Non-Parametric Hypothesis Testing Paper

Non-Parametric Hypothesis Testing Paper

Non-parametric Hypothesis Testing Paper
It is unclear if the home-run data follows a normal distribution. It is necessary for the data to be roughly normal so team B can use the standard-normal curve to make inferences. As a precaution team B will use a non-parametric test which does not make the assumption of normality by converting the home-run data into ranks, then comparing the ranks between the two team-types.
Five-Step Hypothesis Test
Step 1: State the null and alternative hypothesis
Null hypothesis statement: There is no difference in homeruns between teams with high and low payrolls.
Alternative hypothesis statement: Higher paid teams generate more home-runs than lower-paid teams.
First team B will rank the home-runs for each team from lowest to highest. For ties team B will assign the same value.
MLB Teams 2005 Team Salaries 2005 Home Runs Number Group HR-Rank
Boston $123,505,125.00 199 2 Top 8
New York Mets $101,305,821.00 175 3 Top 6
San Francisco $90,199,500.00 128 7 Top 1
Los Angeles Dodgers $83,039,000.00 149 11 Top 3
Baltimore $73,914,333.00 189 14 Top 7
Cincinnati $61,892,583.00 222 3 Bottom 10
Florida $60,408,834.00 128 4 Bottom 1
Colorado $48,155,000.00 150 9 Bottom 4
Cleveland $41,502,500.00 207 11 Bottom 9
Tampa Bay $29,679,067.00 157 15 Bottom 5

Step 2: Select the level of significance
Team B will accept a level of significance for this hypothesis test of α = 0.05. Team B feels comfortable with this amount of risk in our willingness to reject the null hypothesis. The level of significance is the level of risk that the researcher is willing to accept in making an incorrect decision.
Next team B finds the critical value for the Wilcoxon test by using a table of values for sample sizes of 5 and 5 and 1-tailed alpha of .05 which gives us a critical value of 20.
Sum of Ranks for Top 25
Sum of Ranks for Bottom 29
Test Stat W (1 Tailed) 20

Top Ranks > Test Stat Fail to Reject Null

Step 3: Choose a test...

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