／var／logmarcus chiu

Satterthwaite's Approximation

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Satterthwaite’s Approximation

  • 𝑣 =Β [𝑠𝑋2/𝑛𝑋 +Β π‘ π‘Œ2/π‘›π‘Œ]2/Β [ 𝑠𝑋4/(𝑛𝑋2(𝑛𝑋-1)) +Β π‘ π‘Œ4/(π‘›π‘Œ2(π‘›π‘ŒΒ -1))Β ]

for example, the 100(1-𝛼)% CI for (πœ‡π‘‹-πœ‡π‘Œ) when

  • (𝑋̅-π‘ŒΜ…) ± 𝑑𝛼/2,π‘£Β·π‘Ÿπ‘œπ‘œπ‘‘(𝑠𝑋2/𝑛𝑋 +Β π‘ π‘Œ2/π‘›π‘Œ)