Question

Aron
	1	2	3	4	Average
8/6/2017	90	138	118	105	112.8
8/19/2017	162	101	120	145	132
9/16/2017	101	129	132	111	118.3
Average	117.7	122.7	123.3	120.3	121

Mjorgan
	1	2	3	4	Average
8/6/2017	115	88	94	102	99.8
8/19/2017	89	75	77	90	82.8
9/16/2017	74	110	117	90	97.8
Average	92.7	91	96	94	93.4

Aron believes there is a distinct difference between not only the games played each night, AND within the date on which they bowled, but also between himself and Mjorgan. Construct a statistical test to determine if this might be the case – where are the real variations in their bowling? Interpret your results in a few sentences.

Answer 1

First we perform 2 way ANOVA: Factor 1: Date and Factor 2: Player and Date has three levels: Level 1(8/6/2017), Level 2 (8/19/2017), Level 3 (9/16/2017) and Player has two levels: Level 1: Aron, Level 2: Mjorgan. ANOVA Table is as follows:

Two-way ANOVA: C1 versus Date, Player

Source DF SS MS F P
Date 2 12.6 6.29 0.02 0.981
Player 1 4565.0 4565.04 14.14 0.001
Interaction 2 1464.6 732.29 2.27 0.132
Error 18 5809.8 322.76
Total 23 11852.0

From the ANOVA table we see that p-value corresponding to interaction (DatexPlayer) is 0.132 which is greater than 0.05 (level of significance) and this implies that the interaction between Date and Player is insignificant. Again there are no significant difference between three dates since the p-value corresponding to date=0.981>0.05. However the two players perform significantly different since p-value= 0.001<0.05. So there is no reason to believe that there is a distinct difference between games played each neight and within the date on which they bowled. However there is a distinct difference betweenAron and Mjorgan.