Dash the Kelpie ❤️

Agility course times: A statistical comparison of heights and their speeds

Introduction

In dog Agility, handlers and dogs compete in a race to get around an obstacle course in the fastest possible time without making any mistakes (knocking bars over, going the wrong way, and so on). It’s pretty fun, but some people take it a bit more seriously than others! Recently, I was sucked into a debate about whether the taller dogs (‘500’ dogs, who are in the height category that encompasses most Border Collies, as well as my own little Kelpie rescue dog Dash) run faster than dogs of other heights (200, 300, 400, and 600). As it turns out, somewhat unsurprisingly, they do. You wouldn’t have really thought you’d need statistics to show that, but some people are hard to persuade, so since I had access to some data on the topic, I wrote an R script to show that.

A small dog doing Agility as fast as it can

This analysis is based on data extracted from K9 Entries (https://www.k9entries.com/), for both Victorian and Queensland Agility competitions from 2016 to 2018. Thanks to Alison Muddle for extracting the data and to Judy Kloeden for initial analyses. There are almost 18,000 individual entries in this analysis.

All of the data analyses were conducted in R Statistical Software and compiled using R Markdown in the R Studio package. Note that where there was more than one entry per dog, entries were averaged for the analysis. In addition, speeds faster than 10 m/s and slower than .8 m/s were cropped from the analysis to reduce the effect of outliers. Pariwise comparisons are corrected with the Tukey method, which is fairly conservative.

Results for Novice Agility

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4, 594) = 25.98, p < .001. The 500 height dogs were significantly faster than all the other heights, all p-values < .01, corrected (see tables below for estimated marginal means and details).

Novice Agility overall statistics

Table 1: Overall results for ROT by height, Novice Agility - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 594 0.5922 25.9814 0.1489 0

Novice Agility estimated marginal mean ROTs for each height

Table 2: Estimated marginal means for ROT by height, Novice Agility
Height emmean SE df lower.CL upper.CL
200 2.5613 0.1382 594 2.2898 2.8327
300 2.7693 0.0744 594 2.6232 2.9154
400 3.1474 0.0926 594 2.9655 3.3294
500 3.5066 0.0448 594 3.4186 3.5946
600 3.0847 0.0781 594 2.9313 3.2382

Novice Agility pairwise comparisons between ROTs for each height

Table 3: Pairwise comparisons for ROT by height, Novice Agility
contrast estimate SE df t.ratio p.value
200 - 300 -0.2081 0.1570 594 -1.3257 0.6753
200 - 400 -0.5862 0.1664 594 -3.5231 0.0042
200 - 500 -0.9453 0.1453 594 -6.5064 0.0000
200 - 600 -0.5235 0.1588 594 -3.2971 0.0091
300 - 400 -0.3781 0.1188 594 -3.1824 0.0133
300 - 500 -0.7373 0.0868 594 -8.4894 0.0000
300 - 600 -0.3154 0.1079 594 -2.9234 0.0295
400 - 500 -0.3591 0.1029 594 -3.4900 0.0047
400 - 600 0.0627 0.1212 594 0.5175 0.9856
500 - 600 0.4219 0.0901 594 4.6837 0.0000

Plot of Novice Agility ROT by height

Results for Excellent Agility

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,346) =11.08, p < .001. The 500 height dogs were significantly faster than 300 and 200 but not 400 and 600 dogs, with p-values < .01, corrected (see tables below for estimated marginal means and details).

Table 4: Overall results for ROT by height, Excellent Agility - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 346 0.5173 11.0779 0.1135 0
Table 5: Estimated marginal means for ROT by height, Excellent Agility
Height emmean SE df lower.CL upper.CL
200 2.6870 0.1650 346 2.3625 3.0115
300 3.0459 0.0961 346 2.8569 3.2350
400 3.3862 0.1137 346 3.1625 3.6099
500 3.5851 0.0533 346 3.4802 3.6899
600 3.4038 0.0979 346 3.2113 3.5963
Table 6: Pairwise comparisons for ROT by height, Excellent Agility
contrast estimate SE df t.ratio p.value
200 - 300 -0.3589 0.1909 346 -1.8796 0.3303
200 - 400 -0.6992 0.2004 346 -3.4891 0.0049
200 - 500 -0.8980 0.1734 346 -5.1791 0.0000
200 - 600 -0.7168 0.1918 346 -3.7363 0.0020
300 - 400 -0.3403 0.1489 346 -2.2854 0.1521
300 - 500 -0.5391 0.1099 346 -4.9055 0.0000
300 - 600 -0.3579 0.1372 346 -2.6089 0.0709
400 - 500 -0.1989 0.1256 346 -1.5834 0.5090
400 - 600 -0.0176 0.1500 346 -0.1173 1.0000
500 - 600 0.1813 0.1114 346 1.6265 0.4815

Plot of Excellent Agility ROT by height

Results for Masters Agility

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,407) =23.43, p < .001. The 500 height dogs were significantly faster than all other heights, with p-values < .001, except for the difference between 500 and 600 (p = .011), corrected (see tables below for estimated marginal means and details).

Table 7: Overall results for ROT by height, Masters Agility - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 407 0.4522 23.4262 0.1871 0
Table 8: Estimated marginal means for ROT by height, Masters Agility
Height emmean SE df lower.CL upper.CL
200 3.1782 0.1319 407 2.9189 3.4374
300 3.1921 0.0810 407 3.0329 3.3512
400 3.4474 0.0971 407 3.2565 3.6382
500 3.9537 0.0452 407 3.8647 4.0426
600 3.6075 0.0971 407 3.4167 3.7983
Table 9: Pairwise comparisons for ROT by height, Masters Agility
contrast estimate SE df t.ratio p.value
200 - 300 -0.0139 0.1547 407 -0.0899 1.0000
200 - 400 -0.2692 0.1637 407 -1.6438 0.4702
200 - 500 -0.7755 0.1394 407 -5.5622 0.0000
200 - 600 -0.4293 0.1637 407 -2.6218 0.0683
300 - 400 -0.2553 0.1264 407 -2.0196 0.2584
300 - 500 -0.7616 0.0927 407 -8.2124 0.0000
300 - 600 -0.4154 0.1264 407 -3.2867 0.0097
400 - 500 -0.5063 0.1071 407 -4.7282 0.0000
400 - 600 -0.1601 0.1373 407 -1.1667 0.7704
500 - 600 0.3462 0.1071 407 3.2327 0.0115

Plot of Masters Agility ROT by height

Results for Open Agility

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,392) = 14.68, p < .001. The 500 height dogs were significantly faster than all other dogs, with p-values < .01, corrected (see tables below for estimated marginal means and details).

Table 10: Overall results for ROT by height, Open Agility - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 392 0.6929 14.6787 0.1303 0
Table 11: Estimated marginal means for ROT by height, Open Agility
Height emmean SE df lower.CL upper.CL
200 2.8281 0.2019 392 2.4312 3.2250
300 3.2549 0.1241 392 3.0110 3.4989
400 3.4758 0.1300 392 3.2202 3.7314
500 3.9551 0.0530 392 3.8509 4.0592
600 3.5490 0.1214 392 3.3103 3.7877
Table 12: Pairwise comparisons for ROT by height, Open Agility
contrast estimate SE df t.ratio p.value
200 - 300 -0.4268 0.2370 392 -1.8010 0.3744
200 - 400 -0.6477 0.2401 392 -2.6973 0.0561
200 - 500 -1.1270 0.2087 392 -5.3992 0.0000
200 - 600 -0.7209 0.2356 392 -3.0599 0.0199
300 - 400 -0.2209 0.1797 392 -1.2290 0.7344
300 - 500 -0.7002 0.1349 392 -5.1893 0.0000
300 - 600 -0.2941 0.1736 392 -1.6938 0.4389
400 - 500 -0.4793 0.1404 392 -3.4141 0.0063
400 - 600 -0.0732 0.1779 392 -0.4115 0.9940
500 - 600 0.4061 0.1325 392 3.0654 0.0196

Plot of Open Agility ROT by height

Jumping Results

Results for Novice Jumping

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,619) = 41.16, p < .001. The 500 height dogs were significantly faster than all the other heights, all p-values < .001, corrected (see tables below for estimated marginal means and details).

Table 13: Overall results for ROT by height, Novice Jumping - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 619 1.0544 41.1608 0.2101 0
Table 14: Estimated marginal means for ROT by height, Novice Jumping
Height emmean SE df lower.CL upper.CL
200 3.1824 0.1644 619 2.8595 3.5053
300 3.5644 0.1032 619 3.3617 3.7671
400 4.1355 0.1141 619 3.9115 4.3596
500 4.7522 0.0586 619 4.6371 4.8673
600 4.0367 0.1037 619 3.8330 4.2404
Table 15: Pairwise comparisons for ROT by height, Novice Jumping
contrast estimate SE df t.ratio p.value
200 - 300 -0.3820 0.1941 619 -1.9675 0.2832
200 - 400 -0.9531 0.2001 619 -4.7623 0.0000
200 - 500 -1.5698 0.1746 619 -8.9929 0.0000
200 - 600 -0.8543 0.1944 619 -4.3942 0.0001
300 - 400 -0.5712 0.1538 619 -3.7125 0.0021
300 - 500 -1.1878 0.1187 619 -10.0087 0.0000
300 - 600 -0.4723 0.1463 619 -3.2280 0.0114
400 - 500 -0.6167 0.1283 619 -4.8079 0.0000
400 - 600 0.0988 0.1542 619 0.6409 0.9683
500 - 600 0.7155 0.1191 619 6.0057 0.0000

Plot of Novice Jumping ROT by height

Results for Excellent Jumping

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,495) = 22.87, p < .001. The 500 height dogs were significantly faster than all other dogs, with p-values < .01, corrected (see tables below for estimated marginal means and details).

Table 16: Overall results for ROT by height, Excellent Jumping - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 495 0.8172 22.8652 0.156 0
Table 17: Estimated marginal means for ROT by height, Excellent Jumping
Height emmean SE df lower.CL upper.CL
200 3.2651 0.1598 495 2.9511 3.5790
300 3.6653 0.0986 495 3.4715 3.8591
400 4.0013 0.1167 495 3.7721 4.2306
500 4.4821 0.0580 495 4.3682 4.5960
600 3.9922 0.1004 495 3.7948 4.1895
Table 18: Pairwise comparisons for ROT by height, Excellent Jumping
contrast estimate SE df t.ratio p.value
200 - 300 -0.4002 0.1878 495 -2.1314 0.2084
200 - 400 -0.7363 0.1979 495 -3.7209 0.0021
200 - 500 -1.2171 0.1700 495 -7.1592 0.0000
200 - 600 -0.7271 0.1887 495 -3.8523 0.0012
300 - 400 -0.3360 0.1528 495 -2.1993 0.1816
300 - 500 -0.8168 0.1144 495 -7.1389 0.0000
300 - 600 -0.3269 0.1408 495 -2.3219 0.1396
400 - 500 -0.4808 0.1303 495 -3.6892 0.0023
400 - 600 0.0092 0.1540 495 0.0597 1.0000
500 - 600 0.4900 0.1160 495 4.2244 0.0003

Plot of Excellent Jumping ROT by height

Results for Masters Jumping

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,608) = 30.42, p < .001. The 500 height dogs were significantly faster than all other heights, with p-values < .001, corrected (see tables below for estimated marginal means and details).

Table 19: Overall results for ROT by height, Masters Jumping - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 608 0.6615 30.4158 0.1667 0
Table 20: Estimated marginal means for ROT by height, Masters Jumping
Height emmean SE df lower.CL upper.CL
200 3.1782 0.1319 407 2.9189 3.4374
300 3.1921 0.0810 407 3.0329 3.3512
400 3.4474 0.0971 407 3.2565 3.6382
500 3.9537 0.0452 407 3.8647 4.0426
600 3.6075 0.0971 407 3.4167 3.7983
Table 21: Pairwise comparisons for ROT by height, Masters Jumping
contrast estimate SE df t.ratio p.value
200 - 300 -0.1329 0.1715 608 -0.7746 0.9379
200 - 400 -0.4219 0.1804 608 -2.3392 0.1340
200 - 500 -0.9748 0.1573 608 -6.1964 0.0000
200 - 600 -0.4788 0.1778 608 -2.6923 0.0562
300 - 400 -0.2891 0.1278 608 -2.2613 0.1591
300 - 500 -0.8419 0.0925 608 -9.1030 0.0000
300 - 600 -0.3459 0.1242 608 -2.7846 0.0437
400 - 500 -0.5529 0.1080 608 -5.1184 0.0000
400 - 600 -0.0569 0.1362 608 -0.4176 0.9936
500 - 600 0.4960 0.1037 608 4.7817 0.0000

Plot of Masters Jumping ROT by height

Results for Open Jumping

Overall, there was a strongly significant difference between rates of travel for the different heights, F(4,552) = 19.28, p < .001. The 500 height dogs were significantly faster than all other dogs, with p-values < .001, corrected, for 200 and 300 dogs, p = .032 for 400 dogs and p = .006 for 600 dogs (see tables below for estimated marginal means and details).

Table 22: Overall results for ROT by height, Open Jumping - ANOVA table
num Df den Df MSE F ges Pr(>F)
Height 4 552 0.9311 19.2803 0.1226 0
Table 23: Estimated marginal means for ROT by height, Open Jumping
Height emmean SE df lower.CL upper.CL
200 3.2240 0.2274 552 2.7772 3.6708
300 3.6872 0.1197 552 3.4521 3.9223
400 4.1781 0.1246 552 3.9334 4.4228
500 4.5692 0.0526 552 4.4658 4.6726
600 4.1564 0.1093 552 3.9418 4.3710
Table 24: Pairwise comparisons for ROT by height, Open Jumping
contrast estimate SE df t.ratio p.value
200 - 300 -0.4632 0.2570 552 -1.8024 0.3732
200 - 400 -0.9541 0.2593 552 -3.6791 0.0024
200 - 500 -1.3452 0.2335 552 -5.7623 0.0000
200 - 600 -0.9324 0.2523 552 -3.6953 0.0022
300 - 400 -0.4908 0.1728 552 -2.8413 0.0374
300 - 500 -0.8820 0.1308 552 -6.7456 0.0000
300 - 600 -0.4692 0.1621 552 -2.8952 0.0321
400 - 500 -0.3911 0.1352 552 -2.8923 0.0323
400 - 600 0.0217 0.1657 552 0.1307 0.9999
500 - 600 0.4128 0.1213 552 3.4038 0.0064

Plot of Open Jumping ROT by height

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Deborah Apthorp
Senior Lecturer in Psychology

My research interests include visual perception, Parkinson’s disease, postural sway, and EEG.