Question

player 1 player 2 player 3
290   274   297
293   279   295
306   283   300
307   276   309 this one is also with player 3 "287"

The data in the accompanying table indicate the driving​ distance, in​ yards, from a random sample of drives for three golfers.

a. Perform a​ one-way ANOVA using alphaαequals=0.05 to determine if there is a difference in the average driving distance these three players.

b. Perform a multiple comparison test to determine which pairs are different using alphaαequals=0.05

Answer 1

One-way ANOVA: Player 1, Player 2, Player 3

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Player 1, Player 2, Player 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	1250.2	625.08	14.40	0.002
Error	9	390.8	43.42
Total	11	1640.9

Yes, there is a difference.

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Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
6.58913	76.19%	70.90%	57.67%

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b)

Means

Factor	N	Mean	StDev	95% CI
Player 1	4	299.00	8.76	(291.55, 306.45)
Player 2	4	278.00	3.92	(270.55, 285.45)
Player 3	4	300.25	6.18	(292.80, 307.70)

Pooled StDev = 6.58913

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
Player 3	4	300.25	A
Player 1	4	299.00	A
Player 2	4	278.00		B

Means that do not share a letter are significantly different.

Player 1 and Player2 are different.

Player 2 and Player 3 are different