In therbootcamp/BaselRBootcamp2017:
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Statistics
.pull-left3[
In this tutorial we will cover
-
How to calculate basic descriptive statistics
mean(), median(), sd(), ...
-
How to conduct hypothesis tests and how to work with htest objects
t.test(), cor.test(), aov(), ...
]
.pull-right3[
Examples
# mean weight
mean(ChickWeight$weight)
# Standard deviation of Time
sd(ChickWeight$Time)
# T-test comparing weights from Diets 1 and 2
t.test(formula = weight ~ Diet,
data = Chickweight,
subset = Diet %in% c(1, 2))
# Correlation test between weight and Time
cor.test(formula = ~ weight + Time,
data = ChickWeight)
]
Two types of statistics: Descriptive and Inferential
.pull-left3[
Descriptive
- Also called sample statistics
- Used to describe general characteristics of a sample
- Descriptive statistics typically a single scaler value
Examples
| Statistic| R Function|
|------:|----:|
| Mean| mean(x)|
| Median| median(x)|
| Mode| mode(x)|
| Standard Deviation| sd(x)|
]
.pull-right3[
R implimentation
sd(c(5, 3, 6, 3, 2, 6)) # Standard deviation
mean(ChickWeight$weight) # Mean weight
median(ChickWeight$Time) # Mean Time
]
Two types of statistics: Descriptive and Inferential
.pull-left3[
Inferential
- Used to make inferences about a larger population. Typically done in tandem with a hypothesis test
Examples
| Hypothesis Test| R Function|
|------:|----:|
| T-test| t.test()|
| Correlation Test| cor.test()|
| Chi-Square Test| chisq.test()|
| ANOVA, Post-hoc| aov(), TukeyHSD()|
- Hypothesis tests typically return lists of outputs (e.g.; p-value, test statistic)
]
.pull-right3[
R implimentation
t.test(x = c(4, 3, 6, 5, 3, 2),
mu = 0,
alternative = "two.sided")
]
Inferential Statistics
.pull-left3[
Different tests require different arguments
- A one-sample t-test requires just a vector, while an ANOVA requires more arguments.
- To see what arguments a test needs, consult the help menu (e.g.;
?t.test)
Examples
| Hypothesis Test| Help code|
|------:|:----|
| T-test| ?t.test()|
| Correlation Test| ?cor.test()|
| Chi-Square Test| ?chisq.test()|
| ANOVA| ?aov()|
]
.pull-right3[
Always check help menus!
?t.test
knitr::include_graphics("images/ttesthelp_ss.png")
]
Inferential Statistics
.pull-left3[
Arguments to hypothesis tests
- Some arguments are manditory, and some are optional.
- If you don't specify an optional argument, R will use a default value
Ex) Arguments to t.test
| Argument| Description| Default |
|------:|----:|:---|
| x, formula, data|Vector OR a formula and data | Required |
| mu| Null hypothesis| 0 |
| alternative| Alternative Hyp| "two.sided"|
]
.pull-right3[
Specifying arguments to a hypothesis test
# 0: Won't work! Manditory arguments not specified
t.test()
# 1: Will work and use default arguments
t.test(x = ChickWeight$weight)
# 1b: Same as above
t.test(x = ChickWeight$weight,
mu = 0,
alternative = "two.sided")
# 2: Specified arguments
t.test(x = ChickWeight$weight,
mu = 120,
alternative = "greater")
]
Inferential Statistics
.pull-left3[
Formula
- Many tests allow you to include a
formula argument
formula = y ~ a + b + ...
Means...
Model a dependent variable y as a function of a and b and ...
- Formulas go together with dataframes
data containing all variables in the formula, and optional subset arguments to specify which cases in data to include.
]
.pull-right3[
General structure of a hypothesis test and formula
my.test(formula = y ~ a + b, # Formula
data = my.data, # Dataframe
... # Additional
)
y is the dependent variable (e.g.; age), a and b are independent variablesdata is a dataframe containing the variables in formula; (y, a, b)... additional arguments specific to test
]
Inferential Statistics
.pull-left3[
Assigning hypothesis test objects
- Most hypothesis tests return an object of class
"htest" which contain many values
- You can assign the results of a hypothesis test to an object, and then extract the info you want with the
$ operator:
Examples of what's in htest objects
| Element| Result|
|------:|----:|
| x$statistic| A test statistic|
| x$parameter| Degrees of freedom|
| x$p.value| The p-value|
| x$conf.int| Confidence interval|
]
.pull-right3[
What's in an htest object?
# One-sample t-test comparing the weights of chicks to 120
weight.tt <- t.test(x = ChickWeight$weight,
mu = 120,
alternative = "two.sided")
class(weight.tt)
# What's in the weight.tt object?
names(weight.tt)
]
Examples with ChickWeight Data
.pull-left3[
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right3[
knitr::include_graphics("images/cutechicken.jpg")
]
t-tests with t.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right4[
One sample t-test
Is the mean weight of the chicks significantly different from 120?
A <- t.test(x = ChickWeight$weight, # Vector of values
alternative = "two.sided", # Two sided test
mu = 120) # Null is 120
A
]
t-tests with t.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right4[
Two sample t-test
Is the mean weight of the chicks on Diet 1 different from Diet 2?
B <- t.test(formula = weight ~ Diet, # Formula
data = ChickWeight, # Data in Chickweight
subset = Diet %in% c(1, 2), # Only Diets 1,2
alternative = 'two.sided') # Two-sided test
B
]
Correlation test with cor.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right4[
Correlation Test
Is there a correlation between weight and Time?
- For
cor.test(), formula looks like formula = ~ a + b
C <- cor.test(formula = ~ weight + Time, # Formula
data = ChickWeight) # Data in Chickweight
C
]
Chi-Square test with chisq.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right4[
Chi-Square test
Are there more observations from one Diet than another?
- For
chisq.test(), main argument should be a table of values created from the table() function:
table(ChickWeight$Diet) # Table of counts
D <- chisq.test(x = table(ChickWeight$Diet))
D
]
ANOVA with aov()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right4[
ANOVA
Is there difference in weights based on Diet?
- Applying
summary() to an aov object prints a nice table.
E <- aov(formula = weight ~ Diet, # Formula
data = ChickWeight) # Data in Chickweight
summary(E) # Sow a summary of the results
]
Post-hoc tests with TukeyHSD()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102)
x <- ChickWeight[sample(nrow(ChickWeight)),]
rownames(x) <- NULL
head(x)
]
.pull-right4[
Post Hoc
Which specific pairs of Diets differed?
- Apply
TukeyHSD() to an aov object to get post-hoc tests.
D <- aov(formula = weight ~ Diet, # Formula
data = ChickWeight) # Data in Chickweight
TukeyHSD(D) # Conduct post-hoc tests on D
]
Final notes
.pull-left2[
- When using a hypothesis test, always ask:
What are the arguments?
What format or class should the arguments be?
-
When in doubt, always look at the help files and examples at the end.
-
Save hypothesis tests as new objects, then apply names() to see what elements it contains, then extract what you want with S
# Run test and save as test_A
test_A <- t.test(formula = weight ~ Diet,
data = ChickWeight,
subset = Diet %in% c(1, 2))
names(test_A) # What is in the object?
test_A$statistic # Ah ok! Show me the test statistic
]
.pull-right2[
?t.test
knitr::include_graphics("images/ttesthelp_ss.png")
Questions?
]
Statistics Practical
therbootcamp/BaselRBootcamp2017 documentation built on May 3, 2019, 10:45 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
options(htmltools.dir.version = FALSE) # see: https://github.com/yihui/xaringan # install.packages("xaringan") # see: # https://github.com/yihui/xaringan/wiki # https://github.com/gnab/remark/wiki/Markdown options(width=110) options(digits = 4)
Statistics
.pull-left3[
In this tutorial we will cover
-
How to calculate basic descriptive statistics
mean(),median(),sd(), ...
-
How to conduct hypothesis tests and how to work with
htestobjectst.test(),cor.test(),aov(), ...
]
.pull-right3[
Examples
# mean weight mean(ChickWeight$weight) # Standard deviation of Time sd(ChickWeight$Time) # T-test comparing weights from Diets 1 and 2 t.test(formula = weight ~ Diet, data = Chickweight, subset = Diet %in% c(1, 2)) # Correlation test between weight and Time cor.test(formula = ~ weight + Time, data = ChickWeight)
]
Two types of statistics: Descriptive and Inferential
.pull-left3[
Descriptive
- Also called sample statistics
- Used to describe general characteristics of a sample
- Descriptive statistics typically a single scaler value
Examples
| Statistic| R Function|
|------:|----:|
| Mean| mean(x)|
| Median| median(x)|
| Mode| mode(x)|
| Standard Deviation| sd(x)|
]
.pull-right3[
R implimentation
sd(c(5, 3, 6, 3, 2, 6)) # Standard deviation mean(ChickWeight$weight) # Mean weight median(ChickWeight$Time) # Mean Time
]
Two types of statistics: Descriptive and Inferential
.pull-left3[
Inferential
- Used to make inferences about a larger population. Typically done in tandem with a hypothesis test
Examples
| Hypothesis Test| R Function|
|------:|----:|
| T-test| t.test()|
| Correlation Test| cor.test()|
| Chi-Square Test| chisq.test()|
| ANOVA, Post-hoc| aov(), TukeyHSD()|
- Hypothesis tests typically return lists of outputs (e.g.; p-value, test statistic)
]
.pull-right3[
R implimentation
t.test(x = c(4, 3, 6, 5, 3, 2), mu = 0, alternative = "two.sided")
]
Inferential Statistics
.pull-left3[
Different tests require different arguments
- A one-sample t-test requires just a vector, while an ANOVA requires more arguments.
- To see what arguments a test needs, consult the help menu (e.g.;
?t.test)
Examples
| Hypothesis Test| Help code|
|------:|:----|
| T-test| ?t.test()|
| Correlation Test| ?cor.test()|
| Chi-Square Test| ?chisq.test()|
| ANOVA| ?aov()|
]
.pull-right3[
Always check help menus!
?t.test
knitr::include_graphics("images/ttesthelp_ss.png")
]
Inferential Statistics
.pull-left3[
Arguments to hypothesis tests
- Some arguments are manditory, and some are optional.
- If you don't specify an optional argument, R will use a default value
Ex) Arguments to t.test
| Argument| Description| Default |
|------:|----:|:---|
| x, formula, data|Vector OR a formula and data | Required |
| mu| Null hypothesis| 0 |
| alternative| Alternative Hyp| "two.sided"|
]
.pull-right3[
Specifying arguments to a hypothesis test
# 0: Won't work! Manditory arguments not specified t.test() # 1: Will work and use default arguments t.test(x = ChickWeight$weight) # 1b: Same as above t.test(x = ChickWeight$weight, mu = 0, alternative = "two.sided") # 2: Specified arguments t.test(x = ChickWeight$weight, mu = 120, alternative = "greater")
]
Inferential Statistics
.pull-left3[
Formula
- Many tests allow you to include a
formulaargument
formula = y ~ a + b + ...
Means...
Model a dependent variable
yas a function ofaandband...
- Formulas go together with dataframes
datacontaining all variables in the formula, and optionalsubsetarguments to specify which cases indatato include.
]
.pull-right3[
General structure of a hypothesis test and formula
my.test(formula = y ~ a + b, # Formula data = my.data, # Dataframe ... # Additional )
yis the dependent variable (e.g.; age),aandbare independent variablesdatais a dataframe containing the variables informula; (y,a,b)...additional arguments specific to test ]
Inferential Statistics
.pull-left3[
Assigning hypothesis test objects
- Most hypothesis tests return an object of class
"htest"which contain many values - You can assign the results of a hypothesis test to an object, and then extract the info you want with the
$operator:
Examples of what's in htest objects
| Element| Result|
|------:|----:|
| x$statistic| A test statistic|
| x$parameter| Degrees of freedom|
| x$p.value| The p-value|
| x$conf.int| Confidence interval|
]
.pull-right3[
What's in an htest object?
# One-sample t-test comparing the weights of chicks to 120 weight.tt <- t.test(x = ChickWeight$weight, mu = 120, alternative = "two.sided") class(weight.tt) # What's in the weight.tt object? names(weight.tt)
]
Examples with ChickWeight Data
.pull-left3[
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right3[
knitr::include_graphics("images/cutechicken.jpg")
]
t-tests with t.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right4[
One sample t-test
Is the mean weight of the chicks significantly different from 120?
A <- t.test(x = ChickWeight$weight, # Vector of values alternative = "two.sided", # Two sided test mu = 120) # Null is 120 A
]
t-tests with t.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right4[
Two sample t-test
Is the mean weight of the chicks on Diet 1 different from Diet 2?
B <- t.test(formula = weight ~ Diet, # Formula data = ChickWeight, # Data in Chickweight subset = Diet %in% c(1, 2), # Only Diets 1,2 alternative = 'two.sided') # Two-sided test B
]
Correlation test with cor.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right4[
Correlation Test
Is there a correlation between weight and Time?
- For
cor.test(), formula looks likeformula = ~ a + b
C <- cor.test(formula = ~ weight + Time, # Formula data = ChickWeight) # Data in Chickweight C
]
Chi-Square test with chisq.test()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right4[
Chi-Square test
Are there more observations from one Diet than another?
- For
chisq.test(), main argument should be a table of values created from thetable()function:
table(ChickWeight$Diet) # Table of counts D <- chisq.test(x = table(ChickWeight$Diet)) D
]
ANOVA with aov()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right4[
ANOVA
Is there difference in weights based on Diet?
- Applying
summary()to anaovobject prints a nice table.
E <- aov(formula = weight ~ Diet, # Formula data = ChickWeight) # Data in Chickweight summary(E) # Sow a summary of the results
]
Post-hoc tests with TukeyHSD()
.pull-left4[
ChickWeight data
ChickWeight
set.seed(102) x <- ChickWeight[sample(nrow(ChickWeight)),] rownames(x) <- NULL head(x)
]
.pull-right4[
Post Hoc
Which specific pairs of Diets differed?
- Apply
TukeyHSD()to anaovobject to get post-hoc tests.
D <- aov(formula = weight ~ Diet, # Formula data = ChickWeight) # Data in Chickweight TukeyHSD(D) # Conduct post-hoc tests on D
]
Final notes
.pull-left2[
- When using a hypothesis test, always ask:
What are the arguments?
What format or class should the arguments be?
-
When in doubt, always look at the help files and examples at the end.
-
Save hypothesis tests as new objects, then apply
names()to see what elements it contains, then extract what you want withS
# Run test and save as test_A test_A <- t.test(formula = weight ~ Diet, data = ChickWeight, subset = Diet %in% c(1, 2)) names(test_A) # What is in the object? test_A$statistic # Ah ok! Show me the test statistic
]
.pull-right2[
?t.test
knitr::include_graphics("images/ttesthelp_ss.png")
Questions?
]
Statistics Practical
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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