EL JUEGO COMO MEDIO DE SOCIALIZACION

In all cluster analyses (original and three replication subsets) evaluating weight transfer swing styles, both the C-Index and Point Biserial Correlation indicated the same solution as optimal in the original analysis and all subset analyses. This provided strong support in each analysis for the particular cluster solution being optimal. It also provided support for the findings of Milligan and Cooper (1985) who reported that these methods were considered strong (C-Index = 3rd; Point Biserial Correlation = 7th of 30 methods). As they were always in agreement, and as the cluster solution indicated was strongly validated, this would support these techniques as being good indicators of the optimal number of clusters in the data.

An interesting aspect of this analysis was that for all analyses (original and three replication subsets), the stepwise method (agglomerative schedule) indicated the same number of clusters as optimal as the Point Biserial Correlation and C-Index calculated on non-hierarchical data. Milligan and Cooper (1985) ranked stepwise method only 11th of the 30 tested and described it as ‘mediocre’. However, in this study, the stepwise method performed similarly to the stronger statistical tests used. While generalisation of this finding is limited as the number of analyses performed was low (N = 4) and all used the same data set (or subset of the data set), it does highlight differences in performance that might occur with different types of data, as noted by a number of authors (e.g. Everitt, 1979; Milligan and Cooper, 1985; Hair et al., 1995). In the case of this analysis, the use of the agglomerative schedule would have resulted in the same cluster solution (note: the 4-cluster solution was indicated as optimal

using hierarchical as well as non-hierarchical data by both C-index and Point Biserial Correlation).

One aspect of the cluster analysis process in this study differed from that used in the literature (e.g. Hair et al., 1995; Milligan and Cooper, 1985). For this study, statistical indices to determine the number of clusters were applied to non-hierarchical data. Other studies have applied the tests on the hierarchical data, determined the optimal cluster solution, and then recalculated only this solution non-hierarchically. In this study, all solutions below a reasonable cut-off (e.g. 11-cluster to 2-cluster solutions) were reanalysed non-hierarchically and then statistical tests were applied to the non- hierarchical cluster solutions to determine which was optimal. This seemed to be a better approach as the non-hierarchical process eliminates nesting by reclassifying cases better and therefore altering the cluster structure. The altered cluster structure could produce different results for the statistical tests and may lead to a different cluster solution indicated as optimal.

To assess if it was more appropriate to evaluate the optimal solution (number of clusters) on hierarchical data or non-hierarchical data, C-Index and Point Biserial Correlation were applied to both. The results of the comparison for Point Biserial Correlation are reported in table 4.28. As can be noted, the optimal cluster solution indicated by each test was the same for hierarchical cluster data and non-hierarchical data. Although not reported here, similar results were evident in all subset analyses and with C-Index. As both processes provided the same result, either could have been used for this data. With the extra analysis required to evaluate all non-hierarchical cluster group means, application of tests to the hierarchical data would have been

more efficient. However, the theoretical considerations expressed in the previous paragraph may still hold for different data and application of statistical tests to the non-hierarchical data would seem to be the safer option.

Table 4.28: Point Biserial Correlation coefficients calculated on hierarchical and non-hierarchical cluster data

11 10 9 8 7 6 5 4 3 2

Hierarchical data 0.48 0.55 0.55 0.55 0.56 0.56 0.5655 0.5660 0.55 0.51 Non-Hierarchical data 0.47 0.52 0.52 0.54 0.58 0.58 0.621 0.622 0.61 0.58

Another point of note from table 4.28 was the similarity between the 4-cluster and 5- cluster solutions for the Point Biserial Correlation. This indicated that either solution might have been appropriate. However the only difference between the 5-cluster and 4-cluster solutions was that two ‘outlying’ golfers who had remained as clusters of N = 1 (i.e. had not clustered with other golfers), combined together to form a cluster of

N = 2 and did not affect the larger groups in the analysis. As such, either solution would have resulted in the same conclusions as this small group did not pass validity tests.

4.4.6.2

Hierarchical – non-hierarchical process

Point Biserial Correlation results showed stronger effects in the non-hierarchical data in the lower cluster solutions and importantly the optimal solution compared with hierarchical data (refer table 4.28). This indicated that the non-hierarchical process improved the recovery of the underlying cluster structure (i.e. cases were classified

more appropriately). This improvement provides support for the use of the hierarchical – non-hierarchical approach recommended by Milligan (1996).

Seven golfers changed clusters from the hierarchical process to the non-hierarchical process. While five of these clustered more appropriately in the final solution, the remaining two golfers provided interesting data that is worthy of highlighting. Figure 4.22 shows the two golfers along with the final group means for the Front Foot group and the Reverse group. Golfer 1 changed from the Front Foot group to the Reverse group and Golfer 2 changed from the Reverse group to the Front Foot group.

0 10 20 30 40 50 60 70 80 90 100 TA MB LB TB ED MD BC MF Swing Events C P y% ( 10 0% = fr on t fo ot ) Reverse group (N=19) Front Foot group (N=39) Golfer 1: Reverse to Front Foot Golfer 2: Front Foot to Reverse

Figure 4.22: Golfers exhibiting unusual weight transfer patterns

The two golfers in figure 4.22 showed similarities with both the Front Foot and Reverse groups. For Golfer 1, while the overall pattern looks more similar to the Reverse group, particularly in downswing, the CPy% magnitudes are more similar to the Front Foot group. This golfer was referred to in section 4.4.5 as clustering in the Front Foot group if Fz% was used compared to the Reverse group when CPy% was used. On a practical level, this golfer might be considered part of the Reverse Group

who moves too far forward or a Front Foot golfer who moves forward too early. For Golfer 2, CPy% magnitudes are more similar to the Reverse group in downswing but the pattern looks more similar to the Front Foot group. In practical terms this might suggest that this golfer is a Front Foot golfer that does not shift the weight forward enough (scaling error) or a Reverse golfer who does not rapidly shift the weight forward at ED but who still ends up with weight at the desired (Reverse group) position at BC. While Golfer 2 possessed a high handicap (24), Golfer 1 was a low handicapper (2) so the unusual weight transfer patterns cannot necessarily be discounted as technical errors.

On a practical level, these two golfers would have been difficult to classify for coaching. The analysis might require examination of more CP parameters or the use of kinematic analyses to better determine which style might be most appropriate for each golfer. Individual-based statistical analysis of each golfer’s performance would also allow for a more informed decision. However, with only N = 10 trials performed, not enough data existed for this evaluation. It should be noted that these golfers represented only 3% of the golfers tested. For 97% of golfers, cluster analysis allocated without ambiguity.

A future direction which might be of use in respect to these golfers is fuzzy clustering. This method of clustering considers each case in terms of percentage membership rather than belonging to one cluster only (e.g. Chau, 2001). For these two golfers, this analysis would have provided information on how much these golfers belonged to each cluster group which could be used to determine how they might be coached, or in scientific terms, how they might be treated in the next stage of analysis

(i.e. which style they are allocated to, if any). Certainly, its use will introduce its own problems as more work would be required to evaluate what a 50:50 membership golfer should do – move to one particular style or continue to use some of both styles. However, the allocation of a golfer to one style might also hold problems particularly if they show attributes of both styles and the classification of these golfers into one or the other cluster would be based on marginal differences only. Also, irrespective of the information offered by fuzzy clustering (or any other method of classification) the results in this study using cluster analysis were valid and the method used was

appropriate.

4.4.6.3

Measure used in clustering data

Golfer 2 in section 4.4.6.2 also highlighted another issue in cluster analysis – the choice of the measure used to assess differences between cases. While this study used the squared Euclidean distance measure, it may not have been the best measure for classifying golfer 1 and 2 in figure 4.22. For these golfers, more appropriate

clustering may have been obtained by using the Pearson’s correlation measure, which clusters cases that are highly correlated (and so would cluster similar patterns rather than similar positions).

To compare the squared Euclidean distance and Pearson’s correlation methods, clusters were reanalysed using both measures (4-cluster solution). Results indicated that both measures produced similar cluster structures. Cluster means differed only

slightly, as is evident in figure 4.23, which compares the two large groups for both analyses. Further, 85% of cases clustered into the same groups for each analysis (92% of the major groups reclassified). Of note, from section 4.4.6.2, golfer 1 remained in the Front Foot group but Golfer 2 changed to the Front Foot group from

the Reverse group. Both Midstance Backswing Front Foot golfers also moved to the Front Foot group (hence, N = 60 is in the ‘correl’ series in figure 4.23).

0 10 20 30 40 50 60 70 80 90 100 TA MB LB TB ED MD BC MF Swing Events C P y% ( 10 0% = fr on t fo ot ) SE Reverse (N=19) SE Front Foot (N=39) Correl Reverse (N=14) Correl Front Foot (N=46)

Figure 4.23: Mean CPy% at eight swing events for the Front Foot and Reverse group from cluster analysis using the squared Euclidean distance measure (SE)

and Pearson’s correlation (Correl) measure

The measure used to cluster golfers in this study was considered prior to analysis. Both the squared Euclidean distance measure and correlation measure had advantages and disadvantages. While the correlation method was better for clustering golfers with similar patterns of weight transfer, it did so with no information on where the pattern existed in relation to the feet. Conversely, the squared Euclidean distance measure provided this information but was less robust for extracting similar patterns. The squared Euclidean distance measure was chosen as the coaching emphasis is on weight position and previous scientific literature had evaluated positions rather than patterns. Regardless, for 85% of cases, either method provided the same results (92%

of the large cluster cases) and group means for both the Front Foot and Reverse groups were very similar. As such, the two weight transfer styles would have been identified using either measure. This also provides further validation for the existence of the two styles, as both appeared using different measures.