Key Terms
INDEPENDENT GROUPS
Samples from two separate populations; no relationship between individual values. Example: comparing exam scores from tw
MATCHED PAIRS (DEPENDENT SAMPLES)
Two measurements from the same subjects or paired subjects. Example: testing the same people before and after a treatmen
Random variable
X-bar-d (mean of the differences) Parameter tested: mu-d (population mean of the differences) Distribution: Student's t
Null hypothesis
Mu-1 = mu-2 (or equivalently, mu-1 minus mu-2 = 0)
Alternative hypothesis
Not equal, greater than, or less than — depends on the word problem
Standard error of the difference
SE = square root of [ (s1-squared / n1) + (s2-squared / n2) ]
Test statistic (t-score)
T = [ (x-bar-1 minus x-bar-2) minus (mu-1 minus mu-2) ] / SE
Formula
D = (x-bar-1 minus x-bar-2) / s-pooled
Standard deviation of the difference
Square root of [ (sigma-1-squared / n1) + (sigma-2-squared / n2) ]
Test statistic (z-score)
Z = [ (x-bar-1 minus x-bar-2) minus (mu-1 minus mu-2) ] / (standard deviation of the difference)
CALCULATOR
Use the list of differences as data. STAT > TESTS > 2: T-Test.
Conditions required
1. Both samples are simple random samples 2.
Pooled proportion
P-c = (x-A + x-B) / (n-A + n-B)
Distribution
Normal (z-distribution)
Examples
Before-and-after measurements, same person tested under two conditions, two treatments on the same object.