vignettes/web-only/LessVolume-MoreCreativity.Rmd
LessVolume-MoreCreativity.Rmd
mosaic
package
NSF-funded project to develop a new way to introduce mathematics, statistics, computation and modeling to students in colleges and universities.
more information at mosaic-web.org
the mosaic
package is available via
This document was originally created as an R presentation to be used
as slides accompanying various presentations. It has been converted into
a more traditional document for use as a vignette in the
mosaic
package.
The examples below use the mosaic
and
mosaicData
packages. An earlier version of this document
used lattice
graphics, but it has been updated to use
ggformula
Many of the guiding principles of the mosaic
package
reflect the “Less Volume, More Creativity” mantra of Mike McCarthy who
had a large poster with those words placed in the “war room” (where
assistant coaches decide on the game plan for the upcoming opponent) as
a constant reminder not to add too much complexity to the game plan.
A lot of times you end up putting in a lot more volume, because you are
teaching fundamentals and you are teaching concepts that you need to put
in, but you may not necessarily use because they are building blocks for
other concepts and variations that will come off of that … In the
offseason you have a chance to take a step back and tailor it more
specifically towards your team and towards your players.” Mike McCarthy, former Head Coach, Green Bay Packers |
One key to successfully introducing R is finding a set of commands that is
It is not enough to use R, it must be used elegantly.
Two examples of this principle:
Goal: a minimal set of R commands for Intro Stats
Result: Minimal R Vignette
(vignette("MinimalR")
)
Much of the work on the mosaic
package has been
motivated by
The following template is important because we can do so much with it.
It is useful to name the components of the template:
We’re hiding a bit of complexity in the template, and there will be
times that we will want to gussy things up a bit. We’ll indicate that by
adding ...
to the end of the template. Just don’t let
...
become a distractor early on.
Using the template generally requires answering two questions. (These questions are useful in the context of nearly all computer tools, just substitute “the computer” in for R in the questions.)
births ~ date
)data = Births78
)
?Births78
for documentationSome things you will need to know:
Command: gf_boxplot()
The data: HELPrct
age
, substance
?HELPrct
for info about dataSome things you will need to know:
Command: gf_boxploth()
for horizontal
boxplots
The data: HELPrct
age
, substance
?HELPrct
for info about datagf_histogram(~ age, data = HELPrct)
Note: When there is one variable it is on the right side of the formula.
The ggformula
graphics system includes lots of bells and
whistles including
I used to introduce these too early. My current approach:
library(lubridate)
Births78 <- Births78 %>%
mutate(weekday = wday(date, label = TRUE, abbr = TRUE))
gf_line(births ~ date, color = ~ weekday, data = Births78)
Notes
wday()
is in the lubridate
packageThe mosaic
package provides functions that make it
simple to create numerical summaries using the same template used for
graphing (and later for describing linear models).
Big idea:
gf_histogram( ~ age, data = HELPrct) # binwidth = 5 (or 10) might be good here
mean( ~ age, data = HELPrct)
## [1] 35.65342
The mosaic package includes formula aware versions of
mean()
, sd()
, var()
,
min()
, max()
, sum()
,
IQR()
, …
Also provides favstats()
to compute our favorites.
favstats( ~ age, data = HELPrct)
## min Q1 median Q3 max mean sd n missing
## 19 30 35 40 60 35.65342 7.710266 453 0
favstats()
quickly becomes a go-to function in our
courses.
df_stats()
is similar, but
df_stats( ~ age, data = HELPrct)
## response min Q1 median Q3 max mean sd n missing
## 1 age 19 30 35 40 60 35.65342 7.710266 453 0
df_stats( ~ age, data = HELPrct, mean, sd, median, iqr)
## response mean sd median iqr
## 1 age 35.65342 7.710266 35 10
tally(~ sex, data = HELPrct)
## sex
## female male
## 107 346
tally(~ substance, data = HELPrct)
## substance
## alcohol cocaine heroin
## 177 152 124
df_stats(~ substance, data = HELPrct, counts, props)
## response n_alcohol n_cocaine n_heroin prop_alcohol prop_cocaine prop_heroin
## 1 substance 177 152 124 0.3907285 0.3355408 0.2737307
There are three ways to think about this. All do the same thing.
sd(age ~ substance, data = HELPrct)
sd(~ age | substance, data = HELPrct)
sd(~ age, groups = substance, data = HELPrct)
# note option color = ~ substance is used for graphics
## alcohol cocaine heroin
## 7.652272 6.692881 7.986068
This makes it possible to easily convert three different types of plots into the (same) corresponding numerical summary.
df_stats()
can also be used with multiple variables and
provides a different output format.
df_stats(age ~ substance, data = HELPrct, sd)
## response substance sd
## 1 age alcohol 7.652272
## 2 age cocaine 6.692881
## 3 age heroin 7.986068
2-way tables are just tallies of 2 variables.
tally(sex ~ substance, data = HELPrct)
## substance
## sex alcohol cocaine heroin
## female 36 41 30
## male 141 111 94
tally( ~ sex + substance, data = HELPrct)
## substance
## sex alcohol cocaine heroin
## female 36 41 30
## male 141 111 94
df_stats(sex ~ substance, data = HELPrct, counts)
## response substance n_female n_male
## 1 sex alcohol 36 141
## 2 sex cocaine 41 111
## 3 sex heroin 30 94
Other output formats are available
tally(sex ~ substance, data = HELPrct, format = "proportion")
## substance
## sex alcohol cocaine heroin
## female 0.2033898 0.2697368 0.2419355
## male 0.7966102 0.7302632 0.7580645
tally(substance ~ sex, data = HELPrct, format = "proportion", margins = TRUE)
## sex
## substance female male
## alcohol 0.3364486 0.4075145
## cocaine 0.3831776 0.3208092
## heroin 0.2803738 0.2716763
## Total 1.0000000 1.0000000
tally(~ sex + substance, data = HELPrct, format = "proportion", margins = TRUE)
## substance
## sex alcohol cocaine heroin Total
## female 0.07947020 0.09050773 0.06622517 0.23620309
## male 0.31125828 0.24503311 0.20750552 0.76379691
## Total 0.39072848 0.33554084 0.27373068 1.00000000
tally(sex ~ substance, data = HELPrct, format = "percent")
## substance
## sex alcohol cocaine heroin
## female 20.33898 26.97368 24.19355
## male 79.66102 73.02632 75.80645
df_stats(sex ~ substance, data = HELPrct, props, percs)
## response substance prop_female prop_male perc_female perc_male
## 1 sex alcohol 0.2033898 0.7966102 20.33898 79.66102
## 2 sex cocaine 0.2697368 0.7302632 26.97368 73.02632
## 3 sex heroin 0.2419355 0.7580645 24.19355 75.80645
mean(age ~ substance | sex, data = HELPrct)
## A.F C.F H.F A.M C.M H.M F M
## 39.16667 34.85366 34.66667 37.95035 34.36036 33.05319 36.25234 35.46821
mean(age ~ substance | sex, data = HELPrct, .format = "table")
## substance sex mean
## 1 A F 39.16667
## 2 A M 37.95035
## 3 C F 34.85366
## 4 C M 34.36036
## 5 H F 34.66667
## 6 H M 33.05319
mutate()
(in the dplyr
package) or
transform()
.median()
, min()
,
max()
, sd()
, var()
,
favstats()
, etc.This master template can be used to do a large portion of what needs doing in an Intro Stats course.
## female male
## 36.25234 35.46821
## (Intercept) sexmale
## 36.2523364 -0.7841284
It can be learned early and practiced often so that students become secure in their ability to use these functions.
The mosaic
package includes some other things, too
mosaicData
and NHANES
packages)xchisq.test()
, xpnorm()
,
xqqmath()
x
mplot()
mplot(HELPrct)
interactive plot creationplot()
in some situationsgf_histogram()
controls (e.g.,
binwidth
)gf_refine()
)xpnorm(700, mean = 500, sd = 100)
##
## If X ~ N(500, 100), then
## P(X <= 700) = P(Z <= 2) = 0.9772
## P(X > 700) = P(Z > 2) = 0.02275
##
## [1] 0.9772499
##
## If X ~ N(500, 100), then
## P(X <= 300) = P(Z <= -2) = 0.02275 P(X <= 700) = P(Z <= 2) = 0.97725
## P(X > 300) = P(Z > -2) = 0.97725 P(X > 700) = P(Z > 2) = 0.02275
##
## [1] 0.02275013 0.97724987
xchisq.test(phs)
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: x
## X-squared = 24.429, df = 1, p-value = 7.71e-07
##
## 104.00 10933.00
## ( 146.52) (10890.48)
## [12.05] [ 0.16]
## <-3.51> < 0.41>
##
## 189.00 10845.00
## ( 146.48) (10887.52)
## [12.05] [ 0.16]
## < 3.51> <-0.41>
##
## key:
## observed
## (expected)
## [contribution to X-squared]
## <Pearson residual>
Modeling is really the starting point for the mosaic
design.
If you want to teach using randomization tests and bootstrap
intervals, the mosaic
package provides some functions to
simplify creating the random distirubtions involved.
Often used on first day of class
Story
woman claims she can tell whether milk has been poured into tea or vice versa.
Question: How do we test this claim?
We use rflip()
to simulate flipping coins
rflip()
##
## Flipping 1 coin [ Prob(Heads) = 0.5 ] ...
##
## H
##
## Number of Heads: 1 [Proportion Heads: 1]
Note: We do this with students who do not (yet) know
what a binomial distribution is, so we want to avoid using
rbinom()
at this point.
Rather than flip each coin separately, we can flip multiple coins at once.
rflip(10)
##
## Flipping 10 coins [ Prob(Heads) = 0.5 ] ...
##
## H H H T T T H H H T
##
## Number of Heads: 6 [Proportion Heads: 0.6]
heads
= correct; tails
= incorrect than to compare with a given pattern
rflip(10)
simulates 1 lady tasting 10 cups 1 time.
We can do that many times to see how guessing ladies do:
## n heads tails prop
## 1 10 6 4 0.6
## 2 10 5 5 0.5
do()
is clever about what it remembers (in many common
situations)Now let’s simulate 5000 guessing ladies
## n heads tails prop
## 1 10 4 6 0.4
## 2 10 7 3 0.7
gf_histogram(~ heads, data = Ladies, binwidth = 1)
Q. How often does guessing score 9 or 10?
Here are 3 ways to find out
tally( ~ (heads >= 9), data = Ladies)
## (heads >= 9)
## TRUE FALSE
## 52 4948
tally( ~ (heads >= 9), data = Ladies, format = "prop")
## (heads >= 9)
## TRUE FALSE
## 0.0104 0.9896
prop( ~ (heads >= 9), data = Ladies)
## prop_TRUE
## 0.0104
The Lady Tasting Tea illustrates a 3-step process that can be reused in many situations:
mosaic
functions shuffle()
or
resample()
diffmean(age ~ sex, data = HELPrct)
## diffmean
## -0.7841284
## diffmean
## 1 0.09686133
## prop_TRUE
## 0.3412
gf_histogram( ~ diffmean, data = Null) %>%
gf_vline(xintercept = -0.7841)
## Warning: geom_vline(): Ignoring `mapping` because `xintercept` was provided.
Bootstrap <- do(5000) *
diffmean(age ~ sex, data = resample(HELPrct))
gf_histogram( ~ diffmean, data = Bootstrap) %>%
gf_vline(xintercept = -0.7841)
## Warning: geom_vline(): Ignoring `mapping` because `xintercept` was provided.
cdata( ~ diffmean, data = Bootstrap, p = 0.95)
## lower upper central.p
## 2.5% -2.438299 0.8177243 0.95
confint(Bootstrap, method = "quantile")
## name lower upper level method estimate
## 1 diffmean -2.438299 0.8177243 0.95 percentile -0.7841284
confint(Bootstrap) # default uses bootstrap st. err.
## name lower upper level method estimate
## 1 diffmean -2.438299 0.8177243 0.95 percentile -0.7841284
## Intercept length sigma r.squared F numdf dendf .row .index
## 1 2.862276 0.2479478 0.3963356 0.4110041 25.81878 1 37 1 1
## Intercept length sigma r.squared F numdf dendf .row .index
## 1 6.347607 0.10697295 0.4962778 0.076502169 3.0650643 1 37 1 1
## 2 9.877910 -0.03582090 0.5142048 0.008578250 0.3201415 1 37 1 2
## 3 9.840434 -0.03430504 0.5143891 0.007867588 0.2934092 1 37 1 3
## Intercept length sexG sigma r.squared F numdf dendf .row .index
## 1 3.641168 0.221025 -0.2325175 0.3848905 0.4595428 15.30513 2 36 1 1
## Intercept length sexG sigma r.squared F numdf dendf .row .index
## 1 3.068833 0.2378303 0.08945102 0.3993335 0.4182207 12.93957 2 36 1 1
## 2 2.916037 0.2478853 -0.10717940 0.3979148 0.4223471 13.16058 2 36 1 2
## 3 3.351286 0.2334825 -0.26968267 0.3770203 0.4814193 16.71013 2 36 1 3
Null <- do(5000) *
lm(width ~ length + shuffle(sex),
data = KidsFeet)
gf_histogram( ~ sexG, data = Null, boundary = -0.2325) %>%
gf_vline(xintercept = -0.2325)
## Warning: geom_vline(): Ignoring `mapping` because `xintercept` was provided.
gf_histogram(~ sexG, data = Null, boundary = -0.2325) %>%
gf_vline(xintercept = -0.2325)
## Warning: geom_vline(): Ignoring `mapping` because `xintercept` was provided.
prop(~ (sexG <= -0.2325), data = Null)
## prop_TRUE
## 0.0344
More mosaic resources can be found at https://www.mosaic-web.org/mosaic/articles/mosaic-resources.html.
The RJournal paper entitled “mosaic Package: Helping Students to `Think with Data’ Using R (https://journal.r-project.org/archive/2017/RJ-2017-024/index.html) provides further discussion of the mosaic modeling language and approach to teaching.