A slightly different introduction to #Rstats. Data frames, linear models and plots with ggplot2.

1. THE WRIGHT LAB COMPUTATION LUNCHES
An introduction to R
Gene expression from DEVA to differential expression
Handling massively parallel sequencing data

2. R: data frames, plots and
linear models
Martin Johnsson

3. statistical environment

4. free open source

5. scripting language

6. great packages (limma for
microarrays, R/qtl for QTL
mapping etc)

7. You need to write code!

8. (
Why scripting?
harder the first time
easier the next 20 times …
necessity for moderately large data
)

9. R-project.org
Rstudio.com

10. Interface is immaterial
ssh into a server, RStudio,
alternatives
very few platform-dependent
elements that the end user needs to
worry about

11. Scripting
write your code down in a .R file
run it with source ( )
## comments

12. if it runs without intervention
from start to finish, you’re
actually programming

13. Help!
within R: ? and tab
your favourite search engine
ask (Stack Exchange, R-help mailing list,
package mailing lists)

14. First task: make a new script that
imports a data set and takes a subset
of the data

15. Reading in data
Excel sheet to data.frame
one sheet at a time
clear formatting
short succinct column names
export text
read.table

16. Subsetting
logical operators ==, !=, >, <, !
subset(data, column1==1)
subset(data, column1==1 & column2>2)

17. Indexing with [ ]
first three rows: data[c(1,2,3),]
two columns: data[,c(2,4)]
ranges: data[,1:3]

18. Variables
columns in expressions
data$column1 + data$column2
log10(data$column2)
assignment arrow
data$new.column <- log10(data$column2)
new.data <- subset(data, column1==10)

19. Exercise: Start a new script and save
it as unicorn_analysis.R.
Import unicorn_data.csv.
Take a subset that only includes
green unicorns.

20. RStudio: File > New > R Script
data <- read.csv("unicorn_data.csv")
green.unicorns <- subset(data, colour=="green")

21. Anatomy of a function call
function.name(parameters)
mean(data$column)
mean(x=data$column)
mean(x=data$column, na.rm=T)
?mean

22. mean(exp(log(x)))

23. programming in R ==
stringing together functions
and writing new ones

24. Using a package (ggplot2) to make
statistical graphics.

25. install.packages("ggplot2")
library(ggplot2)

26. qplot(x=x.var, y=y.var, data=data)
only x: histogram
x and y numeric: scatterplot
or set geometry (geom) yourself

27. geoms:
point
line
boxplot
jitter – scattered points
tile – heatmap
and many more

28. Exercise: Make a scatterplot of weight
and horn length in green unicorns.
Write all code in the
unicorn_analysis.R script.
Save the plots as variables so you can
refer back to them.

29. 33
horn.length
30
27
24
250
300
350
weight
400
450
green.scatterplot <- qplot(x=weight,
y=horn.length, data=green.unicorns)

30. Exercise: Make a boxplot of horn
length versus diet.

31. 40
horn.length
35
30
25
candy
diet
flowers
qplot(x=diet, y=weight,
data=unicorn.data, geom="boxplot")

32. Small multiples
split the plot into multiple subplots
useful for looking at patterns
qplot(x=x.var, y=y.var, data=data,
facets=~variable)
facets=variable1~variable2

33. Exercise: Again, make a boxplot of
diet and horn length, but separated
into small multiples by colour.

34. green
40
pink
horn.length
35
30
25
candy
flowers
diet
candy
flowers
qplot(x=diet, y=horn.length, data=data,
geom="boxplot", facets=~colour)

35. Comparing means with linear models

36. Wilkinson–Rogers notation
one predictor: y ~ x
additive model: y ~ x1 + x2
interactions: y ~ x1 + x2 + x1:y2
or y ~ x1 * x2
factors: y ~ factor(x)

37. Student’s t-test

38. t.test(variable ~ grouping, data=data)
alternative: two sided, less, greater
var.equal
paired
geoms: boxplot, jitter

39. Carl Friedrich Gauss
least squares estimation

40. 40
horn.length
35
30
25
250
300
350
weight
400
450

41. linear model
y = a + b x + e, e ~ N(0, sigma)
lm(y ~ x, data=some.data)
formula
data
summary( ) function

42. Exercise: Make a regression of horn
length and body weight.

43. model <- lm(horn.length ~ weight, data=data)
summary(model)
Call:
lm(formula = horn.length ~ weight, data = data)
Residuals:
Min
1Q Median
-6.5280 -2.0230 -0.1902
3Q
2.5459
Max
7.3620
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.41236
3.85774
5.291 1.76e-05 ***
weight
0.03153
0.01093
2.886 0.00793 **
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.447 on 25 degrees of freedom
(3 observations deleted due to missingness)
Multiple R-squared: 0.2499, Adjusted R-squared: 0.2199
F-statistic: 8.327 on 1 and 25 DF, p-value: 0.007932

44. What have we actually fitted?
model.matrix(horn.length ~ weight, data)
What were the results?
coef(model)
How uncertain?
confint(model)

45. Plotting the model
regression equation y = a + x b
a is the intercept
b is the slope of the line
pull out coefficients with coef( )
a plot with two layers: scatterplot
with added geom_abline( )

46. 40
horn.length
35
30
25
250
300
350
weight
400
450
scatterplot <- qplot(x=weight, y=horn.length, data=data)
a <- coef(model)[1]
b <- coef(model)[2]
scatterplot + geom_abline(intercept=a, slope=b)

47. A regression diagnostic
the linear model needs several
assumptions, particularly linearity and
equal error variance
the residuals vs fitted plot can help spot
gross deviations

48. 8
residuals(model)
4
0
-4
28
30
32
fitted(model)
34
qplot(x=fitted(model), y=residuals(model))

49. Photo: Peter (anemoneprojectors), CC:BY-SA-2.0
http://www.flickr.com/people/anemoneprojectors/

50. analysis of variance
aov(formula, data=some.data)
drop1(aov.object, test="F")
F-tests (Type II SS)
post-hoc tests
pairwise.t.test
TukeyHSD

51. Exercise: Perform analysis of variance
on weight and the effects of diet while
controlling for colour.

52. We want a two-way anova with an F-test for diet.
model.int <- aov(weight ~ diet * colour, data=data)
drop1(model.int, test="F")
model.add <- aov(weight ~ diet + colour, data=data)
drop1(model.add, test="F")
Single term deletions
Model:
weight ~ diet + colour
Df Sum of Sq
RSS
AIC F value Pr(>F)
<none>
85781 223.72
diet
1
471.1 86252 221.87 0.1318 0.71975
colour 1
13479.7 99260 225.66 3.7714 0.06396 .
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

53. Black magic
none of the is really R’s fault, but things
that come up along the way

54. Black magic
none of the is really R’s fault, but things
that come up along the way
missing values: na.rm=T, na.exclude( )

55. Black magic
none of the is really R’s fault, but things
that come up along the way
missing values: na.rm=T, na.exclude( )
type I, II and III sums of squares in Anova

56. Black magic
none of the is really R’s fault, but things
that come up along the way
missing values: na.rm=T, na.exclude( )
type I, II and III sums of squares in anova
floating-point arithmetic, e.g. sin(pi)

57. Reading
Daalgard, Introductory statistics with R,
electronic resource at the library
Faraway, The linear model in R
Gelman & Hill, Data analysis using regression
and multilevel/hierarchical models
Wickham, ggplot2 book
tons of tutorials online, for instance
http://martinsbioblogg.wordpress.com/a-slightlydifferent-introduction-to-r/

58. Exercise
More (and some of the same) analysis of the
unicorn data set.
Use the R documentation and google.
I will post solutions.