This is problem set #2, in which we hope you will practice the packages tidyr and dplyr. Along with the tutorial we used in class, there are some great cheat sheets from RStudio.

The data set

This data set comes from a replication of Janiszewski and Uy (2008), who investigated whether the precision of the anchor for a price influences the amount of adjustment. (We use these data briefly in the tutorial).

In the data frame, the Input.condition variable represents the experimental condition (under the rounded anchor, the rounded anchor, over the rounded anchor). Input.price1, Input.price2, and Input.price3 are the anchors for the Answer.dog_cost, Answer.plasma_cost, and Answer.sushi_cost items.

Part 1: Making these data tidy

Load the tidyverse package and the data

library(tidyverse)

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

## Warning: package 'tidyr' was built under R version 3.4.2

## Warning: package 'dplyr' was built under R version 3.4.2

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

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

d <- read.csv("data/janiszewski_rep_cleaned.csv")

This data frame is in wide format - that means that each row is a participant and there are multiple observations per participant. This data is not tidy.

To make this data tidy, we’ll do some cleanup. First, remove the columns you don’t need, using the verb select.

HINT: ?select and the examples of helper functions will help you be efficient.

d.tidy <- d %>%
  select(WorkerId, Input.condition, starts_with("Answer"))

Try renaming some variables using rename. A good naming scheme is:

consistent with case
consistent with “.” or “_" ( “_" is usually preferred)
concise as will be comprehensible to others

Try using the %>% operator as well. So you will be “piping” d %>% rename(...).

d.tidy <- d.tidy %>%
  rename(workerid = WorkerId,
         condition = Input.condition,
         dog = Answer.dog_cost,
         plasma = Answer.plasma_cost,
         sushi = Answer.sushi_cost)

OK, now for the tricky part. Use the verb gather to turn this into a tidy data frame.

HINT: look for online examples!

d.tidy <- d.tidy %>%
  gather(item, bet, dog, plasma, sushi)

Now spread these data back into a wide format data frame.

d.wide <- d.tidy %>%
  spread(item, bet)

Part 2: Manipulating the data

NOTE: If you generally use plyr package, note that they do not play nicely together so things like the rename function won’t work unless you load dplyr after plyr.

As we said in class, a good thing to do is always to check histograms of the response variable. Do that now, using either regular base graphics (hist) or ggplot. What can you conclude?

ggplot(d.tidy, aes(x = bet) )  + 
  geom_histogram(bins = 10) + 
  facet_grid(. ~ item, scales="free_x")

## Warning: Removed 1 rows containing non-finite values (stat_bin).

OK, now we turn to the actual data anlysis. We’ll be using dplyr verbs to filter, group,mutate, and summarise the data.

Start by using summarise to compute the grand mean bet. (Note that this is the same as taking the grant mean - the value will come later. Right now we’re just learning the syntax of that verb.)

d.tidy %>% 
  summarise(bet = mean(bet, na.rm=TRUE)) %>%
  knitr::kable(digits = 2)

bet
2022.56

This is a great time to get comfortable with the %>% operator. In brief, %>% allows you to pipe data from one function to another. So if you would have written:

d <- function(d, other_stuff)

you can now write:

d <- d %>% function(other_stufF)

That doesn’t seem like much, but it’s cool when you can replace:

d <- function1(d, other_stuff) d <- function2(d, lots_of_other_stuff, more_stuff) d <- function3(d, yet_more_stuff)

with

d <- d %>% function1(other_stuff) %>% function2(lots_of_other_stuff, more_stuff) %>% function3(yet_more_stuff)

In other words, you get to make a clean list of the things you want to do and chain them together without a lot of intermediate assignments.

Let’s use that capacity to combine summarise with group_by, which allows us to break up our summary into groups. Try grouping by item and condition and taking means using summarise, chaining these two verbs with %>%.

d.tidy %>% 
  group_by(item, condition) %>%
  summarise(bet = mean(bet, na.rm=TRUE)) %>%
  knitr::kable(digits = 2)

item	condition	bet
dog	over	1898.30
dog	rounded	1884.48
dog	under	1906.96
plasma	over	4300.33
plasma	rounded	4091.66
plasma	under	4018.36
sushi	over	8.32
sushi	rounded	7.96
sushi	under	7.74

Are there condition differences?

Perhaps, but there are obvious item-to-item variations that swamp the condition differences.

How are we going to plot condition differences? They are fundamentally different magnitudes from one another. Really we need the size of the deviation from the anchor, which means we need the anchor value. Let’s go back to the data and add that in.

Take a look at these two complex piped expression.s You don’t have to modify it, but see what is being done here with gather, separate and spread. Run each part (e.g. the first verb, the first two verbs, etc.) and after doing each, look at head(d.tidy) to see what they do.

# clean up 
d.tidy <- d %>% 
  select(WorkerId, Input.condition, 
         starts_with("Answer"), 
         starts_with("Input")) %>%
  rename(workerid = WorkerId,
         condition = Input.condition,          
         plasma_anchor = Input.price1,
         dog_anchor = Input.price2,
         sushi_anchor = Input.price3,
         dog_cost = Answer.dog_cost,
         plasma_cost = Answer.plasma_cost, 
         sushi_cost = Answer.sushi_cost) 

# now do the gathering and spreading
d.tidy <- d.tidy %>%
  gather(name, cost, 
         dog_anchor, plasma_anchor, sushi_anchor, 
         dog_cost, plasma_cost, sushi_cost) %>%
  separate(name, c("item", "type"), "_") %>%
  spread(type, cost)

Now we can do the same thing as before but look at the relative difference between anchor and estimate. Let’s do this two ways:

By computing absolute percentage change in price, and
By computing \(z\)-scores over items. (\(z\)-scores are standard scores where you subtract the mean and divide by the standard deviation. They’re a useful way of standardizing data).

To do the first, use the mutate verb to add a percent change column, then comute the same summary as before.

pcts <- d.tidy %>% 
  mutate(pct_change = abs((anchor - cost) / anchor)) %>%
  group_by(item, condition) %>%
  summarise(pct = mean(pct_change, na.rm=TRUE))

To do the second, you will need to group once by item, then to ungroup and do the same thing as before. NOTE: you can use group_by(…, add=FALSE) to set new grouping levels, also.

HINT: scale(x) returns a complicated data structure that doesn’t play nicely with dplyr. try scale(x)[,1] to get what you need.

z.scores <- d.tidy %>% 
  group_by(item) %>%
  mutate(z = scale(anchor - cost)[,1]) %>%
  group_by(item, condition, add=FALSE) %>%
  summarise(z = mean(z, na.rm=TRUE))

OK, now here comes the end: we’re going to plot the differences and see if anything happened. First the percent change:

ggplot(pcts, aes(x = item, y = pct, fill=condition)) + 
  geom_bar(position="dodge", stat="identity")

and the \(z\)-scores:

ggplot(z.scores, aes(x = item, y = z, fill=condition)) + 
  geom_bar(position="dodge", stat="identity")

What do you you see in this replication?

We didn’t see a straightforward replication of the predicted effect.

Psych 251 Problem Set #2

Mike Frank

October 9, 2017

The data set

Part 1: Making these data tidy

Part 2: Manipulating the data

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