Student’s t-Test for Paired Samples

  This version of Student’s t-test evaluates whether two dependent (paired) samples are statistically different. The only required input is the data matrix.


1 Equation:

\[ t = \frac{d}{\sqrt{\frac{s^2}{n}}} \]

Where:

  • d = mean difference between paired observations
  • s² = variance of the differences
  • n = sample size
  The variance of the differences is given by:

\[ s^2 = \frac{\sum d^2 - \frac{(\sum d)^2}{n}}{n - 1} \]

2 Files:

  1. testetDep1matrix program
  2. Program source code

3 Usage and example

  The program performs the test at a 5% significance level.
1. Enter the matrix containing the two paired datasets;
2. Run "testetDep1matrix"

# Output:
1. "tval" – calculated t statistic;
2. "tcr5%" – critical (tabulated) t value at 5%;
3. "pval" – p-value of the test


Table — Observed values for groups A and B (Vieira, 2000).

Group
A 2 3 5 1 4 2 7 6
B 7 6 8 6 8 7 10 9


(a) Insertion of the data matrix.
(b) Results obtained from the paired t-test.
Figure 1: testetDep1matrix program running on the Android version of the HP50G calculator (Go49gp), showing data input and test results.


  The results are identical to those obtained using the HP50G’s internal form-based input and built-in algorithm.
Back to top