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.

Load the included IAT dataset and inspect its documentation.

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

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

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)
)
```

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)
```

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:

- Mean RT of target 1 with attribute 1 is calculated
- Mean RT of target 1 with attribute 2 is calculated
- 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)))
}
```

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))`

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)
)
```

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)
)
```

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)
```