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I am using the manova() function in R to perform multivariate analysis of variance on my dataset. I have tried using different test statistics such as Pillai's trace, Wilks' lambda, Hoteling's trace, and Roy's largest root. While these test statistics give different test values, they result in the same approximate F and p values. This behavior is observed both with a large dataset (10,000 observations) and a small dataset (10 observations).

[![Test Statistic   Df  Statistic Value Approx F    Num Df  Den Df  Pr(>F)
Pillai's trace  1   0.36007 2812.5  2   9997    < 2.2e-16***
Roy's largest root  1   0.56266 2812.5  2   9997    < 2.2e-16***][1]][1]
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  • $\begingroup$ You have two groups? If so, see en.wikipedia.org/wiki/Multivariate_analysis_of_variance: "In the case of two groups, all the statistics are equivalent and the test reduces to Hotelling's T-square" $\endgroup$
    – Glen_b
    Commented Jun 7 at 3:41
  • $\begingroup$ My data is simulated and all are numeric so no groups are there only the variances in error terms for Y1 and Y2 are changed. In total i have 4 metric variables X1 , X2 (independent) and Y1 and Y2 (dependent with covariance of 0.8), is that could be a reason , do you have any reference to literature? $\endgroup$
    – Praful Kumar
    Commented Jun 8 at 11:06

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