Define cut-off value for first SG criterion — define_crit1

Define a cut-off value for the first sudden gains criterion based on the Reliable Change Index (RCI; Jacobson & Truax, 1991) using an estimate for the standard deviation (sd) of the normal population and the reliability of the scale. These values can be entered manually using the arguments sd and reliability or extracted from data using the arguments data_sd and data_reliability. This function calculates the standard error of measurement (se), the standard error of the difference (sdiff) and a value that classifies as reliable change (reliable_change_value) based on the Reliable Change Index (RCI; Jacobson & Truax, 1991). $$se = sd * \sqrt{(1 - reliability)}$$ $$sdiff = \sqrt{(2 * se^2)}$$ $$reliable change value = 1.96 * sdiff$$

Usage

define_crit1_cutoff(
  sd = NULL,
  reliability = NULL,
  data_sd = NULL,
  data_reliability = NULL
)

Arguments

sd: Numeric, standard deviation of normal population or standard deviation at baseline. This argument is not needed if a vector with pretreatment scores is specified in the data_sd argument.
reliability: Numeric, between 0 and 1 indicating reliability of the scale. This argument is not needed if item-by-item data is specified in the data_reliability argument.
data_sd: A vector with pretreatment values. This argument is not needed if the standard deviation is specified in the sd argument.
data_reliability: A dataset in wide format (one row for each individual and one column for each item) including only the item-by-item scores of the SG measure (no ID variable). According to Jacobson & Truax (1991) the test-retest reliability should be used. Martinovich et al. (1996) suggest that the internal consistency (Cronbach's alpha) can be used instead of the test-retest reliability and may be more appropriate for estimating the standard error in some cases. This argument is not needed if the reliability is specified in the reliability argument.

Value

A list with estimates the for standard error of measurement (se), the standard error of the difference (sdiff) and a value that classifies as reliable change (reliable_change_value).

References

Jacobson, N. S., & Truax, P. A. (1991). Clinical significance: A statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59 (1), 12-19. doi:10.1037/0022-006X.59.1.12 .

Martinovich, Z., Saunders, S., & Howard, K. (1996). Some Comments on “Assessing Clinical Significance”. Psychotherapy Research, 6(2), 124–132. doi:10.1080/10503309612331331648 .

Stiles et al. (2003). Early sudden gains in psychotherapy under routine clinic conditions: Practice-based evidence. Journal of Consulting and Clinical Psychology, 71 (1), 14-21. doi:10.1037/0022-006X.71.1.14 .

Examples

# Define cut-off value for first SG criterion
# In this example the standard deviation and the reliability are specified manually
define_crit1_cutoff(sd = 10.5,
                    reliability = 0.931)
#> The reliability of the measure used to identify sudden gains was specified in the arguement 'reliability = 0.931'.
#> $sd
#> [1] 10.5
#> 
#> $reliability
#> [1] 0.931
#> 
#> $standard_error_measurement
#> [1] 2.758124
#> 
#> $standard_error_difference
#> [1] 3.900577
#> 
#> $reliable_change_value
#> [1] 7.645131
#> 

# In this example the reliability is specified manually
# The standard deviation of the variable "bdi_s0" in the dataset "sgdata" gets calculated
define_crit1_cutoff(data_sd = sgdata$bdi_s0,
                    reliability = 0.931)
#> The reliability of the measure used to identify sudden gains was specified in the arguement 'reliability = 0.931'.
#> $sd
#> [1] 6.396073
#> 
#> $reliability
#> [1] 0.931
#> 
#> $standard_error_measurement
#> [1] 1.680111
#> 
#> $standard_error_difference
#> [1] 2.376036
#> 
#> $reliable_change_value
#> [1] 4.65703
#>