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).
$$se = sd * \sqrt{(1 - reliability)}$$
$$sdiff = \sqrt{(2 * se^2)}$$
$$reliable change value = 1.96 * sdiff$$

## 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
#>
```