Was John Adams more consistent his Junior or Senior year of High School Wrestling? An investigation into my Dad s high school Wrestling Career Amanda Adams Period 1 Statistical Reasoning in Sports December 16, 2013
Was Dad more consistent at scoring team points Senior Year than Junior Year? 2 Table of Contents Introduction...3 Data tables...5 Dotplots...6 Raw Data...6 Deviations...6 Mean Absolute Deviation...7 Standard Deviation...8 Test Statistc...9 Simulation...10 Dotplot...10 Conclusion...11 Work Cited...13
Was Dad more consistent at scoring team points Senior Year than Junior Year? 3 Introduction All my life, I ve grown up knowing that my dad was a wrestler, and that he d been a really good wrestler. As I grew up, and my older brother grew up and started to wrestle, we all go to see just h0w much he d loved the sport. He coached my brother as early as he could start, from when my brother was in 7 th grade. Through the 6 years that my brother wrestled we all got to hear the stories of Dad s wresting days and meet all the dads of wrestlers that had come back to the same tournaments. For this investigation, I chose to look into my dad s wrestling career, but he only has his stats from high school, so unfortunately I could not continue the investigation into his college career. We always knew dad was good, we remembered the story of his undefeated senior year, losing only one match, his very last one, at league finals and taking second, unable to advance to CIF. He lost 2-3 to the same guy who had beaten him his junior year. I ve always admired my dad for his dedication to everything he did. He didn t have an easy life growing up, but he was completely self motivated to excel at wrestling. He worked harder to achieve more than anyone in high school that I know today and he taught us that same desire for success and hard work. I got my stats from our attic, dad was more than happy to get them down for me and go ever every single match, all the tournament brackets and all the opponents that he remembered -- a surprising amount actually. He had all the stats from his junior and senior years of wrestling at Rowland High School, with the exception of Masters his junior year. Junior year, he advanced all the way to masters, but unfortunately, he had his only loss for senior year in the last match of league finals and took second the
Was Dad more consistent at scoring team points Senior Year than Junior Year? 4 year that the CIF rules changed to only allow first place to advance. It was a sad end to his high school career to say the least. He went on to wrestle in college, and again one more time at an open tournament that my brother wrestled in (well after my dad was already 50) and decided he was done for good after breaking his finger in the first period. I chose to compare the varsity points (team Points) that he earned because it is the only measurement that gives a numerical value to a pin, rather than using points that he scored or points scored on him because that makes it so that there is no numerical value for a pin. Null Hypothesis: Dad had the same true Standard deviation of team points scored his junior and sophomore years of wrestling in high school. Alternative Hypothesis: Dad had a smaller true Standard deviation of team points scored his senior year than his junior year.
Was Dad more consistent at scoring team points Senior Year than Junior Year? 5 Data Table Junior Year (1974-1975) Senior Year (1975-1976) Date Score Varsity Points Dec 3, 1974 :14 Pin 6 Dec 5, 1974 10-2 3 Dec 9, 1974 8-5 3 Dec 20-21, 1974 6-8 1 Dec 20-21, 1974 5-0 3 Dec 20-21, 1974 Pin 6 Dec 20-21, 1974 0-4 1 Jan 9, 1975 5-11 1 Jan 16, 1975 9-3 3 Jan 21, 1975 1:05 Pin 6 Jan 23, 1975 :30 Pin 6 Jan 30, 1975 0-2 1 Feb 6, 1975 5-3 3 Feb 13, 1975 League Finals (1 st Place) 3-0 3 Feb 13, 1975 11-0 4 Feb 13, 1975 11-0 4 Feb 15, 1975 CIF (4 th Place) 5:45 Pin 6 Feb 15, 1975 3:09 Pin 0 Feb 15, 1975 10-2 3 Feb 15, 1975 2:30 Pin 6 Feb 15, 1975 9-1 3 Feb 15, 1975 5-4 1 Date Score Varsity Points Nov 26, 1975 16-0 5 Dec 4, 1975 4:30 Pin 6 Dec 8, 1975 16-8 4 Dec 11, 1975 5-5 2 Dec 19-20, 1975 Tournament (1 st ) 14-1 5 Dec 19-20, 1975 7-0 3 Dec 19-20, 1975 10-6 3 Dec 19-20, 1975 Pin 6 Dec 19-20, 1975 2-1 3 Jan 8, 1976 1:45 Pin 6 Jan 15, 1976 4:35 Pin 6 Jan 20, 1976 13-0 5 Jan 29, 1976 :44 Pin 6 Feb 5, 1976 11-0 1 Feb 10, 1976 5-3 1 Feb 17, 1976 League Finals (2 nd ) 9-1 8 Feb 17, 1976 12-4 8 Feb 17, 1976 2-3 2
Was Dad more consistent at scoring team points Senior Year than Junior Year? 6 Dotplots Raw Data Team Points Scored Senior Year Junior Year Mean Median 0 1 2 3 4 5 6 7 8 9 Deviations Deviations (Data - Mean) Senior Year Mean Median Junior Year -4.00-3.00-2.00-1.00 0.00 1.00 2.00 3.00 4.00 The raw data dotplot shows an uneven distribution of points between the scores. The data is not skewed either direction, but not quite symmetrical. The senior year mean and median are higher than the junior year mean and median and there are no outliers for either distribution. Both have the same range, but the senior year distribution is higher than the junior year one. For the deviations graph, both distributions are similar in that they have a peak, but most of the data is evenly spread out making it difficult to determine how many peaks it has. The positive values on the deviation dotplot mean that he performed higher than the average and the negative values mean that he performed lower than the average.
Was Dad more consistent at scoring team points Senior Year than Junior Year? 7 Mean Absolute Deviation Junior Year Mean: 3.32 Deviations: 6-3.32= 2.68 3-3.32= -0.32 3-3.32= -0.32 3-3.32= -0.32 6-3.32= 2.68 3-3.32= -0.32 3-3.32= -0.32 6-3.32= 2.68 6-3.32= 2.68 3-3.32= -0.32 0-3.32= 2.68 1-3.32= -2.32 3-3.32= -0.32 1-3.32= -2.32 6-3.32= 2.68 4-3.32= 0.68 3-3.32= -0.32 1-3.32= -2.32 1-3.32= -2.32 1-3.32= -2.32 4-3.32= 0.68 6-3.32= 2.68 Absolute Value 2.68 0.32 0.32 0.32 2.68 0.32 0.32 2.68 2.68 0.32 3.32 2.32 0.32 2.32 2.68 0.68 0.32 2.32 2.32 2.32 0.68 2.68 Mean Absolute deviation: 1.527 Senior Year Mean: 4.35 Deviations: 5-4.35= 0.65 5-4.35= 0.65 3-4.35= -1.35 1-4.35= -3.35 2-4.35= -2.35 6-4.35= 1.65 3-4.35= -1.35 6-4.35= 1.65 1-4.35= -3.35 4-4.35= -0.35 3-4.35= -1.35 5-4.35= 0.65 8-4.35= 3.65 2-4.35= -2.35 6-4.35= 1.65 6-4.35= 1.65 8-4.35= 3.65 Absolute Value 0.65 0.65 1.35 3.35 2.35 1.65 1.35 1.65 3.35 0.35 1.35 0.65 3.65 2.35 1.65 1.65 3.65 Mean Absolute Deviation: 1.862
Was Dad more consistent at scoring team points Senior Year than Junior Year? 8 Standard Deviation Junior Year Mean: 3.32 Deviations: 6-3.32= 2.68 3-3.32= -0.32 3-3.32= -0.32 3-3.32= -0.32 6-3.32= 2.68 3-3.32= -0.32 3-3.32= -0.32 6-3.32= 2.68 6-3.32= 2.68 3-3.32= -0.32 0-3.32= 2.68 1-3.32= -2.32 3-3.32= -0.32 1-3.32= -2.32 6-3.32= 2.68 4-3.32= 0.68 3-3.32= -0.32 1-3.32= -2.32 1-3.32= -2.32 1-3.32= -2.32 4-3.32= 0.68 6-3.32= 2.68 Squared Deviations: 7.19 0.10 0.10 0.10 7.19 0.10 0.10 7.19 7.19 0.10 11.01 5.37 0.10 5.37 7.19 0.46 0.10 5.37 5.37 5.37 0.46 7.19 Standard Deviation: 1.985 Senior Year Mean: 4.35 Deviations: 5-4.35= 0.65 5-4.35= 0.65 3-4.35= -1.35 1-4.35= -3.35 2-4.35= -2.35 6-4.35= 1.65 3-4.35= -1.35 6-4.35= 1.65 1-4.35= -3.35 4-4.35= -0.35 3-4.35= -1.35 5-4.35= 0.65 8-4.35= 3.65 2-4.35= -2.35 6-4.35= 1.65 6-4.35= 1.65 8-4.35= 3.65 Squared Deviations: 0.42 0.42 1.83 11.24 5.54 2.71 1.83 2.71 11.24 0.12 1.83 0.42 13.30 5.54 2.71 2.71 13.30 Standard Deviation: 2.206
Was Dad more consistent at scoring team points Senior Year than Junior Year? 9 Test Statistic Difference in Standard Deviations: Senior year (2.206) - Junior Year (1.985) = 0.221 Test Statistic: 0.221 A positive test statistic means that senior year had a greater standard deviation than junior. To calculate the test statistic I subtracted senior year s standard deviation from junior year s. Notecard Simulation With 42 notecards, label each with a point value, shuffle and deal into two piles, one with 18, one with 22 for each year. Calculate the standard deviation of each pile and subtract senior year from junior year. Plot each value on a dotplot and repeat 100 times for accuracy.
Was Dad more consistent at scoring team points Senior Year than Junior Year? 10 Simulation Simulated Difference in Standard Deviation Senior - Junior Year 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 The dotplot is fairly symmetrical, definitely unimodal, with no outliers. It has a range of less than 2, and a mean and median around zero. The P-value is 31%, with 31 trials of the simulation falling above the test statistic of 0.221. This means that 31% of the time, the standard deviation of his performance will differ from junior to senior year by 0.221 about 31% of the time. The positive values on the dotplot mean that his standard deviation from junior year was larger than his senior. The minimum of the dotplot is -0.8 and the maximum is 0.8 the mean is 0.0299 and the median is 0.
Was Dad more consistent at scoring team points Senior Year than Junior Year? 11 Conclusion Because the p-value is so large, we cannot reject the null hypothesis. Therefore; we support the null and thus it is plausible that dad s true standard deviation Senior year was the same as Junior year. I believe this is a type 2 error, because both my dad and I think that he performed better, and more consistently senior year than junior. This may be due to the fact that scoring points in wrestling is not the best measure of consistency. More realistically, I realized that my investigation probably would have been better if I had treated the data as categorical instead of numerical, but I was curious to see what conclusion would come of using point values as the measurement. The reason that this did not measure his 15-2-1 season as more consistent than his 15-6-0 season is because there are more point values given for a pin than just a win which offsets the data to count some wins as more than others, and some losses count as more than others depending on how many points were scored. I chose to use the team points scored as my testing variable because it was the only one that gave numerical value to a pin, but it turned out to not work as well as I had hoped. Another error that may have caused junior year to be more consistent than senior is that one of the scores on the old paper that I was copying the statistics from was odd in that the dates were out of order, and it was another loss when dad s record was only one loss his senior year. I later asked him why the match was there and he couldn t remember why the loss was recorded so I left it where it was in the investigation since it was written on the paper, but it s still kind of a mystery match. One last reason that the point values were not an accurate measure is because at the end of senior year in league finals, one of the varsity wrestlers realized that he didn t have and wasn t able to get enough
Was Dad more consistent at scoring team points Senior Year than Junior Year? 12 varsity points to earn his letter, but the coach really thought he deserved it so he inflated the point value of a win to 8 points because it was league finals and this greatly threw off the consistency of all of dad s season. As an experiment, I changed the two 8 point values down to 3 for a win and re calculated the standard deviation, as anticipated, this lowered his standard deviation to less than junior year. Rather than changing my investigation to reflect this, I left it so that we could see the authentic result of the actual points that he got. Hopefully, since this investigation did not turn out as accurately as I had hoped, there will be a future opportunity to investigate my dad s wrestling career.
Was Dad more consistent at scoring team points Senior Year than Junior Year? 13 Work Cited "Statistical Reasoning in Sports." Statistical Reasoning in Sports. W H Freeman & Company, n.d. Web. 19 Dec. 2013.