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CPS2099 Takatsugu Yoshioka et al.
Table 1
Upper percentiles and type I error rate
α=0.05 α=0.01
N1 N2 T2 F α1 α2 T2 F α1 α2
10 10 15.16 14.54 0.162 0.057 25.22 22.82 0.073 0.015
20 20 13.43 13.23 0.131 0.053 21.03 20.25 0.049 0.012
40 40 11.12 11.10 0.086 0.050 16.68 16.21 0.027 0.012
80 80 10.31 10.24 0.067 0.050 14.29 14.63 0.016 0.010
2
Note : (0.05) = 9.49, (0.01) = 13.28
2
4
4

4. Discussion and Conclusion
In this study, we have developed the approximate distribution of
Hotelling’s T type test statistics by a constant times an F distribution by
2
adjusting the degrees of freedom. The method of adjusting the degrees of
freedom is estimated unknown parameters of the degrees of freedom of the
F distribution using the asymptotic expansion of the Hotelling’s T type test
2
statistic. The approximate values can be calculated easily and the
approximation is much better than the chi-squared approximation, even when
the sample size is small.

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