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Is there a significant difference between the scores of Olympic Gymnasts born August 1995-December 2000 and born January 1986-July 1995 when analyzing scores from 2016 Rio De Janeiro women’s gymnastics All-Around competition? The Summer Olympics are an event looked forward to by a large population of the world. Athletes from countries all over the world come together to compete and share the love they have for their sport. The Olympics are a chance for countries to show off their best and brightest in each event available. Everyone holds hope that their own country will walk away with the most medals, and a new reputation. The love each athlete carries with them for their sport is seen through their extremely hard work and the most elite level of competition. Women’s gymnastics brings a special kind of athlete to the Olympics.
Gymnasts are some of the youngest athletes to compete, usually sending girls who are just barely hitting the minimum age to attend the Olympics, because gymnasts hit maximum physical fitness at such a young age. The physical demand the sport puts on the body creates conditions in which it becomes hard to seriously continue gymnastics much past a gymnast’s early twenties. There is always, what you might call, and “outlier” who seems much too old to be competing in the sport of gymnastics. To a viewer who has knowledge of the sport, these “outliers” (usually) show a less than top performance when compared to the youngest girls in the arena. This discrepancy in age was always something that intrigued me when I watched the gymnastics events.
Being a gymnast myself, and knowing the harsh conditions the body is put under, I was always shocked when anyone much older than twenty-three had qualified and was competing at the Olympics in women’s gymnastics. The ages of the gymnasts obviously have an effect on their performance, but in what way for each person? Would the older gymnasts compete more efficiently because of their long experience in the sport and with high pressure meets such as the Olympics? Or would the younger gymnasts compete and score better, because of the lesser amount of years waring down their bodies and the more potential they have in front of them? From a gymnast’s perspective, I also noticed that usually, an elite level gymnast’s first Olympics was their most successful. Most extremely successful gymnasts compete at their first Olympics when they would fall into the younger gymnast category. More than those factors could be observed when looking at if age affects the scores of gymnasts, rather than just performance, but that is how I got to thinking about the comparison of the two age groups, to see if the difference in scoring was simply by chance or if their ages played a larger role. This investigate will answer the question: Is there a significant difference between the scores of Olympic Gymnasts born August 1995-December 2000 and born January 1986-July 1995 when analyzing scores from 2016 Rio De Janeiro women’s gymnastics All-Around competition? To begin, the samples are organized into their specific age groups, using the top twenty gymnasts from the women’s individual all-around competition. In their age groups, the gymnasts are organized by their final placing in the meet, starting at the lower numbers at the top and then increasing in place value as the chart goes down. Each sample has ten gymnasts that fall into the age range presented.
The gymnast’s scores and placements come from the Women’s Individual All-Around competition. In one women’s gymnastics competition any given gymnast will compete for four events: vault, bars, beam, and floor. At each event, they are given a score out of ten, which begins at ten and as the routine is performed judges take deductions from. The gymnasts are also awarded a score for difficulty for each event. This score starts at zero and as the routine progresses is awarded points for higher difficulty skills and connections of skills being performed. When the routine is finished the final score out of ten and final difficulty score is added together to be the gymnast’s ultimate score for that event. At the end of competing for all four events, each individual score is added together to create the all-around score, which is what is seen in the charts above. An independent unpaired t-test will be run between the two sets of data to see if there is a significant difference between the age group with birthdates August 1995-December 2000 and the dates of January 1986-July 1995 (“ABA Keywords.”). This will determine if the difference in scoring was due to chance or if there is a truly significant difference caused by another factor, in this case, age.
The t-test will be run using the equation below: tobs=x1-x2s21n1+s22n2The alternative hypothesis for this investigation states that there will be a significant difference present between the two groups of gymnasts. To be able to accept this hypothesis, the end calculated t value would have to be greater than the critical t value. The null hypothesis would consequently be that there is no significant difference between the two groups of gymnasts. The null hypothesis is accepted when the calculated t value is less than the critical t value. T-test calculations begin with the calculation of the mean for each sample, adding up each of the values and then dividing by the total number of terms. Sample 1 mean = 62.198 + 58.298 + 58.032 + 57.965 + 57.632 + 56.965 + 56.883 + 56.665 + 56.365 + 56.299 = 577.302/10 = 57.7302 ? 57.730 Sample 2 mean = 57.5172 ? 57.517 The same method as used to calculate the sample 1 mean was used to calculate sample 2 mean.These values are then used to calculate this part of the t-test equation: x1-x2.57.730-57.517= .213 Following that, the standard deviation is calculated using the following equation: SD=x-2N Sample 1: Mean () = 57.7302 Each data point’s square of distance to the mean = Data Point Squared distance from mean62.19819.96158.2980.3223958.0320.0910857.9650.0551357.6320.0096456.9650.5855356.8830.7177456.6651.134656.3651.863756.2992.0483Addition of all squared distances: 19.961 + 0.32239 + 0.09108 + 0.05513 + 0.00964 + 0.58553 + 0.71774 + 1.1346 + 1.8637 + 2.0483 = 26.78911 ? 26.789 Division by number of data points in sample: 26.789/10= 2.678911 ? 2.6789 Take square root: 2.6789 = 1.636737914 ? 1.6367 Standard Deviation for sample 1 = 1.6367 Sample 2 Standard Deviation =1.241373417 ? 1.2413 The above process is used to determine the standard deviation of sample 2 as well.(“Calculating standard deviation step by step (Article).”) The standard deviations are then divided by the sample size of each group (10) and added together: Sample 1: 1.6367/10 = 0.16367Sample 2: 1.2413/10 = 0.124130.16367 + 0.12413 = 0.2878 This value is square rooted to find the standard error: 0.2878 = 0.5364803174 ? 0.53648 Then the values calculated above (difference in means and standard error) will be divided, which give the calculated t-value: 0.2130.53648= 0.3970325082 ? 0.39703 = Calculated T value From there the degrees of freedom are found: Degrees of freedom = (10 + 10) – 2 = 18 The degrees of freedom and p value are used to find the “Critical T-Value”. This will be found using a critical t-value chart; on this chart, the degrees of freedom are located on the right-hand side and p values on the top. By locating the degrees of freedom (18) and then following across to the selected p-value (5% or 0.05) the critical t-value can be found. The value was found to be 2.101 for this specific t-test. The calculated t-value being less than the critical t-value means the null hypothesis of no significant difference is accepted.
Consequently, the alternative hypothesis is rejected. The results show that there is no significant difference between the ages of Olympic gymnasts and their scores. Graph 1: The graph error bars show a large overlap, this also suggests there is no significant difference between the two age group’s scores. This means that the difference in scores was not due to their ages, it is due to chance. While things like practice hours, experience, coaching, etc. do affect the score a gymnast receives at a competition when they were born does not give them an edge up in the competition, but these results have some surprising factors to them. I realize that judges are not specifically looking for the ages of competitors, and using this as a scoring indicator. Watching recent Summer Olympics and returning gymnasts gave me a strong suggestion that their age had something to do with the obvious decrease in scores. This drop in performance is affected by something over the four years it takes to get from one Olympics to the next, but this analysis allows the ruling out of age as the sole factor. This investigation was limited by the small sample size.
To continue the investigation, I could run the same t-test, but compare different scores and competitions from the 2016 Olympics, as well as previous Olympics. This would create a larger database, and more accurate results would be produced and analyzed. The number of competitors in the competition limited the sample size to ten each, while still being able to stay in the age groups chosen. This investigation answered the question I set out to find an answer too. It provided a straightforward answer to the proposed question at hand. Although it was not the results I expected, the question was still answered.
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