Statistical methods for analysing discrete and categorical data recorded in performance analysis

In this paper, we identify appropriate statistical methods for analysing categorical differences in discrete variables or 'performance indicators' resulting from performance analysis. The random mechanisms associated with discrete events do not follow a normal distribution; that is, the normal distribution is a continuous not a discrete probability distribution. We propose appropriate statistical methods based on two key discrete probability distributions, the Poisson and binomial distributions. Two approaches are proposed and compared using examples from notational analysis. The first approach is based on the classic chi-square test of significance (both the goodness-of-fit test and the test of independence). The second approach adopts a more contemporary method based on log-linear and logit models fitted using the statistical software GLIM. Provided relatively simple one-way and two-way comparisons in categorical data are required, both of these approaches result in very similar conclusions. However, as soon as more complex models or higher-order comparisons are required, the approach based on log-linear and logit models is shown to be more effective. Indeed, when investigating those factors and categorical differences associated with binomial or binary response variables, such as the proportion of winners when attempting decisive shots in squash or the proportion of goals scored from all shots in association football, logit models become the only realistic method available. By applying log-linear and logit models to discrete events resulting from notational analysis, greater insight into the underlying mechanisms associated with sport performance can be achieved.     

Bilateral arm power imbalance in swim bench exercise to exhaustion

We examined the supposition that swimmers may exhibit an imbalance in bilateral arm power output during simulated swimming exercise. Ten competitive front crawl swimmers (5 males, 5 females; age 20.5+/-2.3 years; height 1.74+/-0.09 m; body mass 72.0+/-16.7 kg; 400 m freestyle swim time 278+/-20.5 s; mean +/- s) performed four incremental (10 W x min(-1)) swim ramp tests on a computer-interfaced biokinetic swim bench ergometer. External power output from each arm was measured continuously to exhaustion. The results showed that, throughout the course of the simulated swim, external power output clearly favoured the left arm (F1,9 = 12.5, P= 0.006). This was especially evident in the final 30 s to exhaustion, when 54.0+/-3.87% of external power output was derived from the left arm versus 46.0+/-3.87% from the right arm. The disparity in external power output was further highlighted when the participants were grouped into unilateral and bilateral breathers. Unilateral breathers (n = 5) produced 57.1+/-2.62% of external power output from the left armversus 42.9+/-2.62% from the right arm (P= 0.001). Bilateral breathers (n = 5) exhibited a more balanced external power output of 51.0+/-1.82% from the left arm and 49.0+/-1.82% from the right arm (P = 0.177). Evidence of power imbalance in the simulated swimming stroke may have important implications for optimizing swim performance. The observed power imbalance may be reduced when a bilateral breathing technique is adopted.     

Estimation of thigh muscle and adipose tissue volume using magnetic resonance imaging and anthropometry

Thigh muscle volume is a useful determinant of functional fitness. However, anthropometric prediction of muscle content is influenced by the variability of adipose tissue accumulation. The aims of this study were to predict thigh muscle and adipose tissue volumes from anthropometry and to assess the validity of the method by examining the various components of the measurements and the assumptions involved. The 19 participants (9 men, 10 women; age 23-49 years) varied in adiposity. They all underwent magnetic resonance imaging (MRI) of the upper leg and the eight men and two women with the lowest adiposity underwent detailed anthropometry involving girths and skinfolds. Using MRI as the reference method, muscle volume was predictedfrom anthropometry using a circular concentric model, and the assumptions inherent in the method were tested further using the MRI data alone. Muscle volume was best predicted by anthropometry in the 10 leanest participants using a five-slice truncated cone model that overestimated the mean MRI value by 30% (R2 = 0.95; standard error of estimate = 288 cm3; P < 0.001). A single skinfold plus girth measurement at the mid-thigh almost matched its predictive ability, but with an increased bias. Measurements of leg circumference by means of the two techniques agreed well. The assumption of a circular cross-section was valid. In contrast, the agreement between skinfold thickness measured by caliper and superficial adipose tissue thickness by MRI was poor, contributing to the scatter of fat and lean area comparisons. An anterior skinfold thickness measurement underestimated the area of superficial adipose tissue at that level, particularly at the most proximal and distal sites. Although these limitations increase the uncertainties of muscle volume determination by anthropometry, they do not prevent its valid prediction in leaner individuals. The prediction of superficial adipose tissue was poorer.     

Prediction of maximum oxygen consumption from walking, jogging, or running

The purpose of this study was to develop a submaximal, 1.5-mile endurance test for college-aged students using walking, jogging, or running exercise. College students (N = 101: 52 men, 47 women), ages 18-26years, successfully completed the 1.5-mile test twice, and a maximal graded exercise test. Participants were instructed to achieve a "somewhat hard" exercise intensity (rating of perceived exertion = 13) and maintain a steady pace throughout each 1.5-mile test. Multiple linear regression generated the following prediction equation: VO2 max = 65.404 + 7.707 x gender (1 = male; 0 =female) - 0.159 x body mass (kg) - 0.843 x elapsed exercise time (min; walking, jogging orrunning). This equation shows acceptable validity (R = .86, SEE = 3.37 ml x kg(-1) min(-1)) similar to the accuracy of comparable field tests, and reliability (ICC = .93) is also comparable to similar models. The statistical shrinkage is minimal (R(press) = 0.85, SEE(press) = 3.51 ml x kg(-) x min(-1)); hence, it should provide comparable results when applied to other similar samples. A regression model (R =.90, and SEE = 2.87 ml x kg(-1) min(-1)) including exercise heart rate was also developed: VO2 max = 100.162 +/- 7.301 x gender(1 = male; 0 =female) - 0.164 x body mass (kg) - 1.273 x elapsed exercise time -0.156 x exercise heart rate, for those who have access to electronic heart rate monitors. This submaximal 1.5-mile test accurately predicts maximal oxygen uptake (VO2max) without measuring heart rate and is similar to the 1.5-mile run in that it allowsfor mass testing and requires only a flat, measured distance and a stopwatch. Further, it can accommodate a wide range of fitness levels (from walkers to runners).     

On the acoustic signature of golf ball impact

In this paper, we present results on the measurement and analysis of the sound that is produced by the sharp impact loading of a golf ball by a flat massive object (e.g. the face of a golf club). We discuss: (a) the motivation for such a study; (b) some necessary background information on how golf balls vibrate; (c) the techniques used to acquire and analyse the data; and (d) an analysis of the sound made by dropping balls on a smooth, massive concrete target surface. These results establish a simple method for rapid and non-destructive measurement of the effective high-frequency elastic shear moduli of balls and ball cores.     

Book reviews

Gaining Independence: A Manual for Planning the Launch of a Nonprofit Electronic Publishing Venture, version 1.0 by Howard Goldstein Published by SPARC, available online: http://www.arl.org/sparc/GI Indexers and Indexing in Fact and Fiction edited by Hazel K. Bell The British Library, London, 2001. Pp. 160. Paper, £16. ISBN 0-7123-4729-1 Preservation Management of Digital Materials: A Handbook by Maggie Jones and Neil Beagrie The British Library, Nov. 2001. Pp. 145. Spiral bound, £15.00. ISBN 0 7123 0886 5. Copies can be ordered from Turpin Distribution Services Ltd. Publishing Law, 2nd edn by Hugh Jones and Christopher Benson Routledge, 2002. Cased, £65.00, ISBN 0-415-26153-8; paper, £24.99, ISBN 0-415-26154-6 How to Survive Peer Review by Elizabeth Wager, Fiona Godlee and Tom Jefferson London: BMJ Books, 2002. Pp. v + 62. £12.95. ISBN 0-7279-1686-6     

Convergence: An investment perspective

Conclusion  Convergence is a very exciting model and one that holds, unforeseen opportunities. However in the current economic environment, the investment community is hesitant to recommend that communications companies devote many resources in that area. The convergence mode must prove that it can generate revenue and profits. Yet, it is limited to an advertising-supported model—a part of the communications industry that has struggled during the past, year due to the recession. The increased advertising revenue that would be generated by the convergence model is tainted—most likely taking advertising share away from the traditional media segments that are supporting the model. Tied to the convergence model is a high dependency on the Internet. Internet advertising is not local. In addition, financial data clearly illustrates that the Internet has caused profit margins to decrease substantially, something that the traditional media company supporting the convergence model can not allow to happen. Finally, FCC deregulation with regards to television station cap restrictions, cable system operators owning broadcasters in the same market, and cross ownership of newspapers and television stations in the same market, will most likely have a negative impact on the convergence model. If a communications company should decide to go forward with convergence, there are five rules that should be followed:

The effect of ball carrying method on sprint speed in rugby union football players

Different methods of ball carrying can be used when a player runs with the ball in rugby union. We examined how three methods of ball carrying influenced sprinting speed: using both hands, under the left arm and under the right arm. These methods were compared with running without the ball. Our aim was to determine which method of ball carrying optimizes sprinting speed. Altogether, 48 rugby union players (age 21 +/- 2 years, height 1.83 +/- 0.1 m, body mass 85.3 +/- 12 kg, body fat 14 +/- 5%; mean +/- s) were recruited. The players performed twelve 30-m sprints in total (each player performed three trials under each of three methods of carrying the ball and sprinting without the ball). The design of the study was a form of Latin rectangle, balanced across the trial order for each of the methods and for pairwise combinations of the methods in blocks of four per trial. Each sprint consisted of a 10-m rolling start, followed by a 20-m timed section using electronic timing gates. Compared with sprinting 20 m without the ball (2.58 +/- 0.16 s), using both hands (2.62 +/- 0.16 s) led to a significantly slower time (P < 0.05). Sprinting 20 m with the ball under the left arm (2.61 +/- 0.15 s) or under the right arm (2.60 +/- 0.17 s) was significantly quicker than when using 'both hands' (P < 0.05), and both these methods were significantly slower than when running without the ball (P < 0.05). Accordingly, running with the ball in both hands led to the greatest decrement in sprinting performance, although carrying the ball under one arm also reduced the players' sprinting ability. Our results indicate that to gain a speed advantage players should carry the ball under one arm.     

Motivation for physical activity in young people: entity and incremental beliefs about athletic ability

Three studies are reported of children and youth aged 11-19 years (n = 3478) examining the nature of beliefs about athletic ability. Drawing on related research in academic, moral and stereotyping domains, development of a psychometric instrument assessing athletic ability beliefs is detailed. Support was found for a multidimensional hierarchical structure that is invariant across age and gender. Confirmatory factor analysis revealed a structure comprising two higher-order factors of entity and incremental beliefs underpinned by beliefs that athletic ability is stable and a gift (entity), and is open to improvement and can be developed through learning (incremental). Incremental beliefs, indirectly through a task goal orientation, and entity beliefs directly, predicted self-reported amotivation towards physical education and sport. On the other hand, enjoyment of physical activity in youth was predicted directly by task orientation and incremental beliefs. Predictions concerning the moderating role of perceived competence were not supported. Our findings highlight the importance of ability beliefs and goals in understanding the determinants of physical activity in children and youth.