# [G-Power] - Comparison of a-priori sample sizes of MANOVA and ANOVA

#### nora

##### New Member
Hello,

I wanted to calculate my sample sizes a priori in order to find out how many participants I need for my lab experiment. After my lab experiment I want to calculate MANOVA and ANOVA and thus I also made the G-Power analysis for both of them. The results now indicate that I need less participants for calculating the MANOVA than for calculating the ANOVA which I do not understand, because I thought that I would need less participants for the ANOVA than for the MANOVA because in the MANOVA I integrate more variables. May someone explain this phenomena to me?

Here are the results of the G-Power-Analysis:

[2] -- Thursday, November 27, 2014 -- 10:30:03
F tests - ANOVA: Fixed effects, omnibus, one-way
Analysis: A priori: Compute required sample size
Input: Effect size f = 0.25
α err prob = 0.1
Power (1-β err prob) = 0.8
Number of groups = 5
Output: Noncentrality parameter λ = 10.0000000
Critical F = 1.9814824
Numerator df = 4
Denominator df = 155
Total sample size = 160
Actual power = 0.8028612

[3] -- Thursday, November 27, 2014 -- 10:30:27
F tests - MANOVA: Global effects
Options: Pillai V, O'Brien-Shieh Algorithm
Analysis: A priori: Compute required sample size
Input: Effect size f²(V) = 0.0625
α err prob = 0.1
Power (1-β err prob) = 0.8
Number of groups = 5
Response variables = 5
Output: Noncentrality parameter λ = 18.7500000
Critical F = 1.4473573
Numerator df = 20.0000000
Denominator df = 276
Total sample size = 75
Actual power = 0.8111905
Pillai V = 0.2352941

(I chose a high beta-error, because this error is not that relevant for my calculation and analysis)

Thank you very much!