One Sample t-test

One Sample t-test in R

The One Sample t-test is used to compare a single sample against an expected hypothesis value. In the One Sample t-test, the mean of the sample is compared against the hypothesis value. In R, a One Sample t-test can be performed using the Base R t.test() from the stats package or the proc_ttest() function from the procs package.

Data Used

The following data was used in this example.

# Create sample data
read <- tibble::tribble(
  ~score, ~count,
  40, 2,   47, 2,   52, 2,   26, 1,   19, 2,
  25, 2,   35, 4,   39, 1,   26, 1,   48, 1,
  14, 2,   22, 1,   42, 1,   34, 2 ,  33, 2,
  18, 1,   15, 1,   29, 1,   41, 2,   44, 1,
  51, 1,   43, 1,   27, 2,   46, 2,   28, 1,
  49, 1,   31, 1,   28, 1,   54, 1,   45, 1
)

Normal Data

By default, the R one sample t-test functions assume normality in the data and use a classic Student’s t-test.

Base R

Code

The following code was used to test the comparison in Base R. Note that the baseline null hypothesis goes in the “mu” parameter.

  # Perform t-test
  t.test(read$score, mu = 30)

    One Sample t-test

data:  read$score
t = 2.3643, df = 29, p-value = 0.02497
alternative hypothesis: true mean is not equal to 30
95 percent confidence interval:
 30.67928 39.38739
sample estimates:
mean of x 
 35.03333 

Procs Package

Code

The following code from the procs package was used to perform a one sample t-test. Note that the null hypothesis value goes in the “options” parameter.

  library(procs)

  # Perform t-test
  proc_ttest(read, var = score,
             options = c("h0" = 30))

$Statistics
    VAR  N     MEAN      STD   STDERR MIN MAX
1 score 30 35.03333 11.66038 2.128884  14  54

$ConfLimits
    VAR     MEAN     LCLM     UCLM      STD  LCLMSTD  UCLMSTD
1 score 35.03333 30.67928 39.38739 11.66038 9.286404 15.67522

$TTests
    VAR DF        T     PROBT
1 score 29 2.364306 0.0249741

Viewer Output:

Lognormal Data

The Base R t.test() function does not have an option for lognormal data. Likewise, the procs proc_ttest() function also does not have an option for lognormal data.

One possibility may be the tTestLnormAltPower() function from the EnvStats package. This package has not been evaluated yet.