Reliable Change Index (RCI)

Reliable Change Index (RCI)#

The rci function calculates the Reliable Change Index (RCI) for single-case data. It provides a statistical assessment of whether the change between two phases (typically A and B) is statistically reliable, considering measurement error and reliability.

Function Overview#

The rci function computes the RCI for a single-case dataset. It prints descriptive statistics, confidence intervals, and RCI values for the specified phases.

Arguments#

  • data: DataFrame containing SCED data (single case only).

  • dvar: Name of the dependent variable column (default: “values”).

  • pvar: Name of the phase variable column (default: “phase”).

  • rel: Reliability of the measurement (default: 0.8).

  • ci: Confidence level (default: 0.95).

  • graph: Whether to display a graph of confidence intervals (default: False).

  • phases: Tuple of phases to include (default: (“A”, “B”)).

The function prints all results directly and does not return a value.

import scia as sc

📖 scia 1.101.0.dev6 - For Documentation, visit: https://ahsankhodami.github.io/scia/intro.html

Example 1: Single-Case RCI Calculation#

# Create a single-case AB design
df = sc.create_scd(
    values=[5, 7, 8, 5, 7, 12, 16, 18, 15, 14, 19],
    phase_starts={"A": 1, "B": 6}
)

# Compute and print RCI
sc.rci(df)

Reliable Change Index

Mean Difference = 9.267
Standardized Difference = 1.768
Standard error of differences = 0.849
Reliability of measurements = 0.8

Descriptives:
         n       mean        SD        SE
A-Phase  5   6.400000  1.341641  0.600000
B-Phase  6  15.666667  2.581989  1.154701

95% Confidence Intervals:
             Lower      Upper
A-Phase   5.217270   7.582730
B-Phase  13.390501  17.942832

Reliable Change Indices:
                               RCI
Jacobson et al.          15.444444
Christensen and Mendoza  10.920871

Example 2: RCI for Each Case in a Multiple-Case Design#

The rci function is designed for single-case data. To use it with multiple cases, simply call it for each case in your list.

# Create multiple cases
charlotte_test = sc.create_scd(
    values={"A": [5, 7, 10, 5, 12], "B": [7, 10, 18, 15, 14, 19]},
    name="Charlotte",
    mt=list(range(11))
)

theresa_test = sc.create_scd(
    values={"A": [3, 4, 3, 5], "B": [7, 4, 7, 9, 8, 10, 12]},
    name="Theresa",
    mt=list(range(11))
)

antonia_test = sc.create_scd(
    values={"A": [9, 8, 8, 7, 5, 7], "B": [6, 14, 15, 12, 16]},
    name="Antonia",
    mt=list(range(11))
)

mbd_test = [charlotte_test, theresa_test, antonia_test]

# Compute and print RCI for each case
for case in mbd_test:
    print(f"\nCase: {case['case'].iloc[0]}")
    sc.rci(case)

Case: Charlotte
Reliable Change Index

Mean Difference = 6.033
Standardized Difference = 1.219
Standard error of differences = 1.970
Reliability of measurements = 0.8

Descriptives:
         n       mean        SD        SE
A-Phase  5   7.800000  3.114482  1.392839
B-Phase  6  13.833333  4.622409  2.067204

95% Confidence Intervals:
            Lower      Upper
A-Phase  5.067867  10.532133
B-Phase  9.778394  17.888273

Reliable Change Indices:
                              RCI
Jacobson et al.          4.331681
Christensen and Mendoza  3.062961

Case: Theresa
Reliable Change Index

Mean Difference = 4.393
Standardized Difference = 1.458
Standard error of differences = 0.606
Reliability of measurements = 0.8

Descriptives:
         n      mean        SD        SE
A-Phase  4  3.750000  0.957427  0.428174
B-Phase  7  8.142857  2.544836  1.138085

95% Confidence Intervals:
            Lower      Upper
A-Phase  2.909551   4.590449
B-Phase  5.908949  10.376765

Reliable Change Indices:
                               RCI
Jacobson et al.          10.259504
Christensen and Mendoza   7.254565

Case: Antonia
Reliable Change Index

Mean Difference = 5.267
Standardized Difference = 1.368
Standard error of differences = 0.864
Reliability of measurements = 0.8

Descriptives:
         n       mean        SD        SE
A-Phase  6   7.333333  1.366260  0.611010
B-Phase  5  12.600000  3.974921  1.777639

95% Confidence Intervals:
            Lower      Upper
A-Phase  6.087089   8.579577
B-Phase  8.974247  16.225753

Reliable Change Indices:
                              RCI
Jacobson et al.          8.619607
Christensen and Mendoza  6.094982
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