Intro

library(tidyverse)

## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr

## Conflicts with tidy packages ----------------------------------------------

## filter(): dplyr, stats
## lag():    dplyr, stats

library(ggthemes)
theme_set(theme_few())
sem <- function(x) {sd(x, na.rm=TRUE) / sqrt(sum(!is.na((x))))}
ci <- function(x) {sem(x) * 1.96} # reasonable approximation

This is problem set #4, in which we hope you will practice the visualization package ggplot2, as well as hone your knowledge of the packages tidyr and dplyr. You’ll look at two different datasets here.

First, data on children’s looking at social targets from Frank, Vul, Saxe (2011, Infancy).

Second, data from Sklar et al. (2012) on the unconscious processing of arithmetic stimuli.

In both of these cases, the goal is to poke around the data and make some plots to reveal the structure of the dataset.

Part 1

This part is a warmup, it should be relatively straightforward ggplot2 practice.

Load data from Frank, Vul, Saxe (2011, Infancy), a study in which we measured infants’ looking to hands in moving scenes. There were infants from 3 months all the way to about two years, and there were two movie conditions (Faces_Medium, in which kids played on a white background, and Faces_Plus, in which the backgrounds were more complex and the people in the videos were both kids and adults). An eye-tracker measured children’s attention to faces. This version of the dataset only gives two conditions and only shows the amount of looking at hands (other variables were measured as well).

fvs <- read_csv("data/FVS2011-hands.csv")

## Parsed with column specification:
## cols(
##   subid = col_integer(),
##   age = col_double(),
##   condition = col_character(),
##   hand.look = col_double()
## )

First, use ggplot to plot a histogram of the ages of children in the study. NOTE: this is a repeated measures design, so you can’t just take a histogram of every measurement.

#Because this is a repeated measure design, let's first spread the data.
fvs2 <- spread(fvs, condition, hand.look)

ggplot(fvs2, aes(x=age)) +
  geom_histogram(binwidth=.5, colour="black", fill="blue") + 
  geom_vline(aes(xintercept=mean(age, na.rm=T)), color="red", linetype="dashed", size=1)

#Histogram with a red v-line for the mean age (months)

Second, make a scatter plot showing the difference in hand looking by age and condition. Add appropriate smoothing lines. Take the time to fix the axis labels and make the plot look nice.

ggplot(fvs, aes(x=age, y=hand.look, color=condition))+
  geom_point() +
  geom_smooth(method=lm, se=FALSE, fullrange=TRUE) +
  labs(title="Looking Time by Age and Condition",
       x="Age (months)", y = "Looking Time (sec)")

What do you conclude from this pattern of data?

Children younger than 10 months do not show differences in looking time between conditions - they spend <0.1 seconds on both both faces_medium and faces_plus conditions.

With increasing age, children spend more time viewing the faces_plus condition, compared to the faces_medium condition.

What statistical analyses would you perform here to quantify these differences?

You could use a linear model in which looking time is the outcome variable and both age and condition are predictor variables. It looks like there would be a significant effect of age on looking time and an interaction effect between condition and age.

Part 2

Sklar et al. (2012) claim evidence for unconscious arithmetic processing - they prime participants with arithmetic problems and claim that the authors are faster to repeat the answers. We’re going to do a reanalysis of their Experiment 6, which is the primary piece of evidence for that claim. The dataare generously shared by Asael Sklar. (You may recall these data from the tidyverse tutorial earlier in the quarter).

Data Prep

First read in two data files and subject info. A and B refer to different trial order counterbalances.

subinfo <- read_csv("data/sklar_expt6_subinfo_corrected.csv")

## Parsed with column specification:
## cols(
##   subid = col_integer(),
##   presentation.time = col_integer(),
##   subjective.test = col_integer(),
##   objective.test = col_double()
## )

d_a <- read_csv("data/sklar_expt6a_corrected.csv")

## Parsed with column specification:
## cols(
##   .default = col_integer(),
##   prime = col_character(),
##   congruent = col_character(),
##   operand = col_character()
## )

## See spec(...) for full column specifications.

d_b <- read_csv("data/sklar_expt6b_corrected.csv")

## Parsed with column specification:
## cols(
##   .default = col_integer(),
##   prime = col_character(),
##   congruent = col_character(),
##   operand = col_character()
## )
## See spec(...) for full column specifications.

gather these datasets into long (“tidy data”) form. If you need to review tidying, here’s the link to R4DS (bookmark it!). Remember that you can use select_helpers to help in your gathering.

Once you’ve tidied, bind all the data together. Check out bind_rows.

The resulting tidy dataset should look like this:

    prime prime.result target congruent operand distance counterbalance subid    rt
    <chr>        <int>  <int>     <chr>   <chr>    <int>          <int> <dbl> <int>
 1 =1+2+5            8      9        no       A       -1              1     1   597
 2 =1+3+5            9     11        no       A       -2              1     1   699
 3 =1+4+3            8     12        no       A       -4              1     1   700
 4 =1+6+3           10     12        no       A       -2              1     1   628
 5 =1+9+2           12     11        no       A        1              1     1   768
 6 =1+9+3           13     12        no       A        1              1     1   595

#tidy df a:
d_a2 <- d_a %>%
  gather("subid", "rt", 8:28)

#tidy df b:
d_b2 <- d_b %>%
  gather("subid", "rt", 8:28)

#bind the two dataframes together:
d_ab <- bind_rows(d_a2, d_b2)

Merge these with subject info. You will need to look into merge and its relatives, left_ and right_join. Call this dataframe d, by convention.

#Let's first make subject id a factor in both dataframes
d_ab$subid <- as.factor(d_ab$subid)
subinfo$subid <- as.factor(subinfo$subid)

#Now we can left join the data into a new DF called 'd' 
d <- left_join(d_ab, subinfo)

## Joining, by = "subid"

## Warning: Column `subid` joining factors with different levels, coercing to
## character vector

Clean up the factor structure (just to make life easier). No need to, but if you want, you can make this more tidyverse-ish.

d$presentation.time <- factor(d$presentation.time)
levels(d$operand) <- c("addition","subtraction")

Data Analysis Preliminaries

Examine the basic properties of the dataset. First, show a histogram of reaction times.

ggplot(d, aes(x=rt)) +
  geom_histogram(binwidth=.5, colour="black", fill="blue")

## Warning: Removed 237 rows containing non-finite values (stat_bin).

dd = d[(order(-d$rt) & !(is.na(d$rt))), ]
L = c()
for (i in 1:nrow(dd)){
  L = rbind(L, dd$rt[i]-dd$rt[i+1])
}

L = L[L!=0]
min(L, na.rm = TRUE)

## [1] -1601

ggplot(as.data.frame(L), aes(x=L)) +
  geom_histogram(binwidth=0.1, colour="black", fill="blue")+
  xlim(10, 120) + ylim(0, 60)

## Warning: Removed 4278 rows containing non-finite values (stat_bin).

## Warning: Removed 11 rows containing missing values (geom_bar).

Challenge question: what is the sample rate of the input device they are using to gather RTs?

I sorted the reaction times by thier value and then wrote a four loop that created a new vector, L, containing the difference between each reaction time and the following reaction time. I then removed any differences equal to 0, or identical reaction times.

Then I plotted a histogram of L. Based on the histogram, it looks like there are reactions recorded ever 1/3rd of a second. As sample rate is measured in Hrz, I can divide 1/0.333 sec to find the sample rate of the input device.

The sample rate of the input device they are using is 30Hrz!

Sklar et al. did two manipulation checks. Subjective - asking participants whether they saw the primes - and objective - asking them to report the parity of the primes (even or odd) to find out if they could actually read the primes when they tried. Examine both the unconscious and conscious manipulation checks. What do you see? Are they related to one another?

cor(d$subjective.test, d$objective.test)

## [1] 0.5786542

ggplot(d, aes(subjective.test, objective.test)) +
  geom_boxplot(aes(group = cut_width(subjective.test, 0.5)))

The correlation between subjective test and objective test responses was 0.58, which suggests the two are related.

If a boxplot is drawn for the data, we can see that the mean objective test outcome is higher when subjects reported seeing the primes, and lower when subjects did not report seeing the primes.

In Experiments 6, 7, and 9, we used the binomial distribution to determine whether each participant performed better than chance on the objective block and excluded from analyses all those participants who did (21, 30, and 7 participants in Experiments 6, 7, and 9, respectively). Note that, although the number of excluded participants may seem high, they fall within the normal range of long-duration CFS priming, in which suc- cessful suppression is strongly affected by individual differences (38). We additionally excluded participants who reported any subjective awareness of the primes (four, five, and three participants in Experiments 6, 7, and 9, respectively).

OK, let’s turn back to the measure and implement Sklar et al.’s exclusion criterion. You need to have said you couldn’t see (subjective test) and also be not significantly above chance on the objective test (< .6 correct). Call your new data frame ds.

ds <- d %>% 
  filter(subjective.test==0 & objective.test<0.6)

Replicating Sklar et al.’s analysis

Sklar et al. show a plot of a “facilitation effect” - the amount faster you are for prime-congruent naming compared with prime-incongruent naming. They then show plot this difference score for the subtraction condition and for the two prime times they tested. Try to reproduce this analysis.

HINT: first take averages within subjects, then compute your error bars across participants, using the ci function (defined above). Sklar et al. use SEM (and do it incorectly, actually), but CI is more useful for “inference by eye” as discussed in class.

HINT 2: remember that in class, we reviewed the common need to group_by and summarise twice, the first time to get means for each subject, the second time to compute statistics across subjects.

HINT 3: The final summary dataset should have 4 rows and 5 columns (2 columns for the two conditions and 3 columns for the outcome: reaction time, ci, and n).

means <- ds %>% 
  group_by(operand, presentation.time, subid, congruent) %>%
  summarise(avg_rt=mean(rt, na.rm=TRUE)) %>%
  spread(congruent, avg_rt) %>%
  mutate(difference = no - yes) %>%
  filter(operand=="S") %>%
  group_by(presentation.time, operand) %>%
  summarise(fac_effect=mean(difference), ci=ci(difference))

Now plot this summary, giving more or less the bar plot that Sklar et al. gave (though I would keep operation as a variable here. Make sure you get some error bars on there (e.g. geom_errorbar or geom_linerange).

ggplot(means, aes(x=presentation.time, y=fac_effect))+
  geom_bar(stat="identity") +
  geom_errorbar(aes(ymin=fac_effect-ci, ymax=fac_effect+ci), width=0.2)+
  labs(title="Facilitation Effect by Presentation Time in Subtraction Trials",
       x="Presentation Time", y = "Facilitation Effect")

What do you see here? How close is it to what Sklar et al. report? How do you interpret these data?

Based on the figure (2a) in the Sklar et al., paper, it looks as if the same values were obtained for the facilitation effect accross the two presentation time conditions. However, the error bars are quite different - suggesting a significant effect in the Sklar paper and a non-significant effect in the replication, as indicated by the overlapping error bars in this report.

Problem Set 4: Exploratory Data Analysis

Sean Zion