2AFC Memory Task

• In this memory task, participants are, for example, asked the following:

  • Which of the following two words did you see?
    • Table (old-studied) or Chair (new-not studied)

• In this memory task there are two possible outcomes:

  • hit (H) = recognizing studied item
  • False alarm (FA) = recognizing non studied item

Dataset

• First, I will create a dataset for this type of memory task with
  • 30 questions
  • hits with a mean of 2 and a sd of 2.5
  • false alarm with a mean of 10 and sd of 2.5

# Create variable.
set.seed(2794) #  this is too make sure the results stay the same.
participants <- seq(1,100,1) # This creates a column with 100 participants
hit   <- c(round(c(rnorm(100,20,2.5))))#  this creates a random number of hits that are normally distributed with a mean of 20 and standard deviation of 2.5
FA    <- 30-hit # this create a column with the false alarm rates. 
#put together in dataframe(df)
df <- data.frame(participants, hit,FA)
head(df) #  to show the first 5 participants

  participants hit FA
1            1  23  7
2            2  18 12
3            3  21  9
4            4  21  9
5            5  19 11
6            6  17 13

Analyzable Statistics

• I will show the common statistics that can be calculated based on this type of dataset.

• Hit rate - Rate of choosing the old item out of all items

Click here for source of formula

hit_rate <- df$hit/(df$hit+df$FA) # this will give the hit rate for each participant
cat(paste("The hit rate is",format(round(mean(hit_rate),2)))) # The function mean turns the hit rate into the mean for the group

The hit rate is 0.65

• False Alarm Rate (FAR) - Rate of choosing the new item out of all items

$$ False \ alarm \ rate = \frac{FA}{FA + H} $$ Click here for source of formula

FA_rate <- df$FA/(df$hit+df$FA) # this will give the FA rate for each participant
cat(paste("The false alarm rate is",format(round(mean(FA_rate),2))))

The false alarm rate is 0.35

Corrected hit rate

It is possible to calculate a corrected hit rate. However, this depends on several assumptions. For more information see supplementary information of Brady et al., 2008

Sensitivity d'

It is possible to calculate or look up the sensitivity d’ from the percentage correct. However, this depends on several assumptions. Click here for formula and table