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ANOVA and Goodness of Fit Analysis

The data for the pitchers represent the top 50 pitchers in both leagues when selected on 5-6-2005.
Perform the following analyses on the data, interpret your findings and summarize what each analysis means.

2. Goodness of Fit Analysis -
Is there a difference in how pitchers develop ERAs?
Earned Run Average is a metric that is used to gauge how well pitchers are doing. ERA is an average of the earned runs per innings pitched, a metric of runs that are batted in against that pitcher not counting errors.
Divide the ERA numbers into the following groups: less than 2, 2-3, 3-4, 4-5, 5-6 so that you have a single row of with 5 columns,
it is not necessary to break this down by league or division. The numbers in each of the cells should represent the count in each of the categories.
Is there evidence to suggest that the ERAs are not evenly distributed between 0 and 6?
Is this a significant difference?
What does this mean practically?

4. ANOVA 2 -
Use the Pitcher worksheet for the second analysis. Since It was still early in the year when the data were collected and there had been bad weather in the East coast,
do a statistical analysis to see which of the three regions (West, Central, or East) has the lowest ERA.
Sort the pitching data by region before you do the analysis, there is no need to break these out by League.
·         Is the analysis significant? What does this mean?
·         If the test is significant, run the Tukey analysis and interpret.
Player TEAM League Region ERA HR BB SO
1 MIN American Central 3.29 5 5 52
2 NYM National East 2.51 1 8 52
3 SD National West 2.32 4 8 49
4 HOU National Central 1.29 2 13 44
5 PHI National East 1.34 3 10 44
6 NYY American East 3.74 6 9 43
7 FLA National East 2.72 4 13 43
8 CHC National Central 4.23 6 16 37
9 SF National West 3.76 5 18 37
10 TOR American East 3.78 6 8 36
11 WSH National East 3.72 2 14 36
12 BAL American East 2.5 1 7 36
13 ARI National West 5.11 5 8 36
14 STL National Central 3.86 4 7 35
15 ATL National East 3.22 3 12 34
16 DET American Central 3.92 3 13 33
17 MIN American Central 3.6 7 1 31
18 LAA American West 3.03 4 13 30
19 CWS American Central 4.01 5 9 29
20 BAL American East 3.55 2 16 29
21 ATL National East 2.85 2 8 29
22 PIT National Central 4.91 6 21 28
23 CLE American Central 4.1 3 10 28
24 HOU National Central 3.29 4 12 28
25 STL National Central 2.85 2 12 27
26 ATL National East 2.18 3 11 27
27 COL National West 5.26 6 27 27
28 ARI National West 3.2 2 15 27
29 LAA American West 2.72 5 10 27
30 CIN National Central 3.96 4 12 26
31 LAD National West 1.96 2 9 26
32 WSH National East 4.04 3 18 25
33 BOS American East 2.97 3 11 25
34 HOU National Central 3.23 3 9 24
35 CWS American Central 2.83 3 11 23
36 BOS American East 3.18 4 9 23
37 KC American Central 5.03 3 17 22
38 LAD National West 5.7 2 7 21
39 ARI National West 3.86 6 16 21
40 PIT National Central 3.05 1 12 20
41 STL National Central 2.93 2 9 20
42 TOR American East 2.48 2 13 20
43 OAK American West 5.84 5 11 20
44 SF National West 4.89 3 12 18
45 LAA American West 4.85 2 5 18
46 CWS American Central 1.38 1 6 17
47 PHI National East 2.81 7 8 16
48 ATL National East 2.47 4 11 16
49 TEX American West 2.11 1 14 16
50 SEA American West 4.74 6 14 10

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Solution Summary

This in-depth solution uses statistical methods to apply to data collected on pitchers such as Goodness of Fit Analysis and ANOVA. It also conducts an ANOVA test by providing the null and alternative hypothesis, calculating the chi-square statistic and comparing it to the p-value. A final decision is made to accept or reject the null hypothesis.

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