Question

Langolis and Roggman (1990) took photographs of numerous human faces. From these photographs, they used a computer to average the faces together to create 5 prototypical faces. These prototypes differed in the number of faces averaged together to make each prototype (Faces used to create the prototypes: 2, 4, 8, 16, and 32). Next, participants were randomly placed into 5 groups, with each group tasked with rating the attractiveness of one of the faces. Ratings for attractiveness were whole numbers that ranged from 1 (not attractive) to 5 (very attractive). The results are below. Langolis and Roggman wanted to determine if the number of faces used to make a prototype face influences the attractiveness of the prototype face. Please evaluate their question using an α = .05Langolis and Roggman (1990) took photographs of numerous human faces. From these photographs, they used a computer to average the faces together to create 5 prototypical faces. These prototypes differed in the number of faces averaged together to make each prototype (Faces used to create the prototypes: 2, 4, 8, 16, and 32). Next, participants were randomly placed into 5 groups, with each group tasked with rating the attractiveness of one of the faces. Ratings for attractiveness were whole numbers that ranged from 1 (not attractive) to 5 (very attractive). The results are below. Langolis and Roggman wanted to determine if the number of faces used to make a prototype face influences the attractiveness of the prototype face. Please evaluate their question using an α = .05.

group 1	group 2	group 3	group 4	group 5
2.201	1.893	2.906	3.233	3.200
2.411	3.102	2.118	3.505	3.253
2.407	2.355	3.226	3.192	3.357
2.403	3.644	2.811	3.209	3.169
2.826	2.767	2.857	2.860	3.291
3.380	2.109	3.422	3.111	3.290

1. Calculate Cohen’s d (an estimate of effect size) for the difference between groups 1 and 5.

Answer 1

	group 1	group 2	group 3	group 4	group 5
	2.201	1.893	2.906	3.233	3.2
	2.411	3.102	2.118	3.505	3.253
	2.407	2.355	3.226	3.192	3.357
	2.403	3.644	2.811	3.209	3.169
	2.826	2.767	2.857	2.86	3.291
	3.38	2.109	3.422	3.111	3.29
Mean	2.604666667	2.645	2.89	3.185	3.26
SD	0.431352601	0.657059206	0.44709954	0.20805288	0.068117545

Cohen's d = (M₂ - M₁) ⁄ SD_pooled

SD_pooled = √((SD₁² + SD₂²) ⁄ 2) = √((0.4314² + 0.0681²) ⁄ 2) = √((0.1861 + 0.0046) ⁄ 2) = 0.3088

Cohen's d = (M₂ - M₁) ⁄ SD_pooled = (3.26 - 2.61) / 0.3088 = 2.1049