R Quick Reference - Statistics in the Modern World (MATH 1209)

A one-page cheat sheet for the R this course actually uses: the two packages you load, the one formula pattern that runs through nearly every command, and the mosaic/BSDA functions that match each calculator procedure in the TI-83/84 Quick Guide. Every function here is taught step by step, with real output, in the R-Help lessons — this page is the short version to keep open while you work. Nothing here goes beyond what MATH 1209 covers (Ch 1–7): one proportion, one mean, and the ideas that build up to them. Remember: R is always optional in this course — everything below has a calculator equivalent.

The one idea that unlocks most of it: the formula interface

Almost every mosaic command reads the same way: goal( y ~ x , data = D). Read y ~ x as “y broken down by x.” A ~x with nothing on the left means “just x.” The same shape describes, plots, and tests:

favstats(~ length, data = KidsFeet)             # summary of one variable
favstats(length ~ sex, data = KidsFeet)          # summary by group
gf_histogram(~ length, data = KidsFeet)          # plot of one variable
gf_boxplot(length ~ sex, data = KidsFeet)        # plot y by group
t.test(~ length, data = KidsFeet, mu = 25)       # test on one variable

Learn the pattern once and it carries you through every R box in the book.

11. Getting started, every session¶

library(mosaic)   # summaries, plots (ggformula), simulation
library(BSDA)     # z/t tests from summary statistics (zsum.test, tsum.test)

That is the entire package list for MATH 1209, all semester (see R-Help Lesson 5). On the CSUB JupyterHub (https://csub.jupyter.cal-icor.org/) both are pre-installed — you install nothing, ever.

22. Getting data into R¶

Task	Code	Notes
Load a dataset built into `mosaic`/`mosaicData`	`data(KidsFeet)`	see the dataset index
Peek at structure	`str(KidsFeet)` · `glimpse(KidsFeet)`	variable names, types, first values
Quick summary of every column	`inspect(KidsFeet)`	numeric and categorical summaries at once
First / last rows	`head(KidsFeet)` · `tail(KidsFeet)`	default 6 rows
Dimensions	`nrow(KidsFeet)` · `ncol(KidsFeet)`	rows × columns
Column names	`names(KidsFeet)`
Read your own CSV file (e.g., for a project)	`dat <- read.csv("myfile.csv")`	see R-Help Lesson 6 for CSV, Excel, and URL imports

33. The formula interface at a glance¶

You want…	Formula shape	Example
one variable	`~ y`	`favstats(~ length, data = KidsFeet)`
a variable by a group	`y ~ x`	`favstats(length ~ sex, data = KidsFeet)`
one categorical variable	`~ y`	`tally(~ sex, data = KidsFeet)`
a two-way table	`~ y + x`	`tally(~ sex + biggerfoot, data = KidsFeet)`
a numeric response by a two-level group (the t-tests in Ch 7)	`y ~ x`	`t.test(length ~ sex, data = KidsFeet)`

The ~ is read “by.” You will use these shapes for the whole course.

44. Describe & visualize (Ch 1–2)¶

Goal	Code	Produces
Numerical summary of a variable	`favstats(~ length, data = KidsFeet)`	min, Q1, median, Q3, max, mean, sd, n, missing
Same summary, by group	`favstats(length ~ sex, data = KidsFeet)`	one row of summaries per group
A single statistic	`mean(~ length, data=)` · `sd(...)` · `median(...)` · `IQR(...)`	one number (formula form)
Frequency table (categorical)	`tally(~ sex, data = KidsFeet)`	counts per category
Proportions instead of counts	`tally(~ sex, data = KidsFeet, format = "proportion")`	shares per category
Two-way table	`tally(~ sex + biggerfoot, data = KidsFeet)`	cross-tabulation
Histogram	`gf_histogram(~ length, data = KidsFeet)`	distribution of one numeric variable
Boxplot (optionally by group)	`gf_boxplot(length ~ sex, data = KidsFeet)`	center/spread/outliers across groups
Bar chart (categorical)	`gf_bar(~ sex, data = KidsFeet)`	counts per category

gf_* functions (the “ggformula” family) return plots you can label and color accessibly. R-Help Lesson 10 walks through titles, axis labels, and building an Okabe–Ito colorblind-safe palette step by step:

gf_boxplot(length ~ sex, fill = ~ sex, data = KidsFeet) %>%
  gf_labs(title = "Foot length by sex", x = "Sex", y = "Length (cm)") %>%
  gf_refine(scale_fill_manual(values = c("#0072B2", "#E69F00")))

55. Probability & the Normal model (Ch 3–4)¶

Goal	Code	Notes
Normal area, with picture	`xpnorm(115, mean = 100, sd = 15)`	prints the z-score and both tail probabilities and shades the curve; matches the calculator’s `normalcdf`
Normal percentile (cutoff)	`xqnorm(0.90, mean = 100, sd = 15)`	the value with 90% below it; matches `invNorm`
Draw a Normal curve alone	`plotDist("norm", mean = 100, sd = 15)`	the model on its own, no shading
Binomial probability	`dbinom(3, size = 10, prob = 0.4)`	exactly 3 successes; `pbinom()` for “≤ 3”
Build a sampling distribution (simulation)	`do(1000) * mean(~ length, data = resample(KidsFeet))`	resample-and-recompute; makes the Central Limit Theorem visible
Flip a coin / resample at random	`rflip(10)` · `resample(x)`	the building blocks of a simulation

xpnorm() is the teaching tool of the two: it shows its work — the z-score, both tail areas, and the shaded curve — instead of returning a bare number. Set a seed (set.seed(1209)) before any do() simulation so your result is reproducible; see R-Help Lesson 11.

66. Inference: one proportion, one mean (Ch 5–7)¶

Pick the right procedure with the which-test guide. prop.test() and t.test()/tsum.test() all print a decision and a confidence interval in one call — you never run the interval and the test separately.

Procedure	Code	Matches (TI-83/84)	Used in
One proportion, interval + test	`prop.test(x, n, p = 0.5)`	`1-PropZInt` / `1-PropZTest`	Ch 6
One mean, raw data (t)	`t.test(~ length, data = KidsFeet, mu = 25)`	`TInterval` / `T-Test`	Ch 7
One mean from summary stats, $\sigma$ unknown (t)	`tsum.test(mean.x = 24.72, s.x = 1.32, n.x = 39, mu = 25)`	`TInterval` / `T-Test` (Stats mode)	Ch 7
One mean from summary stats, $\sigma$ known (z)	`zsum.test(mean.x = 24.72, sigma.x = 1.3, n.x = 39, mu = 25)`	`ZInterval` / `Z-Test`	Ch 5 preview

Add alternative = "less" or alternative = "greater" to either prop.test() or a t-procedure for a one-sided test — the same directional choice you make on the calculator’s 1-PropZTest/T-Test screen.

77. Reading the table functions directly¶

When you want a raw probability or critical value without a full test (and want to check software against the distribution tables):

Distribution	Area from a value	Value from an area
Normal	`pnorm(z)`	`qnorm(p)`
t (with `df`)	`pt(t, df)`	`qt(p, df)`

88. Reproducibility habits¶

Habit	Code	Why
Fix randomness	`set.seed(1209)`	same simulation result every run
Comment your steps	`# what this line does`	future-you and your grader thank you
Report your R version	`sessionInfo()`	see R-Help Lesson 11