The Detection of Types among Decathletes using Configural Frequency Analysis (CFA)

Transcription

1 Psychology Science, Volume 47, 2005 (3/4), p The Detection of Types among Decathletes using Configural Frequency Analysis (CFA) MARK STEMMLER 1 & GÜNTHER BÄUMLER 2 Abstract The aim of this exploratory study was to detect among decathletes types of specialization with the help of a one sample configural frequency analysis (CFA). The sample consisted of the performances of 514 decathlon athletes, who were ranked among the top 100 athletes of the world from 1984 to Due to the fact that some athletes were ranked repeatedly among the top 100 world s best athletes, each athlete was listed only once with his best performance. Due to sample size constraints only six out of the ten events were entered into a CFA. Therefore, a total of five CFAs with different combinations of events were conducted. The analysed sets of events were derived from factor analyses which were performed in advance. The resulting number of types varied between one and five. The resulting types could be labelled either allround-types who were proficient in three out of four or in all four factors of performances (i.e., sprinting, ing, ing and stamina) or specialist-types who were proficient in only two factors or two events (e.g., factors ing and stamina; events javelin and 1500m run or shot put and discus or 100m run and 1500m run). In two cases solitary-types evolved with excellent performances in shot put or 1500m run. The 1500m run was part of most types detected. The results suggested that there exist meaningful decathlon types who can be detected with CFA. Key words: Athletics, Configural Frequency Analysis, CFA, Decathlon, Factor Analysis, Types 1 PD Dr. Mark Stemmler, Ph.D., Universität Erlangen-Nürnberg, Institut für Psychologie, Bismarckstr. 1, D Erlangen; mkstemmler@phil.uni-erlangen.de 2 Prof. Dr. em. Günther Bäumler, Technische Universität München, Institut für Sportwissenschaft, Connollystr. 32, D München,

2 448 M. Stemmler & G. Bäumler 1. Types of decathlon athletes The aim of the decathlon is the detection of versatile track-and-field athletes. The abilities required by the multi-events are based on different biomechanical and physiological attributes, therefore decathletes represent a compromise of the different types of track-andfield athletes. That is why decathletes who show excellent performances in all ten events are rare. Bruce Jenner, olympic winner in 1976, Daley Thompson, olympic winner in 1984 and Jürgen Hingsen, winner of the olympic silver medal in 1984, represented those rarely seen allround-athletes, however, all of them had their own specialties. To belong into the group of the 100 top ranking athletes, it is at least necessary to perform exceptionally in several out of the ten events, e.g., in the ing events and in one other event. Such a decathlete, a specialist in ing having an extraordinary body height and body mass, was Vasili Kuznyetsov (owner of a world record, winner of the bronze medal in 1956 and 1960, three times European champion and eight times champion of the Soviet Republic) with a body height of 1,85m and 84 kg weight and with excellent performances, for the time being, in shot put (15,51m), discus (50,52m) and javelin (71,20m) and reasonable performances in the other events (cf. Zarnowski 1988, 91ff, 186, 189). The same principle can be applied to other body types and aptitudes, taking for instance the running and ing events, here other body types and specialties can be expected. Speaking of specialties one often talks about the runner types or er types, or also about the combined runnerer type or the combined sprinting-ing type. Although such terms are frequently used in regard to training or competition, there is no exact method to identify decathlon ability types; therefore, up-to-date every possible combination of exceptional performances in events might be called a type. To avoid such arbitrariness it is of most importance to develop a scientifically based definition of types of performances to differentiate them from artificial pseudo-types. 2. A scientific definition of type In the human and the behavioural sciences, e.g., anthropology, psychology and medicine, types and classifications have a long tradition. However, it was only a few decades ago that G. A. Lienert came up with a scientific definition of types which is based on a stochastic model (used in the analysis of multi-dimensional contingency tables). This sort of type which was closely related to the clinical term of a syndrome and which was also different from the definition of a cluster (cf. Krauth and Lienert 1973, Lienert and von Eye 1985, von Eye and Lienert 1989, Wüpper 1988, p. 20, Lautsch and Lienert 1993, 108 ff., Lautsch and von Weber 1995, 85 ff.) is defined as a multivariate configuration of features, which is based on a significant statistical association. Or put it differently (cf. Lienert 1973, in Krauth and Lienert 1973, p. 31) and more precisely, a type is a feature configuration..., which appears (significantly) more often than the frequencies of the sole features under the null hypothesis of total independence. Lienert and his colleagues suggested configural frequency analysis (CFA) as an appropriate non-parametric tool to detect such types as mentioned above. CFA has proven superiority over traditional statistical tools for the detection of types (e.g., factor analysis or its

3 The detection of types among decathletes using Configural Frequency Analysis (CFA) 449 inversion, the type analysis), because CFA detects not only first order interactions but also interactions of a higher order (Lienert 1969, p. 245, Krauth and Lienert 1973a, p. 13). 3. Aim of the study: The search for scientifically defined types of decathlon athletes Based on substantive (i.e., biomechanical) arguments, the existence of types of decathletes seems to be obvious. Therefore, CFA was applied as an appropriate statistical tool to detect decathlon-types. The nature of the analyses presented below is exploratory. 4. Methods The sample consisted of 514 decathlon athletes who appeared in the Yearbooks of the International Amateur Athletic Federation (IAAF) from 1984 to 2000 as the top 100 of each year. Of the athletes, who were among the top 100 in more than one year, only the very best performance with regard to the obtained total score was used, therefore each athlete s performance was counted only once. The analyses were based on the performances in the ten events, measured in meters and seconds. Anthropometrical data were not available. The 10 events analysed were: 100m dash (sec), long (m), shot put (m), high (m), 400m run (sec), 110m hurdles (sec), discus (m), pole vault (m), javelin (m) und 1500m run (sec). The longest running event is the 1500m run, which belongs to the middle distance races, whereas the 400m run is in between sprint and the middle distance race. The most demanding event of the decathlon in terms of movement technics is the pole vault, which requires years of learning and training, and therefore is not very much loved by the decathletes. A serious methodological problem was based on the fact that an explorative CFA with all ten decathlon events would have required a sample size of more than 5000 subjects (the 10 exact number would be 5 2 = = 5120 subjects). This formula calculates the required minimum expected frequency for the Pearsons s chi-square test statistic which needs the minimum of five subjects per cell; other commonly used test statistics in CFA need less expected frequencies per cell, however, this formula gives you a reasonable estimate of the required optimal sample size. With our sample size of N = 514 only a CFA with a maximum of 6 variables would be meaningful; a CFA with 7 variables would have required a sample size of 640 subjects and with 6 variables the required minimum is 320. Our primary aim was therefore to select six out of the ten decathlon events for detecting types with the help of CFA (cf. Lienert in Lienert and Dunkl 1988, p. 405). For this purpose of pre-selecting appropriate variables Lienert suggested the hierarchical CFA (HCFA; Lienert 1988, p. 45). However, we decided to put this possibility aside and instead used a factor analysis to select appropriate decathlon events. The selection was done according to the results of several factor analyses based on the ten decathlon events. By applying this procedure we were sure to select at least variables based on 1st order interactions of the ten basic events. Using the Kaiser-criterion (eigenvalue >1) a principal components analysis of the raw data (i.e. the 10 decathlon variables measured in units of meters and seconds, N = 514) led to the following Varimax-rotated 4-factor solution (the time variables were transformed into

4 450 M. Stemmler & G. Bäumler speed variables measuring meters per second; therefore they were scaled in the same direction as the length variables): 1. Sprint factor with the loadings of 100m dash (factor loading a =.857), long (a =.550), 400m run (a =.655), 110m-hurdles (a =.609); 2. Throwing factor with the loadings of shot put (a =.858), discus (a =.855) and javelin (a =.562); 3. Jump factor (especially recognizing the feature of high ing) with the loadings of pole high (a =.725), pole vault (a =.646), long (a =.420) and 110m hurdles (a =.311); 4. Middle distance stamina factor with the loadings of 400m run (a =.573) and 1500m run (a =.897). It can be easily seen, that long, 400m run and 110 m hurdles had substantial loadings on two factors (so called factorial hybrid events ). High loadings on just one factor were detected for: 100m dash (sprint factor), shot put and discus (ing factor), high (ing factor) and 1500m run (running or stamina factor). They can be seen as so called pure representatives of a factor. Meaningful interpretation may be obtained also for the five- and six-factors solutions which were calculated without the Kaiser-Guttman criterium (for a meaningful interpretation of different factor solutions in the decathlon see also Bäumler, 2002). Both factor solutions should therefore be also mentioned: In the 5-factor solution pole vault constituted an own specific factor (a =.973), the high factor was represented only by high (a =.878) and long (a =.572) and 110m hurdles loaded only on the sprint factor. In the 6-factor solution javelin (factor loading a =.928) was the sixth factor together with long which had a loading of a =.321. In this factor solution long displayed loadings on three different factors. Since javelin loads on its own specific factor in this solution, the ing factor is now represented only by shot put and discuss. Based on these pre-analyses were built five variable sets with six decathlon events for the CFA analysis: - Set A consisted of the events 100m dash, high, discus, pole vault, javelin and 1500m run and is based on the six factor solution. This set of variables represented also the five and four factor solution (sprint///running stamina/pole vault or sprint///running stamina). In both solutions the ing factor had two substantive loadings (discus and javelin ), but the high factor was represented by high and pole vault in the four factor solution and only by itself in the five factor solution. - Set B consisted of 100m dash, high, shot put, discus, javelin and 1500m run. This set of events represented the four as well as the five factor solution. The six factor solution was not completely reflected in this set, because pole vault was missing. It should be pointed out that in the four as well as in the five factor solution the ing factor was represented through three events (shot put, discus and javelin ). - Set C consisted of 100m dash, hurdle race, high, pole vault, shot put and discus. This set encompasses three factors (sprint//ing) out of the four factor solution (the running stamina factor is missing), four factors out of the five factor solution (sprint///pole vault; running stamina is missing) and four factors out of

5 The detection of types among decathletes using Configural Frequency Analysis (CFA) 451 the six factor solution, here, the factors running stamina and javelin are missing. According to the four factor solution each of the three factors which are represented by this set C (sprint//ing) had two events with substantial loadings. - Set D contained the following events 100m dash, long, shot put, high, 110m hurdles and 1500m run. This set reflected the four factor solution (the so-called basic factors ). Long and hurdles displayed reasonable loadings on the sprint factor and lower loadings on the factor. In this set, the sprint factor and the high factor are represented through more than one event. - Set E included the variables 100m dash, long, shot put, 400m run, 110m hurdles and 1500m run. This set represented essentially three out of the four basic factors: sprint, and running stamina. The sprint factor is represented by one pure event (100m dash) and three hybrid events (110m hurdles, long and 400m run). The ing factor is represented by only one (pure) event, and the running stamina factor is represented by one pure event (1500m run) and one hybrid event (400m run). The ing factor is not represented in set E because of the weak loads of the events long (a =.420) and 110m hurdle race (a =.311). The CFA was applied for explorative purposes, and not for confirming hypothetically expected types (cf. Lautsch & von Weber 1995, p. 65ff). However, it was conjectured that the explorative CFA is sensitive for combinations of events which may represent the factors of the decathlon. Such a decathlon-type might be the sprinter-type or the er-type (encompassing the events of shot put, discus and javelin ). The CFAs were conducted with the help of a program written by Alexander von Eye (CFA.EXE; von Eye, 2002). The decathlon-variables were dichotomised at the median; the events measured in seconds were transformed into speed variables (i.e., measured in meters per second), such that higher values represented higher speed, and the value of 2 performances above the median. Value 1 represented performances below the median. 5. Results 5.1 The performances of the total sample The performances of the total sample (N = 514 decathletes), in terms of the raw data can be seen as the reference points for the performances of the identified decathletes (the listed statistics are mean, standard deviation, minimum and maximum values; see Table 1). 5.2 CFAs of variable set A The CFA for variable set A obtained a global chi-square of χ 2 = , df = 57, p <.001 (in order to keep the article short only the observed and expected frequencies of the types and antitypes will be listed). The Bonferroni adjusted alpha for the local tests throughout this article was " 2 = "/32 = One significant configuration evolved for variable set A (see Table 2a).

6 452 M. Stemmler & G. Bäumler Table 1: The performances of the total sample (514 decathletes) Note. Total score = scores obtained in the competition; age = age in months at the time of the decathlon; sec = seconds; m = meters.

7 The detection of types among decathletes using Configural Frequency Analysis (CFA) 453 Table 2a: Significant type for the variable set A Type 100m High Discus Pole Javelin 1500m F(o) F(e) z- p vault value A <.001 Note. 1 = performances below the median; 2 = performances above the median. f(o) = observed frequencies; f(e) = expected frequencies; z-value = normal approximation of Pearson s chi-square. Interpretation of the type in variable set A Type A1. Type A1 is characterized by above average performances (see Table 2b) in 100m dash, high, discus, pole vault and javelin, and performances below the mean in the 1500m run. Referring to the six factor solution this type can be called the 5- factor-allround-type (sprinting, ing, ing in a narrow sense, and pole vault and javelin ), this type is probably based on a substantive body mass which leads to less running stamina. Referring to the five factor solution this type may represent a four factor all-round-type (sprint///pole vault-combination-type) with no running stamina. Referring to the four factor solution this represents a three factor all-round type (sprint//-combination-type), as well without running stamina. Among those 18 athletes, belonging to this type were also T. Dvorak (1999), D. O Brien (1992) and S. Fritz (1996). This group of 18 athletes revealed an above average total score (8400 points) and was also above average the mean age of the total sample with their 304 months (i.e., 25 years and 4 months). All performances were listed in Table 2b (listed are the means of the raw data in meters and seconds, as well as z-values with positive z-values representing scores above the mean for all events). The z-values revealed that the average performances of the 18 athletes were above average in 8 out of the 10 events (range: 0.77 to 1.05 standard deviations above the mean of the total sample). Accordingly, the average performance in the 1500m run was with z = 1.06 Table 2b: Average performances of 18 decathletes of type A1 (raw data and z-values) Type 100m Long Shot High 400m 110 Discus Pole Javelin 1500m Total Age put hurdles vault score Raw data ,55 15,27 2,08 49,60 14,35 46,15 4,98 63,10 290, z- value (6fac) sprint sp+hi hi sp+st sprint pv javelin stamina (5fac) sprint sp+hi hi sp+st sprint pv stamina (4fac) sprint sp+hi hi sp+st sprint pv+hi stamina Note. The bold events were entered into the CFAs in the variable set A. fac = factor solution. pv = pole vault; hi = high ; st = stamina; sp = sprint.

8 454 M. Stemmler & G. Bäumler about 1 standard deviation below the average of the total sample. The fact that the mean value for the 400m run was close to zero (z = -0.11) of the total sample showed that this event is a mixture of the sprint factor (see positive performances in the 100m dash) and the running stamina factor (see negative performances in the 1500m run), such that the 400m run is a compromise of the two. In short: The type A1 detected in the variable set A can be labelled a sprinter-erer-type in the sense of the four factor solution with a performance below average in running stamina. According to the five factor solution the event pole vault needs to be added as a special performance and according to the six factor solution pole vault and javelin need to be added as special performances. The events not included in this variable set go along with the already detected factors such as shot put which would be part of the ing factor, long and 110 m hurdles which would be part of the sprinting factor and the 400m run which would be a compromise between the sprinting ability and running stamina. 5.3 CFAs of variable set B The variable set B included the events 100m dash, shot put, high, discus, javelin and 1500m run representing the four factor solution and the six factor solution; because pole vault is missing only five factors were represented. According to the four factor solution the ing factor is represented through three events, according to the six factor solution this factor is represented through shot put and discus. The remaining factors were represented through one event each. The global CFA was highly significant Pearson s χ 2 = , df = 57, p <.001, therefore significant local types were included. By using the Bonferroni alpha adjustment of " * = five types were detected. Table 3a: Significant types for the variable set B Type 100m Shot put High Discus Javelin 1500m f(o) f(e) z- value p B B B B B Note. 1 = performances below the median; 2 = performances above the median. f(o) = observed frequencies; f(e) = expected frequencies; z-value = normal approximation of Pearson s chi-square. By scrutinizing the five types one can see that the 1500m run is a critical event, where four out of five types displayed performances above the median (only type B4 had values below the median). In type B1 the 1500m run is positively connected with the javelin, in type B2 the 1500m run is positively connected with the three ing events (again connected with javelin ), in type B3 the 1500 run was positively connected with the 100m

9 The detection of types among decathletes using Configural Frequency Analysis (CFA) 455 dash, in type B4 the 1500m run was negatively associated with the remaining five events and in type B5 it was again positively associated with the remaining five events. It is obvious that the 1500 m run is an important event for generating decathlon types. Another major role might play the exchange of pole vault through shot put in variable set B compared to variable set A. Additional information for interpreting the five types is obtained by checking their z- value-profile for all ten events. Table 3b: Average performances of decathletes of the types in B1 (raw data) Type 100m Long Shot put High 400m 110 hurdles Discus Pole vault Javelin 1500m Total score Age B B B B B Note. The bold events were entered into the CFAs in the variable set B. Table 3c: Average z-values of the performances of the respective types in variable set B Types 100m Long Shot High 400m 110m Discus Pole Javelin 1500m put hurdles vault B B B B B fac sprint sp+hi pv+hi sp+st sp+hi hi st Note. The bold events were entered into the CFAs in the variable set A. fac = factor solution. hi = high ; sp = sprint; st = stamina; fac = factor solution. Interpretation of the types in variable set B Type B1. In comparison to the total sample, the 22 decathletes of type B1 revealed performances above average in javelin and 1500m run and below average performance in the remaining four events. Therefore, 1500m run and javelin do not go along very well, in this type, with 100m dash, shot put, high, and discus. It can be conjectured, that the type B1 athlete has little body mass and only a medium body height which are well suited for javelin and the middle-distance races; extraordinary performances in these two events were sufficient to belong to the top 100 world s best athletes. Based on the

10 456 M. Stemmler & G. Bäumler facts that the total score of 7847 points is 1/2 a standard deviation below the average of 7990 points and the young age of M = 287 months (= short of 24 years) it is possible, that in later years those athletes will climb up to the top 100 athletes, because of their intensive training. The best athletes of type B1 (javelin / 1500m-type) were Szabo (8436 points), Schönbeck (8127 points) and Werthner (8083 points). Type B2. This type displayed excellent performances in the ing events like shot put, discus and javelin and also excellent performances in the 1500m run. Therefore, this type represents a er who is also proficient in middle-distance running. This combination is quite a surprise, because er usually based on their weight have difficulties with the 1500m runs. This type can be interpreted such that, here, we have excellent ers who, based on their intensive 1500m training, moved up to the top ranking athletes. It is also possible that these athletes dispose a cardio-pulmonal system or a muscle fibre structure which enable them to be excellent runners while having a special ing aptitude. In Table 3c (profile of the z-values) one can see that the 400m run which was not among the variables used in set B was close to zero which points to an average ability (z = -.07). This can be explained through the fact that the 400m run loads on the same factor as the 100m run which demonstrated negative z-values while the 1500m had a positive z-value. In contrast, the medium negative value of long, an event which loads as well on the sprinting factor as on the ing factor, is difficult to explain; at the same time 100m run and high showed clearly negative z-values. It may be that this is based on a higher order interaction which cannot be detected while looking at bivariate correlations with ing or 1500m. Three typical representatives of the er-stamina-type were T. Fahner (8362 points, 263 months of age), V. Vashchenko (7997 points, 312 months of age) and V. Kuelvet (8506 points, 304 months of age). Their profiles of performances (all listed values were z-values) were: Table 4: Individual performances of the types of B2 (z-values) 100m Long Shot put High 400m 110m hurdles Discus Pole vault Javelin 1500m Fahner Vashchenko Kuelvet It is remarkable that Kuelvet and also Fahner were as well proficient in the 1500m run as in the 400m run, and both events were in accordance with long and hurdle race. But for Vashchenko the 400m run (same with long and 110m hurdles) represented an event with below average performance like those of the sprinting and ing factor. Type B3. This type is characterized by excellent performances in the 1500m run and 100m dash. Again this positive association is a surprise, because both events usually correlate negatively and do not load on the same factor. Maybe this type is also based on higher order interactions. At first glance type B3 may be interpreted as a general running type, which encompasses the whole range between 100m and 1500m. But a closer look at the

11 The detection of types among decathletes using Configural Frequency Analysis (CFA) 457 profile of their performance revealed that some athletes (e.g., Holger, Magrans and van Wyk) had below average performances on running events like 400m and 110 hurdles, which were not included in the variable set B. This type was with 7769 points not very successful (only two events were above average), this combination is probably a ( twinkle-toed ) running type, who is small in body length. This interpretation goes well with the below average performances in the ing events and high. Well-balanced representatives of the type B3 were J. Hudgens (in 1999, 7857 points), G. Orlikov (in 1987, 7741 points) und V. Tuporshin (in 1985, 7694 points). Type B4. This type with above average performances in all of the variables included, except in the 1500m run, is very similar to type A1. Of the 18 athletes from type A1 16 appeared again in type B4, even though in variable set B shot put replaced pole vault. This is the already detected sprinter-er-er-type. The average total score of 8357 is relatively high. The mean age (310 months) was 12 month (i.e., 0.37 units of SD) above average. This is plausible, because this is a very well trained type. To type B4 belonged T. Dvorak in 1999 (8994 points, 325 months of age, D. O Brien in 1992 (8891 points, 311 months of age), C. Huffins in 1998 (8694 points, 338 months of age) and S. Fritz in 1996 (8644 points, 343 months of age). Type B5. The members of this type demonstrated above average performances in all the variables of variable set B. Accordingly, the average total score of this type B5 was with 8568 points 2.1 units of a standard deviation above the sample mean. In contrast, the average age was with 300 months close to the sample mean. The performances in the ten events (see Tables 3b and 3c) were similar to type B4, except for the performances in the 1500m and 400m run; type B5 is therefore an allround-type based on the four general factors sprinting/ing/ing/stamina. It is also possible to call this a five or even six factor allround ability with sprinting/ing/ing/stamina/pole vault or sprinting/ ing/ing/ stamina/pole vault/javelin. Of course this allround-ability is not only built on aptitude but also on intensive practice and training. This is reflected in the excellent performances of the technically difficult events like pole vault, 110m hurdles, high and javelin. This high level of intensive training is reflected in the above average performances of the 1500m run. By the way, a comparison of the four factor type of B5 with the three-factortype of B4 revealed that the 1500m run is a highly discriminating event also for the highly proficient top decathletes. Kind of training and training diligence may explain the difference between the two types as well as a special profile of aptitudes. Because the age of type B5 is ten months below type B4 the age can be seen as a critical discriminating variable among the two types. Athletes belonging to type B5 were among others D. Thompson in 1984 (8847 points), J. Hingsen in 1984 (8832 points), E. Haemaelainen in 1994 (8735 points), R. Sebrle in 2000 (8757 points) and D. Johnson who was already 29 years old in 1992 (8727 points). 5.4 CFAs of variable set C The variable set C consisted of 100m dash, shot put, high, 110m hurdles, discus, and pole vault. This set represented three factors like sprinting, ing and ing out of the four factor solution, with each factor being represented by two events (if we assign

12 458 M. Stemmler & G. Bäumler Table 5a: Significant types in the variable set C Type 100m Shot put High 110m hurdles Discus Pole vault f(o) f(e) z- value p C C Note. 1 = performances below the median; 2 = performances above the median. f(o) = observed frequencies; f(e) = expected frequencies; z-value = normal approximation of Pearson s chi-square. Table 5b: Average performances of decathletes of the types in C (raw data) Type 100m Long Shot put High 400m 110m hurdles Discus Pole vault Javelin 1500m Total score Age C C Note. The bold events were entered into the CFAs in the variable set B. Tabele 5c: Average z-values of the performances of the respective types in variable set C Type 100m Long Shot High 400m 110m Discus Pole Javelin 1500m put hurdles vault C C fac sprint sp+hi hi sp+st sp+hi hi st Note. The bold events were entered into the CFAs in the variable set C. hi = high ; st = stamina; sp = sprint; fac = factor solution. the 110m hurdles to the ing factor) or the four factors sprinting, ing, ing, pole vault out of the five factor solution. The factor stamina is missing. Two types evolved in our N = 514, using the normal approximation the chi-square value as our test statistic and a Bonferroni-adjusted alpha of " = The global chi-square of the CFA was with P 2 = , df = 57, p <.001 highly significant (see Table 5a). Interpretation of the types in variable set C Again, the low number of detected types seems to be caused by the presence of the pole vault in this set of variables. Type C1. Type C1, who displayed above average performances in shot put and discus is representing a er type. He obtained on average a total score of 7815 points,

13 The detection of types among decathletes using Configural Frequency Analysis (CFA) 459 which is about 0.56 unit of a standard deviation below the sample mean of The mean age was 306 months (i.e., 25 years and 6 months) which is about 8 months (about 0.25 units of SD) above the sample mean of 297 months. The z-values discriminate very well between the above average or below average ing events and the non-ing events with the exception of the 1500m run (z = -0.16) which was not included in the data set. Type C1 is closely related to type B2, where the ing events had a positive relationship with the 1500m run. The main difference in the profile between the two types B2 versus C1 (i.e., good or more bad performances in the 1500m run) lies also in the far below average performance in pole vault (as well as in 110m hurdles) in type C1. Therefore, type C1 can best be characterized as a er-type, with a somewhat weaker contribution of the javelin. It can be hypothesized that this type represented the more heavy weighted decathlete. This would also explain the poor performance in pole vault. Type C2. Type C2 had above average performances in all six variables of variables set C. Accordingly, the average total score of 8490 is way above the sample mean, exactly 1.85 SD above the mean of Age is with 309 months 11 months (0.34 SD) above the total sample. Type C2 is similar to type B5 and also somewhat similar to type B4 (as well as A1). Type C2 had more members (n = 34) than any of the two other types (n = 22 and n = 17). Type C2 can be seen as a conglomerate of the types B4 and B5 (allround-types with or without the 1500m run). This conglomerate was obviously formed through the missing of the 1500m run in variable set C. This result points to a methodological problem, that the resulting types are depending on the variables in the analyses. That is why only 25 athletes of the types B4 (n = 22) and B5 (n = 17) belonged to the 34 athletes of type C2. In the two remaining variable sets D and E, the factorial hybrid events long and 400m run were also included in the variable set. 5.5 CFAs of variable set D Variable set D encompassed 100m run, long, shot put, high, 110m hurdles and 1500m run. It represented exclusively the four general factors based on the four factor solution. Pole vault and javelin which represented specific factors in the five or six factor solution were missing here. The sprinting factor was represented by three variables (i.e., 100m, long, 110m hurdles), the ing factor was represented with one variable (shot put), the ing factor with two variables (high and long ) or with three variables if one assigns 110m hurdles to this factor despite its low loading of a =.31. The stamina factor was represented only by the 1500m run. The global χ 2 was , df = 57, p <.001. Four types evolved.

14 460 M. Stemmler & G. Bäumler Table 6a: Significant types in the variable set D Type 100m Long Shot High 110m 1500m f(o) f(e) z- p put hurdles value D D D D Note. 1 = performances below the median; 2 = performances above the median. f(o) = observed frequencies; f(e) = expected frequencies; z-value = normal approximation of Pearson s chi-square. Table 6b: Average performances of decathletes of the types in D (raw data) Type 100m Long Shot put High 400m 110m hurdles Discus Pole vault Javelin 1500m Total score Age D D D D Note. The bold events were entered into the CFAs in the variable set D. Table 6c: Average z-values of the performances of the respective types in variable set D Type 100m Long Shot High 400m 110m Discus Pole Javelin 1500m put hurdles vault D D D D fac sprint sp+hi hi sp+st sp+hi hi st Note. The bold events were entered into the CFAs in the variable set D. hi = High ; st = stamina; sp = sprint; fac = factor solution. Interpretation of the types in variable set D Type D1. This type is characterized by above average performance in 1500m and below average performances in the remaining five events. Again, the exceptional position of the 1500m run is confirmed. Of the variables not included in the variable set only the javelin had a positive association with the 1500m run. This correponds to type B1, where javelin and 1500m built the same type. The difference to B1 seems to be caused by the

15 The detection of types among decathletes using Configural Frequency Analysis (CFA) 461 missing of javelin in variable set D, it was also caused by the addition of long instead of discus, since long loaded on the same factor as javelin in the six factor solution. Type D2. This type revealed a positive performance only in shot putting. Obviously this is a er type, because discus and javelin, although not included in the variable set displayed above mean performances. While in type D2 the 1500m run showed below average performances, a comparison to type B2 (i.e., er-stamina-type) is not possible, but a similarity to type C1 exists. The reason for this discrepancy is based on the entry of long and 110m hurdles instead of discus and javelin (see the relation of the javelin to the 1500m run in type B1). In sum, type D2 seems to be a heavy weighted shot putter and discus er type (or a general er). Type D3. Type D3 presented positive performances in all events involved, except for the 1500m run. This type is very similar to the types A1 and B4. This is remarkable, because the variable sets A and D had only three out of six events in common and the variable sets B and D had only four out of six in common. Again, the exceptional position of the 1500m run is reflected in type D3, where type D3 seems to be kind of a mirror image of type D1 if one looks only at the variables in the variable set. Type D4. This type demonstrated above mean performances in all of the involved events, therefore this type is similar to our allround-type like type B5. Also the remaining events showed a trend towards positive performances. 5.6 CFAs of variable set E This variable set consisted of the six events 100m run, long, shot put, 400m run, 110m hurdles and 1500m run. In comparison to variable set D, in this set high was replaced by the 400m run. The 400m run functioned as a sort of hybrid variable with about equal loadings (a =.66 and a =.57) on the sprint factor and stamina factor. Contrary, the ing factor was weakened through the missing of its strongest event, the high, such that only medium loadings represented this factor with long (a =.42) and 110m hurdles (a =.31). The global chi-square was highly significant with χ 2 = , df = 57, p <.001. Four types emerged. Interpretation of the types in variable set E Type E1. This type showed only in the 1500m run above average values (z = 0.72). Most strikingly is the negative performance in the 400m run (z = -0.69). E1 therefore represents a pure running-stamina-type, who is not well suited for the 400m run and even less suited for the 100m dash. The average total score was 7751 points which represented a bad performance. His average age is young with on average 287 months (about 24 years). Below average performances could be detected in shot put and discus and average performances in javelin (z = 0.05). This is no surprise, if one bears in mind above detected affinity of the javelin to the 1500m run (see type B1). All athletes belonging to this type revealed at least one performance above average which belonged to the ing factor or the -

16 462 M. Stemmler & G. Bäumler ing factor but not to the sprinting factor. This type can be explained in terms of physiological and biomechanical characteristics (e.g., cardiovascular system, muscle fibre structure, body height, weight), while not all athletes of this type must have the same homogeneous somatic characteristics. An excellent representative of this type was the athlete Stewens, who had exceptional achievements in 1500m run (z = 1.42), medium achievements in javelin (z = -0.07) and pole vault (z = 0.05) as well as below average performances in all the other events including the 400m run (z = -0.23). Table 7a: Significant types in the variable set E Type 100m Long Shot 400m 110m 1500m f(o) f(e) z- p put hurdles value E E E E Note. 1 = performances below the median; 2 = performances above the median. f(o) = observed frequencies; f(e) = expected frequencies; z-value = normal approximation of Pearson s chi-square. Table 7b: Average performances of decathletes of the types in E (raw data) Type 100m Long Shot put High 400m 110m hurdles Discus Pole vault Javelin 1500m Total score Age E E E E Note. The bold events were entered into the CFAs in the variable set E. Table 7c: Average z-values of the performances of the respective types in variable set E Type 100m Long Shot High 400m 110m Discus Pole Javelin 1500m put hurdles vault E E E E fac sprint sp+hi hi sp+st sp+hi hi st 6 fac sprint sp+hi+ja hi sp+st sp pv ja st Note. The bold events were entered into the CFAs in the variable set E. hi = High ; pv = Pole vault; ja = Javelin ; st = stamina; sp = sprint; fac = factor solution.

17 The detection of types among decathletes using Configural Frequency Analysis (CFA) 463 Type E2. The solitary type E2 revealed only in shot putting above average achievements (z = 1.09). In its profile of performances only discus and javelin, both events which were not included in the variable set, showed positive achievements, although not in each and every case of the members of this type. Of the athletes of this type some had good or excellent performances in high or pole vault, but not in the remaining events like 100m dash, long, 400m run, 110m hurdles and 1500m run. This means, that this shot putter- or er-type displayed below average performances in all of the running events from sprint to stamina. The average score for this type is with 7771 low. Type E3. This type is a sprinter-shot putter-type with bad performances in stamina but decent performances in 400m run. This type might convey next to quick power also a large body height. Type E4. This type had above average performances in all variables included in the variable set (100m, long, shot put, 400m, 110m hurdles, 1500m). Of the events not included in the variable set javelin and pole vaults revealed slightly positive z-values. This means, that this type is our four-factor-type sprint///stamina excluding the special events like javelin and pole vault, according to the 6-factor solution. 5.7 A comparison of the detected types Table 8: z-value-profile of the detected types Type 100m Long Shot put High 400m 110 hurdles Discus Pole vault Javelin 1500m N A B B B B B , C C D D D D E E E E Note. The underlined values denote above average performances. Only z-values of the variables included in the variable set are listed.

18 464 M. Stemmler & G. Bäumler The following types were detected for the respective variable sets. Table 9: Kinds of types # of events involved Label Factors or events Types and variable set 6 4-factor-allround-type sprint///stamina B5, D4, E4 6 3-factor-allround-type sprint// (with and C2 without 1500m run) 5 3-factor-allround-type sprint// (without A1, B4, D3 1500m run) 5 sprinter-shot putter-type 100m/long /400m/110m E3 hurdles/shot put 4 er-stamina-type shot put/discus/javelin/1500m B2 2 javelin er-staminatype javelin /1500m B1 2 runner-type sprint/stamina B3 2 er-type shot put/discus/javelin C m-stamina-type 1500m (without 400m) D1, E1 1 shot put- or ertype shot put/(discus/javelin) D2, E2 The ten kinds of types can be reduced to five or six main types based on their similarities: - The allround-type I, a combination type which encompassed all factors of the 4-factor solution, that is sprinting, ing, ing and stamina. This type represented a versatile talented and highly trained top-decathlete with an average total score of about 8500 points. - The allround-type II, is also a highly talented combination type based on three of the four basic factors (sprinting, ing and ing) who possessed probably due to his massive body stature less running stamina. This type obtained on average 8350 points. - The sprinter-shot putter-type, bad performance especially in 1500m run. The decathlete obtained with this two factors combination on average a total of 8298 points. High as a third involved factor seems probable. - The er-stamina-type or javelin er-stamina-type, a two factor combination type who either had a er and running talent or who as a er was involved in an intensive 1500m training, to reach the top of the world s athletes. Usually, this type obtained a medium total score of 7750 to 8000 points. - The pure er-type with excellent achievements in shot putting, discus and javelin, whose performances reached to the lower level of the world s best athletes (on average 7800 points). - The pure runner-type (100m, 400m, 1500m), which combines the two running factors (on average 7800 points).

19 The detection of types among decathletes using Configural Frequency Analysis (CFA) 465 These five to six main types can be further divided into two clearly different areas: a) the versatile-types or three- /four-factor-type or allround-type, with a high level of performance (on average about 8400 points), b) the one- /two-factor-type (i.e., specialists) with a below average or average level of performances (on average 7800 points). The difference in performances was about 2.15 SDs. 6. Methodological issues and outlook on the future The major restraint of the above study was the fact that with a sample size of 514 no complete 10 variable CFA could be conducted; for such a CFA a total sample of more than 5000 athletes would have been required. That was the reason why an exploratory study based on previous factor analyses was conducted using five combinations or variable sets of six decathlon events. A survey of the detected types including their profiles of performances was listed in the above tables. It was remarkable that in variable sets which included pole vault only one or two types emerged. This seems due to the fact that pole vault is a highly specialized event with little or no relationship to the other events. All other events led to a larger number of types, usually four or five. Of most interest were the differences in the profile of performances of the detected ing types. While for instance, the ing type of variable set B (i.e., B2) showed above average performances also in 1500m, the er-types of the variable set D and E (i.e., D2 and E2) showed below average performance in the 1500m run. Shot putting was the only ing event included in the variable sets D and E, at the same time, the missing events like discus and javelin revealed above average performances in the profiles, that means, that these two types were basically no pure shot putter types but general ing-types. This makes it clear, how much the detection of types depended on the sort of variables involved in the analyses. A similar case is the running-stamina-type of the variable sets D and E (i.e., types D1 and E1), where in type E1 the 400m run revealed more below average performances than in type D1. At the same time, a related type (i.e., B1) showed a clear relation between javelin and 1500m run. This type emerged only because javelin was part of variable set B, this event was missing in the sets D and E. This is also true for the er-type with (i.e., B2) and without (i.e., D2 and E2) the 1500m run. Whether some of the detected types are only pseudo-types cannot be confirmed at the moment. Further analyses with varied variable sets are needed. However, it should be noted that quite a number of homogeneous types were detected in somewhat different variable sets. First of all, the allround-type with the 1500m run (i.e., B5, C2, D4, E4) or without the 1500m run (i.e., A1, B4, D3 and E3). This is trivial, because all the athletes included in the variables sets were highly trained top athletes. Nevertheless the 1500m run emerged as a critical event. It is striking, that next to the detected types like the er-stamina-type, the sprinterstamina type and the sprinter-shot putter-type other more complex types were not detected, as for instance, a er-er-type or a sprinter-er-type, although there were more complex allround-types. For the moment one might conjecture, that such types do not exist.

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