AAT - Double Difference of Medians


This vignette describes a scoring method similar to Heuer, Rinck, and Becker (2007); double difference of median reaction times (RTs) for correct responses on Approach Avoidance Task data. It is a subtraction comparing approach bias towards test stimuli relative to approach bias towards control stimuli (avoid_test - approach_test) - (avoid_control - approach_control).


Load the included AAT dataset and inspect its documentation.

data("ds_aat", package = "splithalfr")

Relevant variables

The columns used in this example are:


Only select trials from assessment blocks.

ds_aat <- subset(ds_aat, block_type == "assess")


The variables appr and stim were counterbalanced. Below we illustrate this for the first participant.

ds_1 <- subset(ds_aat, UserID == 1)
table(ds_1$appr, ds_1$stim)

Scoring the AAT

Scoring function

The scoring function calculates the score of a single participant as follows:

  1. selects only correct responses
  2. calculates the median RT of remaining responses
fn_score <- function (ds) {
  median_avoid_test <- median(
    ds[ds$appr == "no" & ds$cat == "test" & ds$response == 1, ]$rt
  median_approach_test <- median(
    ds[ds$appr == "yes" & ds$cat == "test" & ds$response == 1, ]$rt
  median_avoid_control <- median(
    ds[ds$appr == "no" & ds$cat == "control" & ds$response == 1, ]$rt
  median_approach_control <- median(
    ds[ds$appr == "yes" & ds$cat == "control" & ds$response == 1, ]$rt
  return (
    (median_avoid_test - median_approach_test) - 
    (median_avoid_control - median_approach_control)

Scoring a single participant

Let’s calculate the AAT score for the participant with UserID 14. NB - This score has also been calculated manually via Excel in the splithalfr repository.

fn_score(subset(ds_aat, UserID == 14))

Scoring all participants

To calculate the AAT score for each participant, we will use R’s native by function and convert the result to a data frame.

scores <- by(
  UserID = names(scores),
  score = as.vector(scores)

Estimating split-half reliability

Calculating split scores

To calculate split-half scores for each participant, use the function by_split. The first three arguments of this function are the same as for by. An additional set of arguments allow you to specify how to split the data and how often. In this vignette we will calculate scores of 1000 permutated splits. The trial properties app and stim were counterbalanced in the AAT design. We will stratify splits by these trial properties. See the vignette on splitting methods for more ways to split the data.

The by_split function returns a data frame with the following columns:

Calculating the split scores may take a while. By default, by_split uses all available CPU cores, but no progress bar is displayed. Setting ncores = 1 will display a progress bar, but processing will be slower.

split_scores <- by_split(
  replications = 1000,
  stratification = paste(ds_aat$app, ds_aat$stim)

Calculating reliability coefficients

Next, the output of by_split can be analyzed in order to estimate reliability. By default, functions are provided that calculate Spearman-Brown adjusted Pearson correlations (spearman_brown), Flanagan-Rulon (flanagan_rulon), Angoff-Feldt (angoff_feldt), and Intraclass Correlation (short_icc) coefficients. Each of these coefficient functions can be used with split_coef to calculate the corresponding coefficients per split, which can then be plotted or averaged via a simple mean. A bias-corrected and accelerated bootstrap confidence interval can be calculated via split_ci. Note that estimating the confidence interval involves very intensive calculations, so it can take a long time to complete.

# Spearman-Brown adjusted Pearson correlations per replication
coefs <- split_coefs(split_scores, spearman_brown)
# Distribution of coefficients
# Mean of coefficients
# Confidence interval of coefficients
split_ci(split_scores, spearman_brown)