# On the simultaneous anova and manova tests

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## Summary

In the present paper, the simultaneous confidence intervals associated with the Simultaneous Multivariate Analysis of Variance (SMANOVA) tests are derived when the hypotheses can be tested in a “quasi-independentrd manner. With respect to the Simultaneous Analysis of Variance (SANOVA) test, the quasi-independence is weakened and the distribution problems are investigated when the joint distribution of the sums of squares associated with various hypotheses is a “multivariate chi-square ” distribution. It is shown that the lengths of the confidence intervals associated with the SANOVA test (dependent case) are shorter than the lengths of the corresponding confidence intervals obtained by using Scheffé’s method when the hypotheses on several contrasts are tested simultaneously. It is also shown that the SMANOVA test yields narrower confidence intervals than the MANOVA test when several quasi-independent hypotheses are tested simultaneously.

## Keywords

Joint Distribution Large Root Frequency Function Confidence Bound Wishart Distribution## References

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