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Introduction
When to use it
Null hypothesis
How the test works
Assumptions
See the Handbook for information on these topics.
Example
One sample t-test with observations as vector
###
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### One-sample t-test, transferrin example, pp. 124
### --------------------------------------------------------------
observed = c(0.52, 0.20, 0.59, 0.62, 0.60)
theoretical = 0
t.test(observed,
mu = theoretical,
conf.int = 0.95)
One Sample t-test
t = 6.4596, df = 4, p-value = 0.002958
# # #
Graphing the results
See the Handbook for information on this topic.
Similar tests
The paired t-test and two-sample t-test are presented elsewhere in this book.
How to do the test
One sample t-test with observations in data frame
###
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### One-sample t-test, SAS example, pp. 125
### --------------------------------------------------------------
Input =("
Angle
120.6
116.4
117.2
118.1
114.1
116.9
113.3
121.1
116.9
117.0
")
Data = read.table(textConnection(Input),header=TRUE)
observed = Data$ Angle
theoretical = 50
t.test(observed,
mu = theoretical,
conf.int=0.95)
One Sample t-test
t = 87.3166, df = 9, p-value = 1.718e-14
### Does not agree with Handbook. The Handbook results are incorrect.
### The SAS code produces the following result.
T-Tests
Variable DF t Value Pr > |t|
angle 9 87.32 <.0001
Histogram
hist(Data$ Angle,
col="gray",
main="Histogram of values",
xlab="Angle")
Histogram of data in a single population from a one-sample t-test. Distribution of these values should be approximately normal.
# # #
Power analysis
Power analysis for one-sample t-test
###
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### Power analysis, t-test, one-sample,
### hip joint example, pp. 125–126
### --------------------------------------------------------------
M1 = 70 # Theoretical mean
M2 = 71 # Mean to detect
S1 = 2.4 # Standard
deviation
S2 = 2.4 # Standard
deviation
Cohen.d = (M1 - M2)/sqrt(((S1^2) + (S2^2))/2)
library(pwr)
pwr.t.test(
n = NULL, # Observations
d = Cohen.d,
sig.level = 0.05, # Type I
probability
power = 0.90, # 1 minus Type II
probability
type = "one.sample", # Change
for one- or two-sample
alternative = "two.sided")
One-sample t test power calculation
n = 62.47518
# # #