data("ds_iat", package = "splithalfr")
?ds_iat

Relevant variables

The columns used in this example are:

• participation_id, which identifies participants
• block_type, which specifies IAT blocks relevant to calculate the d-score
• attempt, in order to add RTs for trials
• response, in order to select correct responses only
• rt, in order to drop RTs outside of the range [200, 520] and calculate means per level of patt
• cat, which is the category each stimulus belonged to

Preprocessing

The improved d-score algorithm specifies that participants whose RTs for over 10% of reponses are below 300 ms should be dropped. The R-script below identifies such participants.

ds_summary <- ds_iat %>%
  dplyr::group_by(participation_id) %>%
  dplyr::summarize(
    too_fast = sum(rt < 300) / dplyr::n() > 0.1,
  )

One participant (participation_id 29) meets this exclusion criterion. Below, we remove this participant from the dataset.

ds_iat <- ds_iat[
  !(ds_iat$participation_id %in% 
  ds_summary[ds_summary$too_fast,]$participation_id), 
]

Next, delete any attempts with RTs > 10,000 ms. These do not exist in this IAT because a response window of 1500 ms was used, but the R-script is still added below for demonstration purposes.

ds_iat <- ds_iat[ds_iat$rt <= 10000, ]

Keep only data from the combination blocks.

ds_iat <- ds_iat[
  ds_iat$block_type %in% 
  c("tar1att1_1", "tar1att2_1", "tar1att1_2", "tar1att2_2"),
]

Finally, RTs for each participant, block, and trial are summed. The block_type and cat variables are also included, since they are used in further processing steps below.

ds_iat <- ds_iat %>%
  dplyr::group_by(participation_id, block, trial) %>%
  summarise(
    block_type = first(block_type),
    cat = first(cat),
    rt = sum(rt)
  )

Counterbalancing

The variables block_type and cat were counterbalanced. Below we illustrate this for the first participant.

ds_1 <- subset(ds_iat, participation_id == 1)
table(ds_1$block_type, ds_1$cat)

Scoring function

The score function receives these four data frames from a single participant. For both the pair of practice and test blocks, the following ‘block score’ is calculated:

1. Mean RT of target 1 with attribute 1 is calculated
2. Mean RT of target 1 with attribute 2 is calculated
3. The difference in mean RTs of both blocks is divided by the inclusive standard deviation (SD)

The d-score is the mean of the block scores for practice and test blocks.

fn_score <- function(ds) {
  fn_block <- function(ds_tar1att1, ds_tar1att2) {
    m_tar1att1 <- mean(ds_tar1att1$rt)
    m_tar1att2 <- mean(ds_tar1att2$rt)
    inclusive_sd <- sd(c(ds_tar1att1$rt, ds_tar1att2$rt))
    return ((m_tar1att2 - m_tar1att1) / inclusive_sd)
  }      
  d1 <- fn_block(
    ds[ds$block_type == "tar1att1_1", ],
    ds[ds$block_type == "tar1att2_1", ]
  )
  d2 <- fn_block(
    ds[ds$block_type == "tar1att1_2", ],
    ds[ds$block_type == "tar1att2_2", ]
  )
  return (mean(c(d1, d2)))
}

Scoring a single participant

Let’s calculate the IAT score for the participant with UserID 1. NB - This score has also been calculated manually via Excel in the splithalfr repository.

fn_score(subset(ds_iat, participation_id == 1))

Scoring all participants

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

scores <- by(
  ds_iat,
  ds_iat$participation_id,
  fn_score
)
data.frame(
  participation_id = names(scores),
  score = as.vector(scores)
)

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 block_type and cat were counterbalanced in the IAT 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:

• participant, which identifies participants
• replication, which counts replications
• score_1 and score_2, which are the scores calculated for each of the split datasets

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(
  ds_iat,
  ds_iat$participation_id,
  fn_score,
  replications = 1000,
  stratification = paste(ds_iat$block_type, ds_iat$cat)
)

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
hist(coefs)
# Mean of coefficients
mean(coefs)
# Confidence interval of coefficients
split_ci(split_scores, spearman_brown)