Quantitative Research on Marathon Times - Essay Example

? Quantitative Research on Marathon Times Even though marathon running has increased its popularity, there exist no data concerning the relationship between marathon times, age, athlete’s level of fitness (expert runner, beginner), fuel (carbohydrates), weather in the course of the marathon, and the miles ran during training per week. This paper sought to find out whether the performance of marathon is linked to age, athlete’s level of fitness (expert runner, beginner), fuel (carbohydrates), weather in the course of the marathon, and the miles ran during training per week. The study involved 15 marathon runners. The participants were given packets of materials which were inclusive of a questionnaire. After filling the questionnaire, they were brought back for analysis. The study established that there existed some relationship among the variables. Introduction For decades, taking part in marathon running by people of different ages and potentials has been increasing at a repaid rate. A research conducted in this field notes out that the approximate marathon number in U S increased to one hundred and forty in 1975 from forty-four in 1969. In this period, there was an increment in the participants by about 500%. Even though marathon is always popular and requires enough preparation, training practice and knowledge, its effectiveness may tend to remain incomplete. More often than not, many runners come up with their programs of training through taking after marathoners who may look successful. For many years, the philosophy of humans has been adjusted to cover distances that are long in each day so as to obtain food for sustaining the metabolism of the brain (Macarthur & North, 2005). In this regard, the high marathon popularity in humans that are modern of all abilities and ages can be seen as a legacy of the human species’ evolutionary capacity to race for distances that are long and using metabolism that is aerobic (Macarthur & North, 2005). Over the last decade, the starters in marathon have increased from 8,000 to 40,000. This implies that taking part in road racing has been increasing by over 50% in the last decade. This popularity is characterized by the existence of recreational marathon racers who finish the 42,195 km in about two hours. However, marathon has a negative effect to the cardiac status and the existences of cardiac deaths that are sudden during marathon have evoked increased debate (Macarthur & North, 2005). Additionally, endurance and energy cost are the two benchmarks for obtaining exceptional performance in running. This is so because marathon runners show out an increased fractional use of oxygen. Considering the coming up of recreational marathon amid the middle-aged class, the debate concerning physiological strain also comes up. A couple of surveys done in marathoners have failed to give out information which could be generalized for the runner’s broad spectrum. This study explores the relationship between one dependent variable and several independent variables. In this regard, the dependent variable is marathon times, whereas the independent variables are age, athlete’s level of fitness (expert runner, beginner), fuel (carbohydrates), weather in the course of the marathon, and the miles ran during training per week. The paper seeks to develop a multiple regression model in which the variable that is dependent is explained by all the given independent variable. Method Participants The opportunity sample for this study was made up of fifteen participants. The participants were obtained from marathon runners. The participants were selected by using the fact that they had to be individuals whose age was below forty years and that they were recreational runners. The participants were also free of pulmonary and cardiac diseases. The participants of this research were volunteers. Three groups consisting of five participants were made. The three groups were given names according to the age range. The first group, which was the 10 to 20 years group, had two women and two men of ages between 10 and 20 years. The second group, which was the 20 to 30 years group, had equally five participants. Of the five subjects, four were women and one was a man. These participants were of age between 20 and 30 years old. The third group, which was the 30 to 40 years group, had four women and one man of ages between 30 and 40 years respectively. The mean age of the first group was about eighteen point two; the mean age for the second group was about twenty-four point two, and that for the third group was about thirty-eight point two. The total mean age of the entire opportunity sample was 32 years. The standard deviation for the subject’s age was six years, their mean weight was 72 kilograms, and their mean height was 180 cm. The participants were familiarized with the procedures of the experiment before the study measurements. The participants also received an explanation concerning the study nature which included the risks that are linked to the performance of a maximum physical effort. The subjects were also requested to give their informed consent voluntarily. This study satisfied the ethical standards that were set by the Helsinki Declaration and the procedure of the research was also recommended by the review board. Research Design In a period of about three weeks before the marathon participation in London, the participants took a laboratory incremental based test. The performance of the test was until full exhaustion and made the participants note the maximum values of different physiological parameters. The protocol made the participants be familiar with the resources that were to be used during the race. The speed of running was 7 km/h and was increased by 2 km/h in every 2 minutes up to exhaustion. All the participants were given a verbalized encouragement in the progress of the race. The study determined the marathon times, athlete’s age, athlete’s level of fitness (expert runner, beginner), fuel (carbohydrates), weather in the course of the marathon, and the miles ran during training per week. Procedure In this study, a questionnaire was used to gather data. Each runner was given a packet of materials which was inclusive of a questionnaire. This packet was given to the marathon runners during the morning race. The questionnaire was made up to assess the runner’s basic features of the program of training such as age, athlete’s level of fitness, fuel, weather in the course of the marathon, and the miles ran during training per week. The period of training was defined as the period that is always before the marathon and the number of days that have been training ones in each week. In this respect, the period of training included days prior to the exact day of marathon, right away from the start of the year. In this case, there were about 54 training days of that type in 1974. Additionally, a background number of characteristics were also assessed: age, athlete’s level of fitness (expert runner, beginner), fuel (Carbohydrates), weather in the course of the marathon, and the miles ran during training per week. The mileage of training in the week before the race was gathered. The data performance was final and intermediate times and was given by the administration of the race. The questionnaires were brought back during the training dinner and through email. About fifteen marathoners brought the questionnaires back. Among the men that completed within two and half hours, 73 percent responded: 65 percent of the male participants completed the race in three hours. The rate of response reduced to about 40 percent in men who took a period longer than four hours in going through the race. In many situations, the racers were educated individuals still in sedentary occupations and some still in school. Only 5% of participants were blue collar workers and 2% of participants were engaged in physical labor. Results The questions of survey gave about three dozen details concerning each participant in the study. The data collected was recorded in Table 1. This result represents the descriptive statistics concerning the given items for the entire group of subjects. The major interest in this case is the tremendous variations of the minimum and maximum values, as explained by 9 to 890 mi run. Prior to the race, the average of the runners was about 336 mi, especially seven and half weeks before the race. Approximately half of the sample displayed an interruption in the training because of illness or rather injuries. About 35% of the participants managed to finish the marathon. Table 1 : Scores on Y= Marathon times, X1= age, X2= athlete’s level of fitness (expert runner, beginner), X3= Fuel, X4= weather in the course of the marathon, and X5= the miles ran during training per week Group 1 Group 2 Group 3 y x1 x2 x3 x4 x5 y x1 x2 x3 x4 x5 y x1 x2 x3 x4 x5 18 14 74 90 23 13 43 21 64 95 23 13 65 31 40 90 23 13 19 15 87 89 21 14 33 22 77 99 21 14 55 33 47 94 21 14 21 16 85 71 22 15 28 26 80 74 22 15 41 35 55 45 22 15 22 17 45 98 25 20 45 28 40 88 25 20 44 38 65 98 25 20 24 20 52 89 27 29 43 29 55 79 27 29 32 39 78 120 27 29 Table 2A: Descriptive statistics for the data collected (N=15) Y   x1   x2   Mean 20.8 Mean 16.4 Mean 68.6 Standard Error 1.067708 Standard Error 1.029563 Standard Error 8.570881 Median 21 Median 16 Median 74 Mode #N/A Mode #N/A Mode #N/A Standard Deviation 2.387467 Standard Deviation 2.302173 Standard Deviation 19.16507 Sample Variance 5.7 Sample Variance 5.3 Sample Variance 367.3 Kurtosis -1.11727 Kurtosis 1.128515 Kurtosis -2.68207 Skewness 0.205753 Skewness 1.032659 Skewness -0.40964 Range 6 Range 6 Range 42 Minimum 18 Minimum 14 Minimum 45 Maximum 24 Maximum 20 Maximum 87 Sum 104 Sum 82 Sum 343 Count 5 Count 5 Count 5 x3   x4   x5   Mean 87.4 Mean 23.6 Mean 18.2 Standard Error 4.43396 Standard Error 1.077033 Standard Error 2.956349 Median 89 Median 23 Median 15 Mode 89 Mode #N/A Mode #N/A Standard Deviation 9.914636 Standard Deviation 2.408319 Standard Deviation 6.610598 Sample Variance 98.3 Sample Variance 5.8 Sample Variance 43.7 Kurtosis 2.998658 Kurtosis -0.9453 Kurtosis 1.66294 Skewness -1.36557 Skewness 0.601364 Skewness 1.468414 Range 27 Range 6 Range 16 Minimum 71 Minimum 21 Minimum 13 Maximum 98 Maximum 27 Maximum 29 Sum 437 Sum 118 Sum 91 Count 5 Count 5 Count 5 Table 2B: Descriptive statistics for the data collected in the second group (N=15) Y   x1   x2   Mean 38.4 Mean 25.2 Mean 63.2 Standard Error 3.340659 Standard Error 1.593738 Standard Error 7.344386 Median 43 Median 26 Median 64 Mode 43 Mode #N/A Mode #N/A Standard Deviation 7.46994 Standard Deviation 3.563706 Standard Deviation 16.42255 Sample Variance 55.8 Sample Variance 12.7 Sample Variance 269.7 Kurtosis -1.84087 Kurtosis -2.68027 Kurtosis -0.95158 Skewness -0.79986 Skewness -0.27177 Skewness -0.53324 Range 17 Range 8 Range 40 Minimum 28 Minimum 21 Minimum 40 Maximum 45 Maximum 29 Maximum 80 Sum 192 Sum 126 Sum 316 Count 5 Count 5 Count 5 x3   x4   x5   Mean 87 Mean 23.6 Mean 18.2 Standard Error 4.701064 Standard Error 1.077033 Standard Error 2.956349 Median 88 Median 23 Median 15 Mode #N/A Mode #N/A Mode #N/A Standard Deviation 10.5119 Standard Deviation 2.408319 Standard Deviation 6.610598 Sample Variance 110.5 Sample Variance 5.8 Sample Variance 43.7 Kurtosis -2.11458 Kurtosis -0.9453 Kurtosis 1.66294 Skewness -0.16788 Skewness 0.601364 Skewness 1.468414 Range 25 Range 6 Range 16 Minimum 74 Minimum 21 Minimum 13 Maximum 99 Maximum 27 Maximum 29 Sum 435 Sum 118 Sum 91 Count 5 Count 5 Count 5 Table 2C: Descriptive statistics for the third group data collected (N=15) Y   x1   x2   Mean 47.4 Mean 35.2 Mean 57 Standard Error 5.732364 Standard Error 1.496663 Standard Error 6.700746 Median 44 Median 35 Median 55 Mode #N/A Mode #N/A Mode #N/A Standard Deviation 12.81796 Standard Deviation 3.34664 Standard Deviation 14.98332 Sample Variance 164.3 Sample Variance 11.2 Sample Variance 224.5 Kurtosis -0.71408 Kurtosis -1.97545 Kurtosis -0.75515 Skewness 0.38324 Skewness -0.08804 Skewness 0.477145 Range 33 Range 8 Range 38 Minimum 32 Minimum 31 Minimum 40 Maximum 65 Maximum 39 Maximum 78 Sum 237 Sum 176 Sum 285 Count 5 Count 5 Count 5 x3   x4   x5   Mean 89.4 Mean 23.6 Mean 18.2 Standard Error 12.25398 Standard Error 1.077033 Standard Error 2.956349 Median 94 Median 23 Median 15 Mode #N/A Mode #N/A Mode #N/A Standard Deviation 27.40073 Standard Deviation 2.408319 Standard Deviation 6.610598 Sample Variance 750.8 Sample Variance 5.8 Sample Variance 43.7 Kurtosis 2.575091 Kurtosis -0.9453 Kurtosis 1.66294 Skewness -1.17759 Skewness 0.601364 Skewness 1.468414 Range 75 Range 6 Range 16 Minimum 45 Minimum 21 Minimum 13 Maximum 120 Maximum 27 Maximum 29 Sum 447 Sum 118 Sum 91 Count 5 Count 5 Count 5 Table 3A: Table showing the correlation analysis   Y x1 x2 x3 x4 x5 y 1 x1 0.973371 1 x2 -0.69062 -0.67541 1 x3 0.046471 0.111719 -0.66074 1 x4 0.808726 0.847707 -0.90347 0.427179 1 x5 0.921902 0.979056 -0.74906 0.261666 0.917061 1 Table3B: correlation for the second group   Y x1 x2 x3 x4 x5 y 1 x1 0.240415 1 x2 -0.88934 -0.55617 1 x3 0.24515 -0.73409 -0.00579 1 x4 0.733741 0.769003 -0.78128 -0.40488 1 x5 0.473869 0.836226 -0.56695 -0.48568 0.917061 1 Table 3C: Correlation for the third group   Y x1 x2 x3 x4 x5 y 1 x1 -0.91731 1 x2 -0.92812 0.97719 1 x3 -0.12158 0.372408 0.453046 1 x4 -0.62521 0.787863 0.845235 0.662225 1 x5 -0.81254 0.879164 0.954076 0.642614 0.917061 1 Discussion From the results that were collected, it was evident that the multivariate relationship models had a number of variables. This implies that some variables are predictors of the interest of theories, whereas some are control variables. In order to give a prediction, Y =marathon times, using several predictors. These are X1= age, X2= athlete’s level of fitness (expert runner, beginner), X3= fuel, X4= weather in the course of the marathon, and X5= the miles ran during training per week. In this study, there are five explanatory variables. Therefore, the multiple regressions function would be given as E(Y) = ? + B1 x1+ B2x2+ B3x3+ B4x4 + B5x5. In the specific values of x1, x2, x3, x4, and x5, the equation identifies the specific mean of the population (Y) for the subjects having x1, x2, x3, x4, and x5. This equation has five predictors. In comparison, the multiple regression model is extremely difficult to be plotted compared to the bivariate function of regression (Favaloro, Lippi, & Guidi, 2008). In this regard, the bivariate function represents an equation that has only two predictors. In order to come up with inferences concerning the parameters, the multiple model of regression needs to be formulated. The model is made up of the function together with a number of assumptions. These assumptions include: for each collection of x1----x5, the distribution of the Y population is normal; in each value combination, the standard deviation of the distribution that is conditional is similar, and the sample is always randomly selected (Favaloro, Lippi, & Guidi, 2008). According to the assumptions, the actual sampling distribution is similar to the one that is quoted. More often than not, these assumptions fail to be satisfied in a perfect way. The inferences that are two-sided are clear to the common standard deviation and normality assumptions. One of the crucial assumptions includes the randomization assumption and function of regression gives a description of how Y (the mean) is explanatory variable dependent. There are two types of tests that are normally used in the multiple regression models. To start with the first test is the independence global test. This is a test that confirms whether any variable is related statistically to y (Cheuvront & Haymes, 2001). Next is the test of the individually regression coefficients in assessing the explanatory variables having significant effects that are partial on Y. In order to test the explanatory variable's collective influence, it is vital to check whether the variables have a collective statistical effect on the response variable. This test would be done through the following test: H0: ?1 = ?2 = ?3 = ?4 = ?5= 0. The equation above shows that the mean of Y is not dependent on the x1, x2, x3, x4, x5 values. Applying assumptions to this equation, the equation would show that Y is statistically independent of the five explanatory variables. The hypothesis that is alternative would be given by: H? : at least one ?i ? 0. The equation above shows that one variable has a relation with the mean Y and the other explanatory variables remain to be control variables. This test finds out whether it, when the values x1, x2, x3,x4, and x5 are used in predicting Y, with the equation of prediction being y = a + b1x1+ b2x2+ b3x3 + b4x4 + b5x5, is better compared to Y. From Table 1 the first variable had y = 18, x1 =14, x2= 74, x3= 90, x4= 23, x5=13. These variables give a suggestion that marathon times is Y= 28.23 + 0.67541(14) +0.66074 (74) +0.427179 (90)+ 0.917061 (23) + 0.662225 (13) = 154.73 The hypothesis concerning ?i is equal to H0: multiple correlation population =0 H? : multiple correlation population > 0 The equivalent will come up since the multiple correlations would be equal to zero only in those circumstances that the coefficient of partial regression is zero (Kenefick, Cheuvront, & Sawka, 2007). This implies that H0 is equal to H0: population squared R = 0. In this hypothesis concerning the k predictors, the statistics of the test would be equal to F = where n= 15, K = number of predictors and R = correlation coefficient. In this study there are five explanatory variables meaning that the correlation among the variables is strong. In this case, after including two variables in the model and adding the third one, including more variables to the multiple regression model, R2 has an extremely very small effect in R2. For instance, the study using age as the only predictor of marathon times give r2= 0.71. Adding the athlete’s level of fitness increases the value of R2 to 0.77. The value increases to 0.79 when the predictor fuel (carbohydrates) is added. When the variables such as weather in the course of the marathon and the miles ran during training per week are added to the model, the value of R2 increases to 0.795. = = 118.26 This is the sampling distribution of the statistics of this study and is referred to as the F distribution (Vihmas, 2010). Whenever the value of R squared has a small increase, it shows that the other predictors fail to add much power in predicting Y, having the values of all the variables within the model. From the results of the study, there was a clear display of the systematic relationship in the subjects’ marathon times, age, athlete’s level of fitness, fuel, weather in the course of the marathon, and the miles ran during training per week. The relationships between these variables were similar, even though the study involved a number of subjects. The entire relationship was in the direction that was expected. The runners who were faster managed to cover more miles than the other runners. References Favaloro, J., Lippi, G., & Guidi, C. (2008). The genetical basics of human athletics performance. Why the psychology components overlooked. Journal of Physiology, 586, 3017. Macarthur, G., & North, N. (2005). Genes and humans elites athletic performance. Journal of Human Genetics, 16, 331–339. Cheuvront, N., & Haymes, M. (2001). Thermoregulations and marathon running, biology and environmental influence. Journal of Sports Med., 31, 743–762. Kenefick, W., Cheuvront, N., & Sawka, N. (2007).Thermoregulation functions during marathons. Journal of Sports Med., 37, 312–315. Vihmas, T. (2010). Impact of weather on the performances of marathon. International Journal of Biometeorol., 54, 297–306. Read More