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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 206–210 (Mi tvp2705)

Short Communications

Experiment design for comparison of two normal population parameters

I. N. Volodin

Êazan

Abstract: Two normal population with parameters ($m_1$, $\sigma_1$) and ($m_2$, $\sigma_2$) are given, three pairs of alternative hypotheses being considered:
1) $H_0\colon m_1-m_2=0$, $H_1\colon m_1-m_2\ge\Delta$;
2) $H_0\colon m_1-m_2=0$, $H_1\colon|m_1-m_2|\ge\Delta$;
3) $H_0\colon\sigma_1^2/\sigma_2^2\le k$, $H_1\colon\sigma_1^2/\sigma_2^2\ge k(1+\Delta)$.
Given error probabilities of the first ($\alpha$) and the second kind ($\beta$), two-step procedures are constructed for the first two pairs of hypotheses which enable to determine how many extra observations are needed for the given procedures to have the strength ($\alpha$, $\beta$), the initial ($n_0$, $N_0$) observations being available. These tests have been obtained as a result of applying Stein's procedure to the Bartlette-Scheffe and Student's test.
For the third pair of hypotheses, an asymptotic formula is proposed for the number of observations necessary for Fisher's test to have a given strength ($\alpha$, $\beta$).

Full text: PDF file (434 kB)

English version:
Theory of Probability and its Applications, 1973, 18:1, 198–202

Bibliographic databases:

Citation: I. N. Volodin, “Experiment design for comparison of two normal population parameters”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 206–210; Theory Probab. Appl., 18:1 (1973), 198–202

Citation in format AMSBIB
\Bibitem{Vol73} \by I.~N.~Volodin \paper Experiment design for comparison of two normal population parameters \jour Teor. Veroyatnost. i Primenen. \yr 1973 \vol 18 \issue 1 \pages 206--210 \mathnet{http://mi.mathnet.ru/tvp2705} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=317466} \zmath{https://zbmath.org/?q=an:0277.62017} \transl \jour Theory Probab. Appl. \yr 1973 \vol 18 \issue 1 \pages 198--202 \crossref{https://doi.org/10.1137/1118022}