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An R Companion for the Handbook of Biological Statistics

Salvatore S. Mangiafico

Student’s t–test for One Sample

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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

 

### --------------------------------------------------------------
### 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

 

### --------------------------------------------------------------
### 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")  

 

Rplot

 

Histogram of data in a single population from a one-sample t-test.  Distribution of these values should be approximately normal. 

 

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Power analysis

Power analysis for one-sample t-test

 

### --------------------------------------------------------------
### 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

 

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