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The maximum gaze velocity permitted at each fixation zone diameter is shown below in Table 3-5. These velocities were calculated to be the maximum speed with which the gaze position could move in one frame (16.67ms) while remaining inside the defined fixation zone. Based on these calculations, it can be seen that the only fixation zone which represented of a true fixation where the gaze was essentially stable, was the 0.5° fixation zone.

Within the fixation zone diameter of 1.5°, which is equivalent to the size of a golf ball, a maximum gaze velocity of 45°/s was tolerated, indicating that both fixation and pursuit movements could be made without exceeding the criteria for fixation. At a fixation zone diameter of 3.0°, which has been previously used in the literature,28, 30 fixations, pursuits and small saccadic eye movements were permissible within the ‘fixation’ criteria. A fixation criterion of 3.0° is not representative of pure fixations, and cannot be used to analyse putting vision strategy in golf.

Fixation Zone Diameter (°)

Fixation Zone Radius (°)

Maximum gaze velocity permitted (°/s)

Gaze Behaviours 0.5 0.25 15°/s Fixation

1.0 0.50 30°/s Fixation, Slow Pursuit

1.5 0.75 45°/s Fixation, Pursuits

2.0 1.0 60°/s Fixation, Pursuits, Small Saccades

2.5 1.25 75°/s Fixation, Pursuits, Saccades

3.0 1.5 90°/s Fixation, Pursuits, Saccades

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3.3.3.1 Phase Specific Gaze Behaviours

The Pearson correlations of the Total Number of Fixations made in each of the different fixation zones for both the Primary Address and Swing phases of the putt are displayed in Table 3-6 and Figure 3-5.

In the Primary Address phase, the correlation between the Total Number of Fixations measured between the 0.5° fixation zone (pure fixation) and the 1.0° fixation zone (fixation plus small pursuits) was strong, but as the fixation zone size increased, the strength of the correlations with the 0.5° fixation zone decreased dramatically.

The correlations between the 1.0° and 1.5° fixation zones and between 1.5°, 2.0°, 2.5° and 3.0° fixation zones are near perfect in the Primary Address phase with r-values greater than 0.900, suggesting that these fixation zones are all measuring similar gaze behaviours. The 1.0° and 1.5° degree fixation zones both measured all fixation and some pursuit eye movements, while the 2.0°, 2.5° and 3.0° zones measured all fixation and pursuit eye movements and some saccadic eye movements.

0.5 degree 1.0 degree 1.5 degree 2.0 degree 2.5 degree 3.0 degree 0.5 degree 1.0 degree Address Swing 0.798** 0.499** 1.5 degree Address Swing 0.584** 0.247** 0.924** 0.833** 2.0 degree Address Swing 0.469** 0.110** 0.858** 0.741** 0.968** 0.862 2.5 degree Address Swing 0.395** 0.021 0.804** 0.648** 0.940** 0.874** 0.978** 0.867** 3.0 degree Address Swing 0.353** -0.037 0.768** 0.582** 0.917** 0.840** 0.963** 0.908** 0.984** 0.899**

** Correlations are significant at the 0.01 level (2-tailed)

Table 3-6: Pearson correlation (r) values for the Total Number of Fixations between the 0.5°, 1.0°, 1.5°, 2.0°, 2.5° and 3.0° fixation zones during the Address and Swing phases of the putt. All values are reported for an n=964.

The correlation between fixations measured between the 0.5° fixation zone (pure fixation) and the 1.0° fixation zone (fixation and small pursuits) was also high during the Swing phase, but this correlation was not as high as it was Primary Address phase. The correlations

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between the 0.5° fixation zone and the larger fixation zones decreased significantly from 1.5° onwards as seen in the Primary Address, although the decrease was more marked in the Swing phase as the correlations between 0.5° and 2.5° and 0.5° and 3.0° were not statistically significant. As noted previously, the 1.0° and the 1.5° fixations zones, and the 1.5°, 2.0°, 2.5°, and 3.0° fixation zones are again highly correlated with each other.

Figure 3-5: Correlations between the Total Number of Fixations in both the Address (A,B,C) and Swing (D,E,F) phases of golf putts for 0.5° versus 1.0°, 0.5° versus 1.5° and 0.5° versus 3.0° only.

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Table 3-7 and Figure 3-6 depict the Pearson correlations between the Mean Fixation Duration in the different fixation zones for both the Primary Address and Swing phases of the putt. Similar to the results for the Total Number of Fixations on the ball at each fixation zone, the correlation between the Mean Fixation Duration in the 0.5° fixation zone (pure fixation) and the 1.0° fixation zone (fixation plus small pursuits) during the Primary Address phase was very high. The strength of the correlations for Mean Fixation Duration (versus 0.5° fixation zone) in the Primary Address phase decreased as the fixation zone size increased, although not as dramatically as they did with the Total Number of Fixations. The correlations between the 1.0° and 1.5° fixation zones and between 1.5°, 2.0°, 2.5° and 3.0° fixation zones were again quite high during Address.

0.5 degree 1.0 degree 1.5 degree 2.0 degree 2.5 degree 3.0 degree 0.5 degree 1.0 degree Address Swing 0.855** 0.781** 1.5 degree Address Swing 0.774** 0.698** 0.888** 0.819** 2.0 degree Address Swing 0.720** 0.649** 0.800** 0.743** 0.862** 0.776** 2.5 degree Address Swing 0.673** 0.513** 0.774** 0.667** 0.874** 0.677** 0.867** 0.732** 3.0 degree Address Swing 0.666** 0.498** 0.782** 0.594** 0.840** 0.657** 0.908** 0.715** 0.899** 0.779**

** Correlations are significant at the 0.01 level (2-tailed)

Table 3-7: Pearson correlation (r) values for the Mean Fixation Duration between the 0.5°, 1.0°, 1.5°, 2.0°, 2.5° and 3.0° fixation zones during the Address and Swing phases of the putt. All values are reported for an n=964.

The Pearson correlations of Mean Fixation Duration and fixation zone size demonstrated an analogous pattern in the Swing phase of the putt. The correlation between the 0.5° and 1.0° fixation zones were high (r=0.781, p(2-tailed)<0.01); the remaining correlations between the larger fixation zones and the 0.5° fixation zone decreased as the fixation zone diameter increased (1.5°, r=0.698, p(2-tailed)<0.01; 2.0°, r=0.649 , p(2-tailed)<0.01; 2.5°, r=0.513 , p(2-tailed)<0.01; 3.0°, r=0.498 , p(2-tailed)<0.01). The correlation between the 1.0° and 1.5° fixation zones was quite high (r =0.819, p (2-tailed) < 0.01), as were the correlations between the 1.5°, 2.0°, 2.5° and 3.0° fixation zones (r >0.650, p(2-tailed)<0.01). It is worth

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noting, that in the Swing phase, the correlations between the 1.0° fixation zone and the 2.0°, 2.5° fixation zones were also relatively strong (r >0.6500, p(2-tailed)<0.01).

Figure 3-6: Correlations between the Mean Fixation Duration in both the Address (A,B,C) and Swing (D,E,F) phases of golf putts for 0.5° versus 1.0°, 0.5° versus 1.5° and 0.5° versus 3.0° only.

The Total Fixation Duration Pearson correlations for the Primary Address and Swing phases can be found Table 3-8 and Figure 3-7. Unlike the Total Number of Fixations and the Mean Fixation Duration results, the Total Fixation Durations measured in each fixation zone during the Primary Address phase were all highly correlated. Despite this, a trend towards a similar

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pattern in the correlations was still present; the highest correlations were found between the 0.5° and 1.0°, the 1.0° and 1.5°, and the 1.5°, 2.0°, 2.5° and 3.0° fixation zones.

0.5 degree 1.0 degree 1.5 degree 2.0 degree 2.5 degree 3.0 degree 0.5 degree 1.0 degree Address Swing 0.954** 0.768** 1.5 degree Address Swing 0.916** 0.582** 0.980** 0.699** 2.0 degree Address Swing 0.888** 0.514** 0.963** 0.649** 0.979** 0.691** 2.5 degree Address Swing 0.874** 0.426** 0.951** 0.590** 0.967** 0.661** 0.974** 0.725** 3.0 degree Address Swing 0.869** 0.385** 0.936** 0.534** 0.957** 0.611** 0.960** 0.704** 0.967** 0.784**

** Correlations are significant at the 0.01 level (2-tailed)

Table 3-8: Pearson correlation (r) values for the Total Fixation Duration between the 0.5°, 1.0°, 1.5°, 2.0°, 2.5° and 3.0° fixation zones during the Address and Swing phases of the putt. All values are reported for an n=964.

In the Swing phase, the differences in the Total Fixation Duration correlations were much more marked between fixation zones than they were in the Primary Address phase, although none of the correlations were as strong. The correlation between the 0.5° and 1.0° fixation zones was relatively high (r=0.768, p(2-tailed)<0.01), and the strength of the correlations decreased dramatically as the fixation zone diameter increased (1.5°: r=0.582, p(2- tailed)<0.01; 2.0°: r=0.514 , p(2-tailed)<0.01; 2.5°: r=0.426 , p(2-tailed)<0.01; 3.0°: r=0.385 , p(2-tailed)<0.01). The correlations between the 1.0° and 1.5° fixation zones (r=0.699, p(2- tailed)<0.01) and between the 1.5°, 2.0°, 2.5° and 3.0° fixation zones (r>0.610, p(2- tailed)<0.01) were also relatively high as seen previously.

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Figure 3-7: Correlations between the Total Fixation Duration in both the Address (A,B,C) and Swing (D,E,F) phases of golf putts