The frames data set comes from a simple experiment I ran a little while ago (it’s experiment two from this paper). What we were interested in was understanding how people use statistical information to guide inductive inferences. For example, suppose you observe a sample of “robins†that have “plaxium blood†(whatever that is). How likely is it that “sparrows†will possess plaxium blood? Or “cows� Does it matter how many robins you have seen? Does it matter whether you specifically selected robins and they turned out to have plaxium blood (category sampling) as opposed to detecting animals with plaxium blood that then turned out to all be robins (property sampling)? In that paper we had a computational model of inductive reasoning that made specific predictions about how the sample size (number of robins) and sampling method (property or category) would inflence people’s judgments.
In this particular experiment we didn’t show people animals (though we have done those too!) we just showed them small “alien rocks†called “sodor spheresâ€, and asked people to make guesses about new rocks of different sizes: test_loc values of 1 and 2 were very similar to the items they were shown during training, whereas value 7 was quite dissimilar. The number of training observations ranged from 2 (sample_size = “small”) to 12 (sample_size = “large”) and was varied within-subject. So everyone saw two observations, made some generalization judgments (response on a scale from 0 to 9), then saw more training observations and so on. Participants were randomly assigned to a “property” sampling condition or to a category sampling one. We also recorded age, gender, and assigned each person a unique id.
The variable key: - id: the participant id number - gender: male or female - age: numeric, in years - condition: (between subject). category sampling = people were told observations were selected on the basis of their category membership (e.g., because it’s a small bird, or a small rock, or whatever) vs property sampling = people were told observations were selected because of a property they posses (e.g., it has plaxium blood, or a plaxium coating). - sample_size: (within subject) small, medium, large - indicating how many observations they’d been shown at this point in the experiment - n_obs: (within subject). same as “sample_size”, but it’s the actual number (2, 6 or 12) - test_item: (within subject). what stimulus are they now being shown? numeric: 1 to 7. this is ordinal (or really, quasi-interval) where items 1-2 are essentially identical to observations they’d seen before, and 3-7 become progressively less similar (e.g., bigger bird, bigger rock, whatever…) - response: (the outcome, within subject). the rating the person gave (0-9 scale) for “how likely is it that this new stimulus possesses the property (e.g., plaxium blood)?” where 0 = not at all, 9 = certain (or something like that) There’s quite a bit going on in the data since it’s a two within-subject and one between-subject manipulation
Step 1 is making sure you have the packages:
library(here)
library(tidyverse)
library(janitor)
library(skimr)Step 2 is creating an RMarkdown document that will contain your analyses.
Step 3 is loading the data.
data_location <- here("analysis","data","frames_ex2.csv")
data_location## [1] "C:/Users/Dan/GitHub/sites/chdss2018/analysis/data/frames_ex2.csv"Then
frames <- read_csv(file = data_location)## Parsed with column specification:
## cols(
## id = col_integer(),
## gender = col_character(),
## age = col_integer(),
## condition = col_character(),
## sample_size = col_character(),
## n_obs = col_integer(),
## test_item = col_integer(),
## response = col_integer()
## )frames## # A tibble: 4,725 x 8
## id gender age condition sample_size n_obs test_item response
## <int> <chr> <int> <chr> <chr> <int> <int> <int>
## 1 1 male 36 category small 2 1 8
## 2 1 male 36 category small 2 2 7
## 3 1 male 36 category small 2 3 6
## 4 1 male 36 category small 2 4 6
## 5 1 male 36 category small 2 5 5
## 6 1 male 36 category small 2 6 6
## 7 1 male 36 category small 2 7 3
## 8 1 male 36 category medium 6 1 9
## 9 1 male 36 category medium 6 2 7
## 10 1 male 36 category medium 6 3 5
## # ... with 4,715 more rowsIt’s not a bad idea to take a quick glimpse() at the data:
glimpse(frames)## Observations: 4,725
## Variables: 8
## $ id <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
## $ gender <chr> "male", "male", "male", "male", "male", "male", "m...
## $ age <int> 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36...
## $ condition <chr> "category", "category", "category", "category", "c...
## $ sample_size <chr> "small", "small", "small", "small", "small", "smal...
## $ n_obs <int> 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 12, 12, ...
## $ test_item <int> 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3,...
## $ response <int> 8, 7, 6, 6, 5, 6, 3, 9, 7, 5, 6, 4, 4, 2, 8, 7, 6,...I’m also a fan of the skim() function for getting descriptive statistics quickly:
skim(frames)## Skim summary statistics
## n obs: 4725
## n variables: 8
##
## -- Variable type:character -----------------------------------------------------
## variable missing complete n min max empty n_unique
## condition 0 4725 4725 8 8 0 2
## gender 0 4725 4725 4 6 0 2
## sample_size 0 4725 4725 5 6 0 3
##
## -- Variable type:integer -------------------------------------------------------
## variable missing complete n mean sd p0 p25 p50 p75 p100 hist
## age 0 4725 4725 34.92 11.63 20 27 32 40 84 <U+2587><U+2587><U+2583><U+2582><U+2581><U+2581><U+2581><U+2581>
## id 0 4725 4725 113 64.96 1 57 113 169 225 <U+2587><U+2587><U+2587><U+2587><U+2587><U+2587><U+2587><U+2587>
## n_obs 0 4725 4725 6.67 4.11 2 2 6 12 12 <U+2587><U+2581><U+2581><U+2587><U+2581><U+2581><U+2581><U+2587>
## response 0 4725 4725 4.9 3.04 0 2 5 8 9 <U+2586><U+2582><U+2582><U+2583><U+2582><U+2582><U+2583><U+2587>
## test_item 0 4725 4725 4 2 1 2 4 6 7 <U+2587><U+2587><U+2587><U+2587><U+2581><U+2587><U+2587><U+2587>(Side note: the histograms in skim are text-based and rely on unicode characters. In some cases Windows does weird things and doesn’t display them - we’ll talk about data vis later)s
practical notes
Data wrangling in R used to be hard. Ever since the tidyverse family of packages appeared in a stable form, it’s become easy. However, it requires you to have a bit of a shift in mindset:
frames %>% skim(.)The key idea behind %>% is a bit of “magic”, in which the command is reorganised so that the “thing” on the left (i.e., frames) gets inserted into the expression on the right, replacing the .). So when you type the command above, it gets reorganised into this…
skim(frames)… and then this reorganised command is evaluated. Why is that useful? Well, imagine we have a series of operations we want to do, where the output of the first operation is fed (or “piped”) in as the input to the second, and so on. In piped code, it looks like this:
output <- frames %>%
do_thing1(.) %>%
do_thing2(.) %>%
do_thing3(.) %>%
do_thing4(.)In traditional code, it would look like this:
output <- do_thing4(
do_thing3(
do_thing2(
do_thing1(
frames
)
)
)
)which forces you to start reading in the middle and then upwards. It’s pretty uncomfortable to read as it is, and it gets much worse when each of your do_thing functions has additional arguments. So in practice we would write it like this,
a <- do_thing1(frames)
b <- do_thing2(a)
c <- do_thing3(b)
output <- do_thing4(c)which is a little nicer, but the a, b and c values are just dummy variables that we don’t actually want, so then you have to get rid of them. Piped code makes it much more readable, so from now on we’ll tend to work with pipes.
Averaging across subjects.
average_response <- frames %>%
group_by(test_item, sample_size, n_obs, condition) %>%
summarise(response = mean(response))Now let’s look
average_response## # A tibble: 42 x 5
## # Groups: test_item, sample_size, n_obs [?]
## test_item sample_size n_obs condition response
## <int> <chr> <int> <chr> <dbl>
## 1 1 large 12 category 7.60
## 2 1 large 12 property 7.16
## 3 1 medium 6 category 7.32
## 4 1 medium 6 property 6.66
## 5 1 small 2 category 6.07
## 6 1 small 2 property 5.78
## 7 2 large 12 category 7.51
## 8 2 large 12 property 7.20
## 9 2 medium 6 category 7.17
## 10 2 medium 6 property 6.95
## # ... with 32 more rowsWhat statistics can we calculate besides the mean?
frames %>%
group_by(test_item) %>%
summarise(
mean_resp = mean(response),
sd_resp = sd(response),
count = n()
)## # A tibble: 7 x 4
## test_item mean_resp sd_resp count
## <int> <dbl> <dbl> <int>
## 1 1 6.77 2.56 675
## 2 2 6.88 2.10 675
## 3 3 5.71 2.41 675
## 4 4 4.48 2.68 675
## 5 5 3.76 2.81 675
## 6 6 3.43 2.99 675
## 7 7 3.26 3.11 675dplyr (e.g., tally() and count() make it a bit less tedious to construct frequency tables)$ operator, you can use the pull() function)What if we want to include only some cases (e.g., the small sample size)? The filter() command:
average_response %>%
filter(sample_size == "small")## # A tibble: 14 x 5
## # Groups: test_item, sample_size, n_obs [7]
## test_item sample_size n_obs condition response
## <int> <chr> <int> <chr> <dbl>
## 1 1 small 2 category 6.07
## 2 1 small 2 property 5.78
## 3 2 small 2 category 6.26
## 4 2 small 2 property 6.21
## 5 3 small 2 category 5.87
## 6 3 small 2 property 5.24
## 7 4 small 2 category 5.11
## 8 4 small 2 property 4.68
## 9 5 small 2 category 4.55
## 10 5 small 2 property 3.99
## 11 6 small 2 category 4.16
## 12 6 small 2 property 3.68
## 13 7 small 2 category 3.98
## 14 7 small 2 property 3.67Hm, this is nice, but I’d prefer to have it sorted by condition rather than by test item. The arrange() function will do that:
average_response %>%
filter(sample_size == "small") %>%
arrange(condition)## # A tibble: 14 x 5
## # Groups: test_item, sample_size, n_obs [7]
## test_item sample_size n_obs condition response
## <int> <chr> <int> <chr> <dbl>
## 1 1 small 2 category 6.07
## 2 2 small 2 category 6.26
## 3 3 small 2 category 5.87
## 4 4 small 2 category 5.11
## 5 5 small 2 category 4.55
## 6 6 small 2 category 4.16
## 7 7 small 2 category 3.98
## 8 1 small 2 property 5.78
## 9 2 small 2 property 6.21
## 10 3 small 2 property 5.24
## 11 4 small 2 property 4.68
## 12 5 small 2 property 3.99
## 13 6 small 2 property 3.68
## 14 7 small 2 property 3.67Okay, but do we really need the sample size variables? Maybe I only want to select() the other three variables:
average_response %>%
filter(sample_size == "small") %>%
arrange(condition) %>%
select(test_item, condition, response)## Adding missing grouping variables: `sample_size`, `n_obs`## # A tibble: 14 x 5
## # Groups: test_item, sample_size, n_obs [7]
## sample_size n_obs test_item condition response
## <chr> <int> <int> <chr> <dbl>
## 1 small 2 1 category 6.07
## 2 small 2 2 category 6.26
## 3 small 2 3 category 5.87
## 4 small 2 4 category 5.11
## 5 small 2 5 category 4.55
## 6 small 2 6 category 4.16
## 7 small 2 7 category 3.98
## 8 small 2 1 property 5.78
## 9 small 2 2 property 6.21
## 10 small 2 3 property 5.24
## 11 small 2 4 property 4.68
## 12 small 2 5 property 3.99
## 13 small 2 6 property 3.68
## 14 small 2 7 property 3.67Wait why doesn’t that work? The dplyr package is pretty picky about grouping variables, and won’t let you drop them! Remember, to construct the average_response data set, we grouped the original frames data, and when we used group_by() to do this, R has retained some information about this grouping (hidden in an invisible attribute). So if you do want to get rid of this, you’ll need to ungroup() before you select(). So now this version does what we’re expecting:
average_response %>%
filter(sample_size == "small") %>%
arrange(condition) %>%
ungroup() %>%
select(test_item, condition, response)## # A tibble: 14 x 3
## test_item condition response
## <int> <chr> <dbl>
## 1 1 category 6.07
## 2 2 category 6.26
## 3 3 category 5.87
## 4 4 category 5.11
## 5 5 category 4.55
## 6 6 category 4.16
## 7 7 category 3.98
## 8 1 property 5.78
## 9 2 property 6.21
## 10 3 property 5.24
## 11 4 property 4.68
## 12 5 property 3.99
## 13 6 property 3.68
## 14 7 property 3.67At this point, our “chain” of piped operations is getting quite long, and maybe we’d like to save the output to a new variable!
average_response_small <- average_response %>%
filter(sample_size == "small") %>%
arrange(condition) %>%
ungroup() %>%
select(test_item, condition, response)The response data are on a 0 to 9 scale, but maybe it makes more sense to rescale so it to a “generalisation” value that ranges from 0 to 1. That’s a simple transformation (divide by 9), but how do we create a new variable inside the data frame? Enter mutate()
average_response_small <- average_response_small %>%
mutate(generalisation = response/9)Now:
average_response_small## # A tibble: 14 x 4
## test_item condition response generalisation
## <int> <chr> <dbl> <dbl>
## 1 1 category 6.07 0.674
## 2 2 category 6.26 0.696
## 3 3 category 5.87 0.652
## 4 4 category 5.11 0.568
## 5 5 category 4.55 0.506
## 6 6 category 4.16 0.462
## 7 7 category 3.98 0.442
## 8 1 property 5.78 0.643
## 9 2 property 6.21 0.690
## 10 3 property 5.24 0.583
## 11 4 property 4.68 0.521
## 12 5 property 3.99 0.443
## 13 6 property 3.68 0.409
## 14 7 property 3.67 0.407What if we want to have the two conditions as separate variables?
average_response_small %>%
spread(key = condition, value = generalisation)## # A tibble: 14 x 4
## test_item response category property
## <int> <dbl> <dbl> <dbl>
## 1 1 5.78 NA 0.643
## 2 1 6.07 0.674 NA
## 3 2 6.21 NA 0.690
## 4 2 6.26 0.696 NA
## 5 3 5.24 NA 0.583
## 6 3 5.87 0.652 NA
## 7 4 4.68 NA 0.521
## 8 4 5.11 0.568 NA
## 9 5 3.99 NA 0.443
## 10 5 4.55 0.506 NA
## 11 6 3.68 NA 0.409
## 12 6 4.16 0.462 NA
## 13 7 3.67 NA 0.407
## 14 7 3.98 0.442 NAWhy did that not work? Remember we still have response in the data, and there’s a unique value of response for everything. Gr. Okay, so let’s select out that one before spreading…
wide_avrs <- average_response_small %>%
select(-response) %>%
spread(key = condition, value = generalisation)
wide_avrs## # A tibble: 7 x 3
## test_item category property
## <int> <dbl> <dbl>
## 1 1 0.674 0.643
## 2 2 0.696 0.690
## 3 3 0.652 0.583
## 4 4 0.568 0.521
## 5 5 0.506 0.443
## 6 6 0.462 0.409
## 7 7 0.442 0.407Want to gather() it back into long form?
wide_avrs %>% gather(key = "condition", value = "generalisation", category, property)## # A tibble: 14 x 3
## test_item condition generalisation
## <int> <chr> <dbl>
## 1 1 category 0.674
## 2 2 category 0.696
## 3 3 category 0.652
## 4 4 category 0.568
## 5 5 category 0.506
## 6 6 category 0.462
## 7 7 category 0.442
## 8 1 property 0.643
## 9 2 property 0.690
## 10 3 property 0.583
## 11 4 property 0.521
## 12 5 property 0.443
## 13 6 property 0.409
## 14 7 property 0.407Exercise. Try spreading and gathering by test item rather than condition
frames %>%
group_by(test_item, sample_size, condition) %>%
summarise(response = mean(response)) %>%
spread(key = sample_size, value = response)## # A tibble: 14 x 5
## # Groups: test_item [7]
## test_item condition large medium small
## <int> <chr> <dbl> <dbl> <dbl>
## 1 1 category 7.60 7.32 6.07
## 2 1 property 7.16 6.66 5.78
## 3 2 category 7.51 7.17 6.26
## 4 2 property 7.20 6.95 6.21
## 5 3 category 6.39 5.98 5.87
## 6 3 property 5.23 5.49 5.24
## 7 4 category 5.39 4.97 5.11
## 8 4 property 3.07 3.56 4.68
## 9 5 category 4.72 4.22 4.55
## 10 5 property 2.26 2.75 3.99
## 11 6 category 4.43 3.85 4.16
## 12 6 property 1.91 2.50 3.68
## 13 7 category 4.18 3.61 3.98
## 14 7 property 1.90 2.19 3.67Hm, those are ordered wrong. Why? Well, they’re alphabetical.
frames %>%
group_by(test_item, sample_size, condition) %>%
summarise(response = mean(response)) %>%
ungroup() %>%
mutate(
sample_size = sample_size %>%
as_factor() %>%
fct_relevel("small","medium","large")
) %>%
spread(key = sample_size, value = response)## # A tibble: 14 x 5
## test_item condition small medium large
## <int> <chr> <dbl> <dbl> <dbl>
## 1 1 category 6.07 7.32 7.60
## 2 1 property 5.78 6.66 7.16
## 3 2 category 6.26 7.17 7.51
## 4 2 property 6.21 6.95 7.20
## 5 3 category 5.87 5.98 6.39
## 6 3 property 5.24 5.49 5.23
## 7 4 category 5.11 4.97 5.39
## 8 4 property 4.68 3.56 3.07
## 9 5 category 4.55 4.22 4.72
## 10 5 property 3.99 2.75 2.26
## 11 6 category 4.16 3.85 4.43
## 12 6 property 3.68 2.50 1.91
## 13 7 category 3.98 3.61 4.18
## 14 7 property 3.67 2.19 1.90What if we want to spread by two variables at once!!!
new_data <- frames %>%
group_by(test_item, sample_size, condition) %>%
summarise(response = mean(response)) %>%
unite(col = "cond_ss", condition, sample_size) … then you would spread() using cond_ss as the key.
Which brings us to a question. What if you get a data set where you have a variable like cond_ss that needs to be separated into two? Well…
new_data %>% separate(col = cond_ss, into = c("condition", "sample_size"))## # A tibble: 42 x 4
## # Groups: test_item [7]
## test_item condition sample_size response
## <int> <chr> <chr> <dbl>
## 1 1 category large 7.60
## 2 1 property large 7.16
## 3 1 category medium 7.32
## 4 1 property medium 6.66
## 5 1 category small 6.07
## 6 1 property small 5.78
## 7 2 category large 7.51
## 8 2 property large 7.20
## 9 2 category medium 7.17
## 10 2 property medium 6.95
## # ... with 32 more rowsjanitor package (and the clean_names() function specifically)stringr package is your friendlubridate package is the least painful way knownpurrr package will be your friend, but it’s not easy to learn so give it a bit of time.