Where Do the Differences Lie? – an Analysis of Distance Road Running
Total Page：16
File Type：pdf, Size：1020Kb
WHERE DO THE DIFFERENCES LIE? – AN ANALYSIS OF DISTANCE ROAD RUNNING POPULATIONS A Dissertation Submitted to the Graduate Faculty of the North Dakota State University of Agriculture and Applied Science By Jennifer Elizabeth Johnson In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Department: Statistics October 2015 Fargo, North Dakota North Dakota State University Graduate School Title Where Do The Differences Lie? – An Analysis of Distance Road Running Populations By Jennifer Elizabeth Johnson The Supervisory Committee certifies that this disquisition complies with North Dakota State University’s regulations and meets the accepted standards for the degree of DOCTOR OF PHILOSOPHY SUPERVISORY COMMITTEE: Dr. Rhonda Magel Chair Dr. Megan Orr Dr. Ronald Degges Dr. Susan Ray-Degges Approved: 10/30/2015 Dr. Rhonda Magel Date Department Chair ABSTRACT Recently, much research has been focused on the gap in performance between male and female runners. Our research is focused on examining the gap between these two running populations in depth to determine where the specific differences are located. We will investigate three marathons which require some form of qualification before one can participate along with thirty-two races which do not require qualification. For the qualifying marathons, we will examine if the proportion of male and female finishers are equal at predetermined levels of performance. We will also examine the overall descriptive statistics and the age group patterns for each marathon. The non-qualifying races are equally divided among the four popular running distances – marathon, half marathon, ten kilometer (10k) and five kilometer (5k). The proportions of the male and female race finishers were tested to be equal for each individual race at three different levels of performance. To further inspect the population differences, we tested the equality of the distributions through the comparisons of the means, medians, and variances between the two populations. We also examined whether or not the differences followed a specific pattern by investigating the age groups. All results for the individual races were combined using meta-analysis both at the overall race level and for each age group at all four race distances. We performed a separate meta-analysis for the qualifying marathons and for the non-qualifying races. Several differences between the male and female population of distance runners were discovered through our research. These inequalities were not what we expected to see when we began this study. iii ACKNOWLEDGEMENTS I would like to thank Dr. Rhonda Magel for advising me and guiding me throughout the process of researching and writing this dissertation. I would also like to extend thanks to my committee members for taking time out of their busy schedules in order to help me finish this project. Thanks are also due to Dr. Magel in conjunction with the rest of the statistics department for all of the opportunities I was offered during my time at NDSU. I would also like to thank them for the knowledge and inspiration they provided for me to finish this research. I would especially like to thank my fellow graduate students and friends for all of the support they provided for me, whether it was conscientiously done or not. They were always available when I needed someone to bounce ideas off of, for which I am eternally grateful. I would also like to thank my family, related by blood or not, for tolerating all of my complaints and long statistical explanations. They bore all of these instances with only the slightest glossed over looks and rarely asked me to explain all of the terminology used. Thanks to all of you. Finally, I would like to thank my husband, Patrick Simmons, for putting up with all of the late nights, stress, and bad moods that transpired during the completion of my degree as well as the writing and reviewing of this paper. Thank you for compelling me to take breaks when needed as well as keeping me sane. Thank you for everything. iv TABLE OF CONTENTS ABSTRACT ................................................................................................................................... iii ACKNOWLEDGMENTS ............................................................................................................. iv LIST OF TABLES ….. ................................................................................................................... x LIST OF FIGURES .................................................................................................................... xxii CHAPTER 1. INTRODUCTION ................................................................................................... 1 CHAPTER 2. LITERATURE REVIEW ........................................................................................ 6 2.1. Competition between Sexes .................................................................................... 6 2.2. History of Running ............................................................................................... 10 CHAPTER 3. METHODS ............................................................................................................ 14 3.1. Data Description ................................................................................................... 14 3.2. Research Hypotheses ............................................................................................ 16 CHAPTER 4. STATISTICAL TESTS ......................................................................................... 20 4.1. Test of Proportions ................................................................................................ 20 4.2. Test of Variances .................................................................................................. 23 4.3. Test of Means ........................................................................................................ 25 4.4. Test of Medians..................................................................................................... 27 4.5. Test of Distribution ............................................................................................... 29 4.6. Meta-Analysis ....................................................................................................... 31 CHAPTER 5. QUALIFYING RACES ......................................................................................... 33 5.1. Race Descriptions ................................................................................................. 33 5.2. Results .................................................................................................................. 34 CHAPTER 6. NON-QUALIFYING RACES ............................................................................... 61 6.1. Race Descriptions ................................................................................................. 61 6.1.1. Marathon Distributions ............................................................................. 64 v 6.1.1.1. Age Graded Score Distributions ............................................. 64 6.1.1.2. Age Distributions .................................................................... 69 6.1.2. Half Marathon Distributions ..................................................................... 75 6.1.2.1. Age Graded Score Distributions ............................................. 76 6.1.2.2. Age Distributions .................................................................... 82 6.1.3. Ten K Distributions................................................................................... 88 6.1.3.1. Age Graded Score Distributions ............................................. 88 6.1.3.2. Age Distributions .................................................................... 94 6.1.4. Five K Distributions .................................................................................. 99 6.1.4.1. Age Graded Score Distributions ........................................... 100 6.1.4.2. Age Distributions .................................................................. 107 6.2. Test for Proportions ............................................................................................ 113 6.2.1. Marathon Results .................................................................................... 114 6.2.2. Half Marathon Results ............................................................................ 116 6.2.3. Ten K Results .......................................................................................... 119 6.2.4. Five K Results ......................................................................................... 121 6.3. Tests of Distributions .......................................................................................... 123 6.3.1. Marathon Results .................................................................................... 124 6.3.1.1. Age Graded Score Results ....................................................... 124 6.3.1.2. Age Results .............................................................................. 126 6.3.2. Half Marathon Results ............................................................................ 128 6.3.2.1. Age Graded Score Results ...................................................... 128 6.3.2.2. Age Results ............................................................................. 129 6.3.3. Ten K Results .........................................................................................