Testing two samples with matched pairs {sign test} can show if they are from same, not necessarily normally distributed, population.
matched pairs
Before and after comparison has matched pairs.
hypothesis
Hypothesize that first and second samples show no change.
significance
Set significance level to 5%.
degrees of freedom
Degrees of freedom are sample size minus one.
calculation
For all matched pairs, subtract before-value from after-value to get plus, minus, or no sign. Add positive signs.
Use probability of 1/2 for getting positive sign, because samples are the same by hypothesis. Calculate binomial-distribution z score: (P - 0) / (N * 0.5 * 0.5)^0.5, where P is positive-sign number, N is sample size, mean equals zero, and standard deviation equals (N * p * (1 - p))^0.5.
test
If z score is less than normal-distribution value with same degrees of freedom at significance level, do not reject hypothesis.
Mathematical Sciences>Statistics>Tests
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Date Modified: 2022.0224