Chapter 10 extends hypothesis testing and confidence interval concepts to compare two populations. It covers methods for:
Use when two samples are independent and population variances are assumed equal.
Test statistic:
t = (X̄₁ - X̄₂) / sqrt[ sp²(1/n₁ + 1/n₂) ]
where sp² = [(n₁ - 1)s₁² + (n₂ - 1)s₂²] / (n₁ + n₂ - 2)
df: n₁ + n₂ - 2
Use when variances are not assumed equal.
t = (X̄₁ - X̄₂) / sqrt[ s₁²/n₁ + s₂²/n₂ ]
df: complicated Satterthwaite formula (Excel or software handles this)
(X̄₁ - X̄₂) ± tα/2 × SE
Use when comparing two sets of related data, such as before-and-after measurements.
t = (D̄ - 0) / (sD / sqrt(n))
Where D̄ = mean of the differences and sD = std dev of the differences.
To test if two variances are equal:
F = s₁² / s₂² (s₁² > s₂² by convention)
dfnumerator = n₁ - 1, dfdenominator = n₂ - 1
Compare to critical value from F-table or use F.DIST.RT in Excel.
T.TEST(array1, array2, tails, type)CONFIDENCE.T(alpha, std_dev, size)F.TEST(array1, array2)VAR.S, VAR.P, STDEV.S, STDEV.P