# IAT D-Score Repeat Incorrect Responses

    library(splithalfr)
    library(dplyr)

This vignette describes a scoring method introduced by Greenwald, Nosek, and Banaji (2003); the improved d-score for Implicit Association Task (IATs) that require a correct response in order to continue to the next trial. This version of the d-score algorithm adds up all response times of all responses per trial. As this algorithm also specifies which participants to keep and to drop, functions from the dplyr package will be used to produce relevant summary statistics. Note that this vignette is more advanced that the others included in the `splithalfr` package, so it is not recommended as a first introduction on to how to use the splithalfr.

# Dataset

Load the included IAT dataset and inspect its documentation.

    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 the IAT

## 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)
    )

# 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 `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, for instance via a simple `mean`.

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

## Calculating bootstrapped confidence intervals for population reliability coefficient

Finally, we can estimate the Calculate bootstrapped confidence intervals for the value of the reliability coefficient in the population by bootstrapping participants. For this, we’ll need to repeatedly sample participants from the population, calculate a collection of reliability coefficients between the split scores of that sample of participants, and average those coefficients together. Hence, the call to `split_ci` below, takes (1) the split scores produced by calling `by_split` (`split_scores`), (2) the reliability coefficient we used above (`spearman_brown`), and (3) the method for averaging coefficients we used above (`mean`).

The bootstrap can take even longer than the split, and doesn’t show any progress bar, but it also uses all available CPU cores by default.

    # Conduct a bootstrap (of participants)
    bootstrap_result <- split_ci(split_scores, spearman_brown, mean)
    # Report confidence intervals
    library(boot)
    print(boot.ci(bootstrap_result, type="bca"))