan and Pustejovsky (2018) <DOI:10.1080/00273171.2018.1466681>. Standard errors and confidence intervals (based on the assumption that the outcome measurements are mutually independent) are provided for the subset of effect sizes indices with known sampling distributions. |
| Authors: | James E. Pustejovsky [aut, cre], Man Chen [aut], Daniel M. Swan [aut], Paulina Grekov [ctb] |
| Maintainer: | James E. Pustejovsky <[email protected]> |
| License: | GPL-3 |
| Version: | 0.7.3.9999 |
| Built: | 2025-03-08 02:30:59 UTC |
| Source: | https://github.com/jepusto/singlecasees |
Calculates one or more effect size estimates, along with associated standard errors and confidence intervals, if available, for a single-case data series.
batch_calc_ES( dat, grouping, condition, outcome, aggregate = NULL, weighting = "equal", session_number = NULL, baseline_phase = NULL, intervention_phase = NULL, ES = c("LRRd", "LRRi", "SMD", "Tau"), improvement = "increase", scale = "other", intervals = NA, observation_length = NA, goal = NULL, confidence = 0.95, format = "long", warn = TRUE, ... )batch_calc_ES( dat, grouping, condition, outcome, aggregate = NULL, weighting = "equal", session_number = NULL, baseline_phase = NULL, intervention_phase = NULL, ES = c("LRRd", "LRRi", "SMD", "Tau"), improvement = "increase", scale = "other", intervals = NA, observation_length = NA, goal = NULL, confidence = 0.95, format = "long", warn = TRUE, ... )
dat |
data frame containing SCD series for which effect sizes will be calculated. |
grouping |
A variable name or list of (unquoted) variable names that uniquely identify each data series. |
condition |
A variable name that identifies the treatment condition for each observation in the series. |
outcome |
A variable name for the outcome data. Default is |
aggregate |
A variable name of list of (unquoted) variable names that
identify additional grouping variables. Effect sizes will be calculated
separately for each unique value of these variables, after which the effect
size estimates will be averaged across values of these variables (but not
across the values of the |
weighting |
character string specifying the weighting scheme for use
when variables are specified in |
session_number |
A variable name used to order the data within each series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
ES |
character string or character vector specifying which effect size
index or indices to calculate. Available effect sizes are |
improvement |
character string either indicating the direction of uniform improvement ("increase" or "decrease") or the variable name of a variable identifying the direction of improvement for each series. Default is "increase". |
scale |
character string indicating the common scale of the outcome
variable across all of the series in the data set or the name of a variable
within the dataset that identifies the outcome scale within each series.
Possible values for the scale are |
intervals |
for interval recording procedures. Either the total number
of intervals per observation session common to all series in the dataset,
or the name of a variable within the dataset that identifies the number of
intervals for each observation. If a variable name, the mean number of
intervals within each series will be used. Missing values will be ignored.
Defaults to |
observation_length |
Used for the log-response ratio. Either the common
observation session length (in minutes) across all series in the dataset or
a variable name containing the observation session length for each
observation. If a variable name, the mean observation session length within
each series will be used. Missing values will be ignored. Defaults to
|
goal |
Used for the percent of goal obtained. Either a numeric common
goal level across all series in the dataset or a variable name containing
the goal level for each series. If a variable name, the mean goal level
within each series will be used. Missing values will be ignored. Defaults
to |
confidence |
confidence level for the reported interval estimate. Set to
|
format |
character string specifying whether to organize the results in
|
warn |
logical indicating whether warnings should be displayed. Default
is |
... |
further arguments used for calculating some of the effect size indices. |
Calculates one or more effect size indices for each series in a dataset
A tibble containing the estimate, standard error, and/or confidence interval for each specified effect size.
data(McKissick) batch_calc_ES(McKissick, grouping = Case_pseudonym, condition = Condition, outcome = Outcome, ES = c("LRRd","LRRi"), improvement = "decrease", scale = "count", observation_length = 20, format = "long") data(Schmidt2007) batch_calc_ES(dat = Schmidt2007, grouping = c(Behavior_type, Case_pseudonym, Phase_num), condition = Condition, outcome = Outcome, ES = c("LRRi","LRRd"), improvement = direction, scale = Metric, bias_correct = TRUE, confidence = NULL, format = "wide") # Aggregate across phase-pairs batch_calc_ES(dat = Schmidt2007, grouping = c(Behavior_type, Case_pseudonym), aggregate = Phase_num, weighting = "1/V", condition = Condition, outcome = Outcome, ES = c("LRRi", "LRRd", "SMD", "Tau"), improvement = direction, scale = "count", bias_correct = TRUE, confidence = NULL, format = "long")data(McKissick) batch_calc_ES(McKissick, grouping = Case_pseudonym, condition = Condition, outcome = Outcome, ES = c("LRRd","LRRi"), improvement = "decrease", scale = "count", observation_length = 20, format = "long") data(Schmidt2007) batch_calc_ES(dat = Schmidt2007, grouping = c(Behavior_type, Case_pseudonym, Phase_num), condition = Condition, outcome = Outcome, ES = c("LRRi","LRRd"), improvement = direction, scale = Metric, bias_correct = TRUE, confidence = NULL, format = "wide") # Aggregate across phase-pairs batch_calc_ES(dat = Schmidt2007, grouping = c(Behavior_type, Case_pseudonym), aggregate = Phase_num, weighting = "1/V", condition = Condition, outcome = Outcome, ES = c("LRRi", "LRRd", "SMD", "Tau"), improvement = direction, scale = "count", bias_correct = TRUE, confidence = NULL, format = "long")
Data from an ABAB design that evaluated the effectiveness of functional assessment and functional communication training on the Rett syndrome (RTT) of three individuals with RTT novel communicative behaviors. The dependent variable, communicative behavior, was measured using frequency counting for a five minute observation session. A single outcome (percent of switch activated responses) was calculated with appropriate responses per minute divided by inappropriate responses per minute, multiplied by 100. The variables are as follows:
StudyID. Study identifier.
StudyID_CaseID. Participant identifier.
Session_number. Within-series session-number.
Condition. Indicates condition, (A for baseline, B for treatment).
Outcome. Value for the percent of switch activated responses.
Session_length. Length of the session.
Procedure. Scale of the outcome variable.
Goal_level. Indicates the goal level for each series.
phase_pair_calculated. Indicates the unique phase number of each
sequential occurrence of a phase for each participant of ABAB design.
A data frame with 54 rows and 9 variables
Byiers, B. J., Dimian, A., & Symons, F. J. (2014). Functional communication training in Rett syndrome: A preliminary study. American Journal on Intellectual and Developmental Disabilities, 119(4), 340-350. doi:10.1352/1944-7558-119.4.340
Calculates one or more effect size estimates, along with associated standard errors and confidence intervals, if available, for a single-case data series.
calc_ES( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, ES = c("LRRd", "LRRi", "SMD", "Tau"), improvement = "increase", ..., confidence = 0.95, format = "long" )calc_ES( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, ES = c("LRRd", "LRRi", "SMD", "Tau"), improvement = "increase", ..., confidence = 0.95, format = "long" )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
ES |
character string or character vector specifying which effect size
index or indices to calculate. Available effect sizes are |
improvement |
character string indicating direction of improvement. Default is "increase". |
... |
further arguments used for calculating some of the effect size indices. |
confidence |
confidence level for the reported interval estimate. Set to
|
format |
character string specifying whether to organize the results in
|
Calculates one or more effect size indices
A data.frame containing the estimate, standard error, and/or confidence interval for each specified effect size.
# Using the A_data and B_data arguments A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) calc_ES(A_data = A, B_data = B) # Using the condition and outcome arguments phase <- c(rep("A", length(A)), rep("B", length(B))) outcome <- c(A, B) calc_ES(condition = phase, outcome = outcome, baseline_phase = "A") # Example from Parker & Vannest (2009) yA <- c(4, 3, 4, 3, 4, 7, 5, 2, 3, 2) yB <- c(5, 9, 7, 9, 7, 5, 9, 11, 11, 10, 9) calc_ES(yA, yB)# Using the A_data and B_data arguments A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) calc_ES(A_data = A, B_data = B) # Using the condition and outcome arguments phase <- c(rep("A", length(A)), rep("B", length(B))) outcome <- c(A, B) calc_ES(condition = phase, outcome = outcome, baseline_phase = "A") # Example from Parker & Vannest (2009) yA <- c(4, 3, 4, 3, 4, 7, 5, 2, 3, 2) yB <- c(5, 9, 7, 9, 7, 5, 9, 11, 11, 10, 9) calc_ES(yA, yB)
Calculates a vector containing a unique phase number for every sequential occurrence of a phase or treatment condition. This is useful for creating a grouping variable to be used in calculating effect sizes for each pair of A-B phases within treatment reversal designs.
calc_phase_pairs(x, session = seq_along(x))calc_phase_pairs(x, session = seq_along(x))
x |
vector of phase/condition labels. |
session |
numeric vector of measurement occasions, used to sort |
A vector containing an integer phase number for every observation.
# Basic use-case x <- rep(c("A","B","C","B","C","A","C"), c(4:10)) calc_phase_pairs(x) # Using session argument to handle sort order session <- sample(seq_along(x)) x_scrambled <- x[session] dat <- data.frame( x = x_scrambled, session = session, phase_pair = calc_phase_pairs(x_scrambled, session = session) ) dat_sorted <- dat[order(session),] identical(x, dat_sorted$x) # With a grouped data.frame library(dplyr) Schmidt2007 %>% group_by(Behavior_type, Case_pseudonym) %>% mutate(phase_pair = calc_phase_pairs(Condition, session = Session_number))# Basic use-case x <- rep(c("A","B","C","B","C","A","C"), c(4:10)) calc_phase_pairs(x) # Using session argument to handle sort order session <- sample(seq_along(x)) x_scrambled <- x[session] dat <- data.frame( x = x_scrambled, session = session, phase_pair = calc_phase_pairs(x_scrambled, session = session) ) dat_sorted <- dat[order(session),] identical(x, dat_sorted$x) # With a grouped data.frame library(dplyr) Schmidt2007 %>% group_by(Behavior_type, Case_pseudonym) %>% mutate(phase_pair = calc_phase_pairs(Condition, session = Session_number))
Data from a multiple baseline design across participant that evaluated the effectiveness of use of manual signs with verbalizations in improving appropriate communicative behavior and reducing inappropriate behavior. The study aimed to increase positive communicative behavior to 1 and reduce the proportion of intervals engaged in problem behavior to 0. These two outcomes were combined to create the dependent variable: proportion of communicative opportunities with a signed request. The variables are as follows:
StudyID. Study identifier.
StudyID_CaseID. Participant identifier.
Session_number. Within-series session-number.
Condition. Indicates condition, (A for baseline, B for treatment).
Outcome. Value for the outcome variable.
Session_length. Length of the session.
Procedure. Scale of the outcome variable.
Goal_level. Indicates the goal level for each series.
A data frame with 100 rows and 8 variables
Casey, L. O. (1978). Development of communicative behavior in autistic children: A parent program using manual signs. Journal of Autism and Childhood Schizophrenia, 8(1), 45-59. https://doi.org/10.1007/BF01550277
Data from an ABAB design that evaluated a social story intervention on the disruptive behavior of a preschool child with autism. The dependent variable, number of disruptions, was measured using frequency counting for a thirty minute observation session. The variables are as follows:
session. Within-series session-number.
phase. Lable for each unique phase (e.g., A1 is the first baseline phase, B2 is the second treatment phase).
score. Value for the outcome.
A data frame with 24 rows and 3 variables
Crozier, S., & Tincani, M. J. (2005). Using a modified social story to decrease disruptive behavior of a child with autism. Focus on Autism and Other Developmental Disabilities, 20(3), 150-157.
Data from a Repeated acquisition single-case experimental design evaluating vocabulary knowledge using an expressive definition task. The variables are as follows:
Participant. Participant identifier.
Condition. Indicates condition, application (App) or teacher (TCH).
Observation. Within-series session-number
Pre. Pre-intervention score on the expressive definition task.
Post. Post-intervention score on the expressive definition task.
A data frame with 90 rows and 5 variables
Dennis, L. R., & Whalon, K. J. (2021). Effects of teacher-versus application-delivered instruction on the expressive vocabulary of at-risk preschool children. Remedial and Special Education, 42(4), 195-206. doi:10.1177/0741932519900991
Data from a multiple baseline design across participants conducted by English, et al. (1997), which evaluated the effects of peer-training on interaction skills. This dependent variable, number of communicative acts directed by the participant to their peers, was measured using frequency counting for a 10-minute observation session. The variables are as follows:
case. Participant pseudonym given by author
session. Within-series session-number
phase. Label for each unique phase (A for baseline, B for treatment)
score. Value for the outcome.
A data frame with 59 rows and 4 variables
English, K., Goldstein, H., Shafer, K., & Kaczmarek, L. (1997). Promoting interactions among preschoolers with and without disabilities: Effects of a buddy skills-training program. Exceptional Children, 63(2), 229-243.
Data from a changing criterion design conducted by Facon, et al. (2008), which evaluated two operant learning procedures, shaping and fading, for treating selective mutism. The dependent variable, average speech loudness in dB, was measured during 15-minute observation sessions. The variables are as follows:
session. Within-series session-number
phase. Label for each unique phase (A for baseline, each following for a change in criteria.
score. Value for the outcome.
criterion. The fixed criterion value for each of the phases. The student moved to the next criterion when 80
A data frame with 49 rows and 4 variables
Facon, B., Sahiri, S., & Riviere, V. (2008). A controlled single-case treatment of severe long-term selective mutism in a child with mental retardation. Behavior Therapy, 39, 313-321
A function to estimate the gradual effects model for an SCD
gem_scd(Trt, outcome, m, fam)gem_scd(Trt, outcome, m, fam)
Trt |
A vector of treatment assignments where 0 = untreated and 1 = treated. |
outcome |
A vector of outcomes. |
m |
The number of treatment occasions to estimate a treatment effect for. |
fam |
A description of the error distribution and link function to be
used in the model. This can be supplied in any way that 'glm' will accept.
(See |
'gem_scd' returns an object of class glm. In addition to the
normal contents of a glm object, it also contains an estimate of
'omega' and a variance covariance matrix called 'varcov'.
Calculates the robust improvement rate difference index (Parker, Vannest, & Brown, 2009). The range of IRD depends on the number of observations in each phase.
IRD( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )IRD( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
Numeric value
Parker, R. I., Vannest, K. J., & Brown, L. (2009). The improvement rate difference for single-case research. Exceptional Children, 75(2), 135–150. doi:doi:10.1177/001440290907500201
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) IRD(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) IRD(A_data = A, B_data = B)
Data from a randomized control trial with embedded repeated acquisition single- case experimental design evaluating vocabulary knowledge using an expressive definition task. The variables are as follows:
condition. Indicates whether control or treatment group.
observation. Identifier for participant
unit. Classroom unit.
Pre. Pre-intervention score on the expressive definition task.
Post. Post-intervention score on the expressive definition task.
A data frame with 54 rows and 5 variables
Kelley, E. S., Goldstein, H., Spencer, T., & Sherman, A. (2015). Effects of automated Tier 2 storybook intervention on vocabulary and comprehension learning in preschool children with limited oral language skills. Early Childhood Research Quarterly, 31, 47-61. doi:10.1016/j.ecresq.2014.12.004
Calculates the log-odds ratio effect size index, with or without bias correction (Pustejovsky, 2015)
LOR( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", scale = "percentage", intervals = NULL, D_const = NULL, bias_correct = TRUE, confidence = 0.95 )LOR( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", scale = "percentage", intervals = NULL, D_const = NULL, bias_correct = TRUE, confidence = 0.95 )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
scale |
character string indicating the scale of the outcome variable.
Must be either |
intervals |
for interval recording procedures, the total number of intervals per observation session. If a vector, the mean number of intervals will be used. |
D_const |
constant used for calculating the truncated sample mean (see Pustejovsky, 2015). If a vector, the mean value will be used. |
bias_correct |
logical value indicating whether to use bias-correction.
Default is |
confidence |
confidence level for the reported interval estimate. Set to
|
The odds ratio parameter is the ratio of the odds of the outcome. The log-odds ratio is the natural logarithm of the odds ratio. This effect size is appropriate for outcomes measured on a percentage or proportion scale. Unlike the LRRd and LRRi, the LOR is symmetric in valence, so that the LOR for an positively-valenced outcome is equal to -1 times the LOR calculated after reversing the scale of the outcome so that it is negatively valenced.
Without bias correction, the log-odds ratio is estimated by substituting the sample mean level in each phase in place of the corresponding parameter. A delta-method bias correction to the estimator is used by default.
The standard error of LOR is calculated based on a delta-method approximation, allowing for the possibility of different degrees of dispersion in each phase. The confidence interval for LOR is based on a large-sample (z) approximation.
To account for the possibility of sample means of zero, a truncated mean is
calculated following the method described in Pustejovsky (2015). Truncated
sample variances are also calculated to ensure that standard errors will be
strictly larger than zero. The truncation constant depends on the total
number of intervals per session (or the total number of items for other
percentage/proportion scales). The arguments scale and
intervals must be specified in order to calculate an appropriate
truncation constant. For outcomes measured using continuous recording
procedures, set intervals equal to 60 times the length of the
observation session in minutes.
A data.frame containing the estimate, standard error, and approximate confidence interval.
Pustejovsky, J. E. (2015). Measurement-comparable effect sizes for single-case studies of free-operant behavior. Psychological Methods, 20(3), 342–359. doi:doi:10.1037/met0000019
A_pct <- c(20, 20, 25, 25, 20, 25) B_pct <- c(30, 25, 25, 25, 35, 30, 25) LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", intervals = 20, bias_correct = FALSE) LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", intervals = 20) LOR(A_data = A_pct, B_data = B_pct, scale = "percentage") LOR(A_data = A_pct / 100, B_data = B_pct / 100, scale = "proportion") LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", improvement = "decrease")A_pct <- c(20, 20, 25, 25, 20, 25) B_pct <- c(30, 25, 25, 25, 35, 30, 25) LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", intervals = 20, bias_correct = FALSE) LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", intervals = 20) LOR(A_data = A_pct, B_data = B_pct, scale = "percentage") LOR(A_data = A_pct / 100, B_data = B_pct / 100, scale = "proportion") LOR(A_data = A_pct, B_data = B_pct, scale = "percentage", improvement = "decrease")
Calculates the log ratio of medians effect size index
LRM( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", delta_method = FALSE, confidence = 0.95 )LRM( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", delta_method = FALSE, confidence = 0.95 )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
delta_method |
logical value indicating whether to use delta method to
approximate variance of log ratio of medians. Default is |
confidence |
confidence level for the reported interval estimate. Set to
|
The ratio of medians effect size parameter is defined as the ratio of the medians of the outcomes in different phases. The log ratio of the medians is the natural logarithm of the ratio of medians. This effect size is appropriate for outcomes that are skewed, symmetric but highly leptokurtic, or right-censored (Bonett & Price Jr, 2020).
A data frame containing the estimate, standard error, and confidence interval.
Bonett, D. G. & Price Jr, R. M. (2020). Confidence Intervals for Ratios of Means and Medians. Journal of Educational and Behavioral Statistics, 45(6), 750–770. doi:doi:10.3102/1076998620934125
Bonett, D. G., & Price, R. M. (2020). Interval estimation for linear functions of medians in within-subjects and mixed designs. British Journal of Mathematical and Statistical Psychology, 73(2), 333-346. doi:doi:10.1111/bmsp.12171
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) LRM(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) LRM(A_data = A, B_data = B)
Calculates the increasing or decreasing version of the log-response ratio effect size index, with or without bias correction (Pustejovsky, 2015)
LRRd( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "decrease", scale = "count", observation_length = NULL, intervals = NULL, D_const = NULL, bias_correct = TRUE, pct_change = FALSE, confidence = 0.95 ) LRRi( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", scale = "count", observation_length = NULL, intervals = NULL, D_const = NULL, bias_correct = TRUE, pct_change = FALSE, confidence = 0.95 )LRRd( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "decrease", scale = "count", observation_length = NULL, intervals = NULL, D_const = NULL, bias_correct = TRUE, pct_change = FALSE, confidence = 0.95 ) LRRi( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", scale = "count", observation_length = NULL, intervals = NULL, D_const = NULL, bias_correct = TRUE, pct_change = FALSE, confidence = 0.95 )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
scale |
character string indicating the scale of the outcome variable,
with possible values |
observation_length |
length of observation session (in minutes). If a vector, the mean observation session length will be used. |
intervals |
for interval recording procedures, the total number of intervals per observation session. If a vector, the mean number of intervals will be used. |
D_const |
constant used for calculating the truncated sample mean (see Pustejovsky, 2018). If a vector, the mean value will be used. |
bias_correct |
logical value indicating whether to use bias-correction.
Default is |
pct_change |
logical value indicating whether to convert the LRR estimate and confidence interval into percentage change. |
confidence |
confidence level for the reported interval estimate. Set to
|
The response ratio parameter is the ratio of the mean level of the
outcome during phase B to the mean level of the outcome during phase A. The
log response ratio is the natural logarithm of the response ratio. This
effect size is appropriate for outcomes measured on a ratio scale (so that
zero corresponds to the true absence of the outcome. There are two versions
of the LRR. The LRR-increasing (LRRi) is defined so that positive
values correspond to therapeutic improvements. The LRR-decreasing
(LRRd) is defined so that negative values correspond to therapeutic
improvements. For outcomes measured as frequency counts or rates, the two
versions will have the same magnitude but opposite sign; for outcomes
measured as percentages or proportions, the LRRd and LRRi will differ in
both sign and magnitude (Pustejovsky, 2018).
Without bias correction, the log response ratio is estimated as the natural logarithm of the phase B sample mean, minus the natural logarithm of the phase A sample mean. A delta-method bias correction to the estimator is used by default.
The standard error of LRR is calculated based on a delta-method approximation, allowing for the possibility of different degrees of dispersion in each phase. The confidence interval for LRR is based on a large-sample (z) approximation.
To account for the possibility of sample means of zero, a truncated mean is
calculated following the method described in Pustejovsky (2018). Truncated
sample variances are also calculated to ensure that standard errors will be
strictly larger than zero. The truncation constant depends on the scale of
the outcome, the length of the observation sessions used to measure the
dependent variable, and (for interval recording procedures) the total
number of intervals per session (or the total number of items for other
percentage/proportion scales). The argument scale must be specified
in order to calculate an appropriate truncation constant. For standardized
rates, the argument observation_length must also be specified; for
percentages or proportions, the argument intervals must be
specified. For outcomes measured using continuous recording procedures, set
intervals equal to 60 times the length of the observation session in
minutes.
If pct_change is TRUE, then the LRR estimate and confidence
interval are converted into percentage change using the formula
Percentage change = 100 * (exp(LRR) - 1).
A data.frame containing the estimate, standard error, and approximate confidence interval.
Pustejovsky, J. E. (2015). Measurement-comparable effect sizes for single-case studies of free-operant behavior. Psychological Methods, 20(3), 342–359. doi:doi:10.1037/met0000019
Pustejovsky, J. E. (2018). Using response ratios for meta-analyzing single-case designs with behavioral outcomes. Journal of School Psychology, 16, 99-112. doi:doi:10.1016/j.jsp.2018.02.003
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) LRRd(A_data = A, B_data = B, bias_correct = FALSE) LRRd(A_data = A, B_data = B) LRRd(A_data = A, B_data = B, pct_change = TRUE)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) LRRd(A_data = A, B_data = B, bias_correct = FALSE) LRRd(A_data = A, B_data = B) LRRd(A_data = A, B_data = B, pct_change = TRUE)
Disruptive behavior data from a study by McKissick et al. (2010). All data were collected via event counting. The variables are as follows:
Case_Pseudonym. Case Pseudonym provided by the authors.
Session_number. Within-series session-number
Condition. Describes whether the outcome is in the baseline (A) or treatment (B) phase.
Outcome. Value for the outcome.
Session_length. Length of the observation session.
Procedure. The metric in which the outcome measurement is expressed, all "count".
Session_length. The length of the observation session.
A data frame with 35 rows and 4 variables
McKissick, C., Hawkins, R. O., Lentz, F. E., Hailley, J., & McGuire, S. (2010). Randomizing multiple contingency components to decrease disruptive behaviors and increase student engagement in an urban second-grade classroom. Psychology in the Schools, 47(9), 944-959. https://doi.org/10.1002/pits.20516
Calculates the non-overlap of all pairs index (Parker & Vannest, 2009).
NAP( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE )NAP( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
SE |
character value indicating which formula to use for calculating the
standard error of NAP, with possible values |
confidence |
confidence level for the reported interval estimate. Set to
|
trunc_const |
logical value indicating whether to return the truncation constant used to calculate the standard error. |
NAP is calculated as the proportion of all pairs of one observation from each phase in which the measurement from the B phase improves upon the measurement from the A phase, with pairs of data points that are exactly tied being given a weight of 0.5. The range of NAP is [0,1], with a null value of 0.5.
The unbiased variance estimator was described by Sen (1967) and Mee (1990). The Hanley estimator was proposed by Hanley and McNeil (1982). The null variance is a known function of sample size, equal to the exact sampling variance when the null hypothesis of no effect holds. When the null hypothesis does not hold, the null variance will tend to over-estimate the true sampling variance of NAP.
The confidence interval for NAP is calculated based on the symmetrized score-inversion method (Method 5) proposed by Newcombe (2006).
A data.frame containing the estimate, standard error, and/or confidence interval.
Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143, 29–36. doi:doi:10.1148/radiology.143.1.7063747
Mee, W. (1990). Confidence intervals for probabilities and tolerance regions based on a generalization of the Mann-Whitney statistic. Journal of the American Statistical Association, 85(411), 793-800. doi:doi:10.1080/01621459.1990.10474942
Newcombe, R. G. (2006). Confidence intervals for an effect size measure based on the Mann-Whitney statistic. Part 2: Asymptotic methods and evaluation. Statistics in Medicine, 25(4), 559–573. doi:doi:10.1002/sim.2324
Parker, R. I., & Vannest, K. J. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy, 40(4), 357–67. doi:doi:10.1016/j.beth.2008.10.006
Sen, P. K. (1967). A note on asymptotically distribution-free confidence bounds for P{X<Y}, based on two independent samples. The Annals of Mathematical Statistics, 29(1), 95-102. https://www.jstor.org/stable/25049448
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) NAP(A_data = A, B_data = B) # Example from Parker & Vannest (2009) yA <- c(4, 3, 4, 3, 4, 7, 5, 2, 3, 2) yB <- c(5, 9, 7, 9, 7, 5, 9, 11, 11, 10, 9) NAP(yA, yB)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) NAP(A_data = A, B_data = B) # Example from Parker & Vannest (2009) yA <- c(4, 3, 4, 3, 4, 7, 5, 2, 3, 2) yB <- c(5, 9, 7, 9, 7, 5, 9, 11, 11, 10, 9) NAP(yA, yB)
Data from a multiple baseline design across behavior looking at four fluency measures (blends, segmenting, first part ID, first sound ID). The dependent variable is a score on a subtest, with a maximum score of 20. The variables are as follows:
behavior. Outcome measure description (blends, segmenting, first part ID, or first sound ID)
session. Within-series session-number
phase. Label for each unique phase (A for baseline, B for treatment)
score. Value for the outcome.
Include. Value for inclusion in POGO calculation (0 if included in article, 1 if not included)
A data frame with 72 rows and 4 variables
Olszewski, A., Soto, X., & Goldstein, H. (2017). Modeling alphabet skills as instructive feedback within a phonological awareness intervention. American Journal of Speech-Language Pathology, 26(3), 769-790. doi:10.1044/2017_AJSLP-16-0042
Calculates the percentage of all non-overlapping data index (Parker, Hagan-Burke, & Vannest, 2007; Parker, Vannest, & Davis, 2011).
PAND( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )PAND( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
For an outcome where increase is desirable, PAND is calculated as the proportion of observations remaining after removing the fewest possible number of observations from either phase so that the highest remaining point from the baseline phase is less than the lowest remaining point from the treatment phase. For an outcome where decrease is desirable, PAND is calculated as the proportion of observations remaining after removing the fewest possible number of observations from either phase so that the lowest remaining point from the baseline phase is greater than the highest remaining point from the treatment phase. The range of PAND depends on the number of observations in each phase.
Numeric value
Parker, R. I., Hagan-Burke, S., & Vannest, K. J. (2007). Percentage of all non-overlapping data (PAND): An alternative to PND. The Journal of Special Education, 40(4), 194–204. doi:doi:10.1177/00224669070400040101
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(4), 303–22. doi:doi:10.1177/0145445511399147
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PAND(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PAND(A_data = A, B_data = B)
Calculates the percentage exceeding the median (PEM) index (Ma, 2006).
PEM( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )PEM( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
For an outcome where increase is desirable, PEM is calculated as the proportion of observations in the B phase that exceed the median observation from the A phase. For an outcome where decrease is desirable, PEM is calculated as the proportion of observations in the B phase that are less than the median observation from the A phase. Ties are counted with a weight of 0.5. The range of PEM is [0,1].
Numeric value
Ma, H.-H. (2006). An alternative method for quantitative synthesis of single-subject researches: Percentage of data points exceeding the median. Behavior Modification, 30(5), 598–617. doi:doi:10.1177/0145445504272974
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PEM(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PEM(A_data = A, B_data = B)
Data from a Repeated acquisition single-case experimental design evaluating vocabulary knowledge using an expressive definition task. The variables are as follows:
observation. Identifier for participant
Book.Book used for evaluation.
Pre. Pre-intervention score on the expressive definition task.
Post. Post-intervention score on the expressive definition task.
A data frame with 153 rows and 4 variables
Peters-Sanders, L., Kelley, E., Haring, C., Madsen, K., Soto, X., Seven, Y., Hull, K., & Goldstein, H. (2020). Moving forward four words at a time: Effects of a supplemental preschool vocabulary. Language, Speech, and Hearing Services in Schools, 51, 165-175. doi:10.1044/2019_LSHSS-19-00029
Calculates the percentage of non-overlapping data index (Scruggs, Mastropieri, & Castro, 1987).
PND( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )PND( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
For an outcome where increase is desirable, PND is calculated as the proportion of observations in the B phase that exceed the highest observation from the A phase. For an outcome where decrease is desirable, PND is the proportion of observations in the B phase that are less than the lowest observation from the A phase. The range of PND is [0,1].
Numeric value
Scruggs, T. E., Mastropieri, M. A., & Casto, G. (1987). The quantitative synthesis of single-subject research: Methodology and validation. Remedial and Special Education, 8(2), 24–43. doi:doi:10.1177/074193258700800206
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PND(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PND(A_data = A, B_data = B)
Calculates the percent of goal obtained effect size index
PoGO( A_data, B_data, condition, outcome, goal, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", confidence = 0.95 )PoGO( A_data, B_data, condition, outcome, goal, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", confidence = 0.95 )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
goal |
a numerical value indicating the goal level of behavior. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
confidence |
confidence level for the reported interval estimate. Set to
|
The percent of goal obtained (PoGO) effect size parameter is defined as the ratio of the difference in the mean level of behavior during phase B versus during phase A to the difference between the goal level of behavior and the mean level of behavior during phase A, multiplied by 100.
The standard error of PoGO is calculated based on Dunlap and Silver's (1986) approximation for the standard error of a ratio. The confidence interval for LRR is based on a large-sample (z) approximation.
A data frame containing the estimate, standard error, and confidence interval.
Dunlap, W. P., & Silver, N. C. (1986). Confidence intervals and standard error for ratios of normal variables. Behavior Research Methods, Instruments, & Computers, 18, 469-471. doi:doi:10.3758/BF03201412
Ferron, J., Goldstein, H., Olszewski, A., & Rohrer, L. (2020). Indexing effects in single-case experimental designs by estimating the percent of goal obtained. Evidence-Based Communication Assessment and Intervention, 14(1-2), 6-27. doi:doi:10.1080/17489539.2020.1732024
Patrona, E., Ferron, J., Olszewski, A., Kelley, E., & Goldstein, H. (2022). Effects of explicit vocabulary interventions for preschoolers: An exploratory application of the percent of goal obtained (PoGO) effect size metric. Journal of Speech, Language, and Hearing Research, forthcoming.
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PoGO(A_data = A, B_data = B, goal = 30)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) PoGO(A_data = A, B_data = B, goal = 30)
An interactive tool for calculating effect size indices for single-case designs.
SCD_effect_sizes(browser = TRUE)SCD_effect_sizes(browser = TRUE)
browser |
logical value indicating whether to launch the app in the
system's default web-browser. Defaults to |
Data from a study by Schmidt (2007). The variables are as follows:
Behavior_type. Outcome measure description
(disruptive behavior or on task behavior).
Procedure. The
observation recording procedure used to measure the outcome.
Metric. The metric in which the outcome measurement is expressed
("count" for natural counts; "percentage" for percentage of intervals)
Session_length. Length (in minutes) of the observation
sessions
Interval_length. If an interval method was used, the
length of the intervals (in seconds); NA otherwise.
Case_Pseudonym. Case Pseudonym provided by the authors.
Session_number. Within-series session-number.
Phase.
Label for each unique phase (e.g., A1 is the first baseline phase, B2 is
the second treatment phase).
Condition. Label indicating
whether the outcome is in the baseline (A) or treatment (B) phase.
Outcome. Outcome measurement.
Phase_num. Indicator for
each pair of baseline and treatment phases.
direction.
Direction of therapeutic improvement for the outcome.
n_Intervals. If an interval method was used, the total number of
intervals; NA otherwise.
A data frame with 172 rows and 13 variables
Data were reconstructed from figures in the source document. Consequently, outcome measurements in this dataset include additional error from the reconstruction process and may not exactly match the original source data.
In earlier versions of the package (0.5.0 and earlier), the
Case_Pseudonym variable contained incorrect labels for each case,
which did not match the labels in the source document. Specifically, Faith
was incorrectly labeled as Albert; Lilly was incorrectly labeled as Faith;
and Albert was incorrectly labeled as Lilly.
Schmidt, A. C. (2007). The effects of a group contingency on group and individual behavior in an urban first-grade classroom. Masters Thesis, University of Kansas, Department of Applied Behavioral Sciences. ProQuest Dissertations & Theses Global, thesis number 1443719. https://kuscholarworks.ku.edu/bitstream/handle/1808/32097/Schmidt_Anna_C_2007_5349292.pdf
Data from an ABAB design conducted by Schmidt and Stichter (2012). All data were collected via continuous recording. The variables are as follows:
Case. Participant identifier.
Behavior. Behavior type (Conversation, Initiations, or Responses).
Trt Treatment indicators.
Outcome. Outcome scores.
Session_num. Measurement occasion.
Session_length Length of the observation session.
Procedure The metric in which the outcome measurement is expressed, all "other".
A data frame with 180 rows and 5 variables
Schmidt, C., & Stichter, J. P. (2012). The use of peer-mediated interventions to promote the generalization of social competence for adolescents with high-functioning autism and Asperger's syndrome. Exceptionality, 20(2), 94-113. doi:10.1080/09362835.2012
Open an interactive tool for calculating the gradual effects model for SCDs.
shine_gem_scd(browser = TRUE)shine_gem_scd(browser = TRUE)
browser |
logical value indicating whether to launch the app in the
system's default web-browser. Defaults to |
## Not run: shine_gem_scd() ## End(Not run)## Not run: shine_gem_scd() ## End(Not run)
Data from a systematic review by Shogren et al. (2004) on the effects of choice-making interventions. These data were compiled and re-analyzed in Pustejovsky (2015). The variables are as follows:
Study. An ID for each study in the systematic review.
Case. Case Pseudonym provided by the authors.
Measure. Type of behavior observed as the outcome measure
Phase. Phase indicator, baseline phase is "No Choice" and treatment phase is "Choice."
Percentage. For those outcomes measured as percentage, outcomes value. NA for count outcomes.
Observed. For those outcomes measured as count, outcome value. NA for percentage outcomes.
Possible. For counts out of a maximum, lists the maximum value.
Recording_procedure Recording procedure. CDR = "Continuous Duration Recording", EC = "Event Counting", "MTS = "Momentary Time Sampling", and PIR = "Partial Interval Recording."
Session_length. Length of the observation session in minutes.
interval_length. Length of the observation intervals for data observed using MTS or PIR.
outcome. Value for the outcome for all outcome types.
direction. Direction of therapeutic improvement for the outcome.
A data frame with 634 rows and 15 variables
Shogren, K. A., Faggella-Luby, M. N., Bae, S. J., & Wehmeyer, M. L. (2004). The effect of choice-making as an intervention for problem behavior. Journal of Positive Behavior Interventions, 6(4), 228-237.
Pustejovsky, J.E. (2015). Measurement-comparable effect sizes for single-case studies of free-operant behavior. Psychological Methods, 20(3), 342-359.
Calculates the within-case standardized mean difference effect size index
SMD( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", std_dev = "baseline", bias_correct = TRUE, confidence = 0.95 )SMD( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", std_dev = "baseline", bias_correct = TRUE, confidence = 0.95 )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
std_dev |
character string controlling how to calculate the standard
deviation in the denominator of the effect size. Set to |
bias_correct |
logical value indicating whether to use bias-correction
(i.e., Hedges' g). Default is |
confidence |
confidence level for the reported interval estimate. Set to
|
The standardized mean difference parameter is defined as the difference between the mean level of the outcome in phase B and the mean level of the outcome in phase A, scaled by the within-case standard deviation of the outcome in phase A. The parameter is estimated using sample means and sample standard deviations and (optionally) making a small-sample correction.
By default, the scaling factor is estimated using the sample standard
deviation in phase A (the baseline phase) only. Set std_dev = "pool"
to use the sample standard deviation pooled across both phases. Hedges'
(1981) small-sample bias correction is applied by default.
A list containing the estimate, standard error, and confidence interval.
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) SMD(A_data = A, B_data = B, bias_correct = FALSE) SMD(A_data = A, B_data = B) SMD(A_data = A, B_data = B, std_dev = "pool")A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) SMD(A_data = A, B_data = B, bias_correct = FALSE) SMD(A_data = A, B_data = B) SMD(A_data = A, B_data = B, std_dev = "pool")
Data from a repeated acquisition single-case experimental design evaluating vocabulary knowledge using an expressive definition task. The variables are as follows:
Observation. Participant number.
Book. Book used for evaluation.
Pre. Pre-intervention score on the expressive definition task.
Post. Post-intervention score on the expressive definition task.
A data frame with 81 rows and 4 variables
Spencer, E., Goldstein, H., Sherman, A., Noe, S., Tabbah, R., Ziolkowski, R., & Schneider, N. (2012). Effects of an automated vocabulary and comprehension intervention: An early efficacy study. Journal of Early Intervention, 34, 195-221. doi:10.1177/1053815112471990
Data from a multiple baseline design across participant that evaluated the effectiveness of an iPod-based speech generating device and a peer mediated intervention on improving sophisticated communication skills of children with autism. The variables are as follows:
StudyID. Study identifier.
StudyID_CaseID. Participant identifier.
Session_number. Within-series session-number.
Condition. Indicates condition, (A for baseline, B for intervention).
Outcome. The number of independent 2-step mands.
Session_length. Length of the session.
Procedure. Scale of the outcome variable.
Goal_level. Indicates the goal level for each series.
A data frame with 47 rows and 8 variables
Strasberger, S. K., & Ferreri, S. J. (2014). The effects of peer assisted communication application training on the communicative and social behaviors of children with autism. Journal of Developmental and Physical Disabilities, 26, 513-526. https://doi.org/10.1007/s10882-013-9358-9
Calculates the Tau (non-overlap) index (Parker, Vannest, Davis, & Sauber 2011).
Tau( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE )Tau( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
SE |
character value indicating which formula to use for calculating the
standard error of NAP, with possible values |
confidence |
confidence level for the reported interval estimate. Set to
|
trunc_const |
logical value indicating whether to return the truncation constant used to calculate the standard error. |
Tau (non-overlap) a linear re-scaling of NAP to the
range [-1,1], with a null value of 0.
Standard errors and confidence intervals for Tau are based on
transformations of the corresponding SEs and CIs for NAP.
A list containing the estimate, standard error, and/or confidence interval.
Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42(2), 284–299. doi:doi:10.1016/j.beth.2010.08.006
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) Tau(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) Tau(A_data = A, B_data = B)
Calculates the baseline-corrected Tau index (Tarlow 2017).
Tau_BC( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE, Kendall = FALSE, pretest_trend = FALSE, report_correction = FALSE, warn = TRUE )Tau_BC( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE, Kendall = FALSE, pretest_trend = FALSE, report_correction = FALSE, warn = TRUE )
A_data |
vector of numeric data for A phase. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
SE |
character value indicating which formula to use for calculating the
standard error of Tau-BC, with possible values |
confidence |
confidence level for the reported interval estimate. Set to
|
trunc_const |
logical value indicating whether to return the truncation constant used to calculate the standard error. |
Kendall |
logical value indicating whether to use Kendall's rank
correlation to calculate the Tau effect size measure. If |
pretest_trend |
significance level for the initial baseline trend test.
The raw data are corrected and |
report_correction |
logical value indicating whether to report the
baseline corrected slope and intercept values. Default is |
warn |
logical value indicating whether to print a message regarding the
outcome of the baseline trend test. Default is |
Tau-BC is an elaboration of the Tau that includes a
correction for baseline trend. The calculation of Tau-BC involves two or
three steps, depending on the pretest_trend argument.
If pretest_trend = FALSE (the default), the first step involves
adjusting the outcomes for baseline trend estimated using Theil-Sen
regression. In the second step, the residuals from Theil-Sen regression are
used to calculate the Tau (using either Kendall's rank correlation,
with adjustment for ties, or computing Tau directly, without adjustment for
ties).
Alternately, pretest_trend can be set equal to a significance level
between 0 and 1 (e.g. pretest_trend = .05, as suggested by Tarlow
(2017). In this case, the first step involves a significance test for the
slope of the baseline trend based on Kendall's rank correlation. If the
slope is not significantly different from zero, then no baseline trend
adjustment is made and Tau-BC is set equal to Tau index. If the
slope is significantly different from zero, then in the second step, the
outcomes are adjusted for baseline trend using Theil-Sen regression. Then,
in the third step, the residuals from Theil-Sen regression are used to
calculate the Tau index. If Kendall = FALSE (the default),
then Tau (non-overlap) index is calculated. If Kendall
= TRUE, then Kendall's rank correlation is calculated, including
adjustment for ties, as in Tarlow (2017).
Note that the standard error formulas are based on the standard errors for
Tau (non-overlap) and they do not account for the additional
uncertainty due to use of the baseline trend correction (nor to the
pre-test for statistical significance of baseline trend, if used).
A list containing the estimate, standard error, and/or confidence interval.
Tarlow, K. R. (2017). An improved rank correlation effect size statistic for single-case designs: Baseline corrected Tau. Behavior modification, 41(4), 427-467. doi:doi:10.1177/0145445516676750
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) Tau_BC(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) Tau_BC(A_data = A, B_data = B)
Calculates the Tau-U index with baseline trend correction (Parker, Vannest, Davis, & Sauber 2011).
Tau_U( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )Tau_U( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase" )
A_data |
vector of numeric data for A phase, sorted in order of session number. Missing values are dropped. |
B_data |
vector of numeric data for B phase. Missing values are dropped. |
condition |
vector identifying the treatment condition for each observation in the series. |
outcome |
vector of outcome data for the entire series. |
baseline_phase |
character string specifying which value of
|
intervention_phase |
character string specifying which value of
|
improvement |
character string indicating direction of improvement. Default is "increase". |
Tau-U is an elaboration of the Tau that includes a
correction for baseline trend. It is calculated as Kendall's S statistic
for the comparison between the phase B data and the phase A data, plus
Kendall's S statistic for the A phase observations, scaled by the product
of the number of observations in each phase.
Note that A_data must be ordered by session number.
Numeric value
Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42(2), 284–299. doi:doi:10.1016/j.beth.2010.08.006
A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) Tau_U(A_data = A, B_data = B)A <- c(20, 20, 26, 25, 22, 23) B <- c(28, 25, 24, 27, 30, 30, 29) Tau_U(A_data = A, B_data = B)
Data from an ABAB design conducted by Thorne and Kamps (2008). These data were used as an example in Swan and Pustejovsky (2017). Academic engagement was collected via continuous recording (marked as "other") and inappropriate verbalizations were collected via event counting (marked as "count"). The variables are as follows:
Measure. Outcome measure description (academic engagement or inappropriate verbalizations).
Case. Participant identifier.
Session_number. Measurement occasion.
Outcome. Outcome scores
Trt. Treatment indicators.
Session_length. Length of the observation session.
Measure. The metric in which the outcome measurement is expressed (count or other).
A data frame with 776 rows and 5 variables
Thorne, S., & Kamps, D. (2008). The effects of a group contingency intervention on academic engagement and problem behavior of at-risk students. Behavior Analysis in Practice, 1(2), 12-18.
Swan, D. M., & Pustejovsky, J. E. (2017). A gradual effects model for single-case designs. http://doi.org/10.17605/OSF.IO/GAXRV
Data from a multiple baseline design conducted by Wright and McCathren (2012), which evaluated the effects of two types of social story interventions (a basic social story and a modified social story) on the behavior of four children with autism. Both dependent variables were measured using frequency counting for 10 minute observation sessions. The variables are as follows:
Participant Participant identifier.
Session Session number.
Condition Phase of the design (baseline, intervention A, or intervention B.
Problem_behavior Outcome scores.
A data frame with 97 rows and 5 variables
Wright, L. A., & McCathren, R. B. (2012). Utilizing social stories to increase prosocial behavior and reduce problem behavior in young children with autism. Child Development Research, 2012, 1-13. doi:10.1155/2012/357291