Calculating a Paired t-Test Equation

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SUMMARY

The equation for a paired t-test is defined as t0 = d(bar) / (sd / √n), where d(bar) represents the sample mean of the differences between paired observations, sd is the sample standard deviation of these differences, and n is the number of pairs. This method tests the null hypothesis H0: μD = 0, indicating that there is no difference between the paired observations. The paired t-test is fundamentally similar to a standard t-test, with the key distinction being the focus on the differences between pairs rather than individual observations.

PREREQUISITES
  • Understanding of statistical hypothesis testing
  • Familiarity with t-test concepts
  • Knowledge of sample mean and standard deviation calculations
  • Basic grasp of paired data analysis
NEXT STEPS
  • Study the derivation of the paired t-test formula
  • Learn about the assumptions underlying the paired t-test
  • Explore software tools for conducting paired t-tests, such as R or Python's SciPy library
  • Investigate alternative statistical tests for non-normal data distributions
USEFUL FOR

Statisticians, data analysts, researchers conducting experiments with paired observations, and anyone interested in hypothesis testing methodologies.

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What is the equation for a paired t-test?
 
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It's the same as a normal t-test. You just have to keep in mind that you're testing against the null hypothesis H0: μD = 0, where μD is the population mean of differences between pairs of observations. So it's

t0 = d(bar) / (sd / √n)

where d(bar) and sd are the sample mean and sample standard deviation for the differences between each pair.

edit: And just to be clear, n is the number of pairs of observations.

Basically, you treat this like a regular t-test problem, except your random variable is the difference between each pair of observations.
 
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