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).

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]

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).

        Df  Pillai approx F num Df den Df    Pr(>F)    

X 1 0.36007 2812.5 2 9997 < 2.2e-16 *** Residuals 9998

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

        Df     Roy approx F num Df den Df    Pr(>F)    

X 1 0.56266 2812.5 2 9997 < 2.2e-16 *** Residuals 9998

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

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).