Embodied Navigation in Immersive Abstract Data Visualization:
Is Overview+Detail or Zooming Better for 3D Scatterplots?
This document includes detailed statistic results for the submitted paper.
𝑝𝑝 ≤ 0.05 is highlighted withAs described in the submission, we use the linear mixed modeling when the normality assumption ismet. We model with/without overview and with/without zooming as two effects in our models. For theDistance task, we also model the difficulty (i.e., close vs. far, short for Diff). For the Count task, we do
not have the level of difficulty. We include all interactions between effects in our models.
We use the Friedman test when the data did not meet the normality assumption.

1 Performance
1.1 Distance Task
1.1.1 TimeThe results of linear mixed modeling are:Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
baseline
3 1855.4 1867.9 -924.71
1849.4zoomModel
4 1857.4 1874.1 -924.71
1849.4 0.0043
1 0.9475878
overviewModel 5 1846.8 1867.6 -918.38
1836.8 12.6621
1 0.0003731 ***diffModel
6 1808.3 1833.4 -898.16
1796.3 40.4274
1 2.041e-10 ***zoomOverview
7 1809.6 1838.8 -897.78
1795.6 0.7649
1 0.3818079
zoomDiff
8 1807.9 1841.3 -895.95
1791.9 3.6699
1 0.0554026 .
overviewDiff
9 1808.6 1846.2 -895.30
1790.6 1.2899
1 0.2560603
interModel
10 1805.5 1847.2 -892.74
1785.5 5.1286
1 0.0235349 *We can see the highest interaction level, i.e., interModel (with/without overview X with/without
zooming X Diff) is statistically significant. We then conducted pair-wise comparisons with
Tukey’s HSD post-hoc tests:
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview,1 - Zoom,NoOverview,1-0.6939 0.271 453 -2.560 0.1737
NoZoom,NoOverview,1 - NoZoom,Overview,1-0.7803 0.271 453 -2.878 0.0794
NoZoom,NoOverview,1 - Zoom,Overview,1-0.6253 0.271 453 -2.307 0.2921
NoZoom,NoOverview,1 - NoZoom,NoOverview,2 -1.2964 0.271 453 -4.783 0.0001
NoZoom,NoOverview,1 - Zoom,NoOverview,2-0.8594 0.271 453 -3.171 0.0345
NoZoom,NoOverview,1 - NoZoom,Overview,2-1.7732 0.271 453 -6.541 <.0001
NoZoom,NoOverview,1 - Zoom,Overview,2-1.7092 0.271 453 -6.305 <.0001
Zoom,NoOverview,1 - NoZoom,Overview,1-0.0864 0.271 453 -0.319 1.0000
Zoom,NoOverview,1 - Zoom,Overview,10.0686 0.271 453 0.253 1.0000
Zoom,NoOverview,1 - NoZoom,NoOverview,2-0.6025 0.271 453 -2.223 0.3400
Zoom,NoOverview,1 - Zoom,NoOverview,2-0.1656 0.271 453 -0.611 0.9987
Zoom,NoOverview,1 - NoZoom,Overview,2-1.0793 0.271 453 -3.982 0.0020
Zoom,NoOverview,1 - Zoom,Overview,2-1.0153 0.271 453 -3.745 0.0050
NoZoom,Overview,1 - Zoom,Overview,10.1550 0.271 453 0.572 0.9992
NoZoom,Overview,1 - NoZoom,NoOverview,2-0.5162 0.271 453 -1.904 0.5487
NoZoom,Overview,1 - Zoom,NoOverview,2-0.0792 0.271 453 -0.292 1.0000
NoZoom,Overview,1 - NoZoom,Overview,2-0.9930 0.271 453 -3.663 0.0067
NoZoom,Overview,1 - Zoom,Overview,2-0.9289 0.271 453 -3.427 0.0152
Zoom,Overview,1 - NoZoom,NoOverview,2-0.6711 0.271 453 -2.476 0.2085
Zoom,Overview,1 - Zoom,NoOverview,2-0.2342 0.271 453 -0.864 0.9890
Zoom,Overview,1 - NoZoom,Overview,2-1.1479 0.271 453 -4.235 0.0007
Zoom,Overview,1 - Zoom,Overview,2-1.0839 0.271 453 -3.999 0.0019
NoZoom,NoOverview,2 - Zoom,NoOverview,20.4370 0.271 453 1.612 0.7429
NoZoom,NoOverview,2 - NoZoom,Overview,2-0.4768 0.271 453 -1.759 0.6483
NoZoom,NoOverview,2 - Zoom,Overview,2-0.4128 0.271 453 -1.523 0.7950
Zoom,NoOverview,2 - NoZoom,Overview,2-0.9138 0.271 453 -3.371 0.0183
Zoom,NoOverview,2 - Zoom,Overview,2-0.8497 0.271 453 -3.135 0.0384
NoZoom,Overview,2 - Zoom,Overview,20.0640 0.271 453 0.236 1.0000

We are not interesting in the comparison of different visualizations in different difficulties (e.g.,
NoZoom,NoOverview,1 vs. Zoom,NoOverview,2 which is Rm in close vs. Zm in far). After
deleting these results, we have significant comparisons within:
NoZoom,NoOverview,1 - NoZoom,NoOverview,2 => Rm in close vs. far
NoZoom,Overview,1 - NoZoom,Overview,2 => RmO in close vs. far
Zoom,Overview,1 - Zoom,Overview,2 => ZmO in close vs. far
Zoom,NoOverview,2 - NoZoom,Overview,2 => Zm vs. RmO in far
Zoom,NoOverview,2 - Zoom,Overview,2 => Zm vs. ZmO in far

1.1.2 Accuracy
We used Friedman test for comparing the accuracy.
For the Distance-Close task:
Asymptotic Friedman Test
data: accuracy by Vis (Rm, RmO, Zm, ZmO)
stratified by UserName
chi-squared = 10.114, df = 3, p-value = 0.01762

The Post-hoc test:$PostHoc.Test
RmO - Rm 0.03334459
Zm - Rm
0.99984650
ZmO - Rm 0.76092218
Zm - RmO 0.02670443
ZmO - RmO 0.30607470
ZmO - Zm 0.71674455

For the Distance-Far task:
Asymptotic Friedman Test
data: accuracy by Vis (Rm, RmO, Zm, ZmO)
stratified by UserName
chi-squared = 0.15909, df = 3, p-value = 0.9839

1.2 Count Task
1.2.1 TimeWe use the linear mixed modeling.
baseline
zoomModel
overviewModelinterModel

Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
3 1039.6 1050.9 -516.81
1033.6
4 1022.2 1037.3 -507.11
1014.2 19.3919
1 1.065e-05 ***5 1018.2 1037.0 -504.10
1008.2 6.0191
1
0.01415 *6 1013.7 1036.3 -500.87
1001.7 6.4672
1
0.01099 *We then conduct pair-wise comparison:$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview - Zoom,NoOverview -0.88320 0.176 297 -5.014 <.0001
NoZoom,NoOverview - NoZoom,Overview -0.62575 0.176 297 -3.552 0.0025
NoZoom,NoOverview - Zoom,Overview-0.87523 0.176 297 -4.969 <.0001
Zoom,NoOverview - NoZoom,Overview
0.25745 0.176 297 1.462 0.4621
Zoom,NoOverview - Zoom,Overview
0.00798 0.176 297 0.045 1.0000
NoZoom,Overview - Zoom,Overview-0.24947 0.176 297 -1.416 0.4901

We have significant comparisons within:

NoZoom,NoOverview - Zoom,NoOverview => Rm vs. Zm
NoZoom,NoOverview - NoZoom,Overview => Rm vs. RmO
NoZoom,NoOverview - Zoom,Overview => Rm vs. ZmO

1.2.2 Accuracy
The Post-hoc test:
Asymptotic Friedman Test
data: accuracy by Vis (Rm, RmO, Zm, ZmO)
stratified by UserName
chi-squared = 2.1579, df = 3, p-value = 0.5403

2 Interaction
2.1 Camera moving distance
2.1.1 Distance task
We use the linear mixed modeling:
Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
baseline
3 1115.31 1127.68 -554.66 1109.31
zoomModel
4 939.65 956.14 -465.83
931.65 177.6627
1 < 2.2e-16 ***overviewModel 5 939.61 960.22 -464.81
929.612.0402
1
0.15319
diffModel
6 913.95 938.69 -450.98
901.95 27.6586
1 1.447e-07 ***zoomOverview
7 889.51 918.36 -437.75
875.51 26.4456
1 2.711e-07 ***zoomDiff
8 887.02 920.00 -435.51
871.024.48931
0.03411 *overviewDiff
9 888.30 925.40 -435.15
870.300.72181
0.39555
interModel
10 885.49 926.72 -432.75
865.494.8045
1
0.02839 *We then conducted post-hoc test:$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview,1 - Zoom,NoOverview,10.9477 0.113 430
8.390 <.0001
NoZoom,NoOverview,1 - NoZoom,Overview,10.2111 0.113 430
1.869 0.5732
NoZoom,NoOverview,1 - Zoom,Overview,10.8133 0.113 430
7.200 <.0001
NoZoom,NoOverview,1 - NoZoom,NoOverview,2 -0.6029 0.113 430 -5.337 <.0001
NoZoom,NoOverview,1 - Zoom,NoOverview,20.8306 0.113 430
7.353 <.0001
NoZoom,NoOverview,1 - NoZoom,Overview,2-0.0498 0.113 430 -0.441 0.9999
NoZoom,NoOverview,1 - Zoom,Overview,20.5457 0.113 430
4.831 0.0001
Zoom,NoOverview,1 - NoZoom,Overview,1-0.7366 0.113 430 -6.521 <.0001
Zoom,NoOverview,1 - Zoom,Overview,1-0.1344 0.113 430 -1.190 0.9346
Zoom,NoOverview,1 - NoZoom,NoOverview,2-1.5506 0.113 430 -13.727 <.0001
Zoom,NoOverview,1 - Zoom,NoOverview,2-0.1171 0.113 430 -1.037 0.9686
Zoom,NoOverview,1 - NoZoom,Overview,2-0.9974 0.113 430 -8.831 <.0001
Zoom,NoOverview,1 - Zoom,Overview,2-0.4020 0.113 430 -3.559 0.0098
NoZoom,Overview,1 - Zoom,Overview,10.6022 0.113 430
5.331 <.0001
NoZoom,Overview,1 - NoZoom,NoOverview,2-0.8140 0.113 430 -7.206 <.0001
NoZoom,Overview,1 - Zoom,NoOverview,20.6195 0.113 430
5.485 <.0001
NoZoom,Overview,1 - NoZoom,Overview,2-0.2609 0.113 430 -2.309 0.2908
NoZoom,Overview,1 - Zoom,Overview,20.3346 0.113 430
2.962 0.0634
Zoom,Overview,1 - NoZoom,NoOverview,2-1.4161 0.113 430 -12.537 <.0001
Zoom,Overview,1 - Zoom,NoOverview,20.0173 0.113 430
0.153 1.0000
Zoom,Overview,1 - NoZoom,Overview,2-0.8630 0.113 430 -7.641 <.0001
Zoom,Overview,1 - Zoom,Overview,2-0.2676 0.113 430 -2.369 0.2593
NoZoom,NoOverview,2 - Zoom,NoOverview,21.4335 0.113 430 12.691 <.0001
NoZoom,NoOverview,2 - NoZoom,Overview,20.5531 0.113 430
4.897 <.0001
NoZoom,NoOverview,2 - Zoom,Overview,21.1485 0.113 430 10.168 <.0001
Zoom,NoOverview,2 - NoZoom,Overview,2-0.8804 0.113 430 -7.794 <.0001
Zoom,NoOverview,2 - Zoom,Overview,2-0.2849 0.113 430 -2.523 0.1887
NoZoom,Overview,2 - Zoom,Overview,20.5954 0.113 430
5.271 <.0001

We again deleting the comparisons of different visualizations in different difficulties. We havesignificant comparisons within:
NoZoom,NoOverview,1 - Zoom,NoOverview,1 => Rm vs. Zm in close
NoZoom,NoOverview,1 - Zoom,Overview,1 => Rm vs. ZmO in close
Zoom,NoOverview,1 - NoZoom,Overview,1 => Zm vs. RmO in close
NoZoom,Overview,1 - Zoom,Overview,1 => RmO vs. ZmO in close
NoZoom,NoOverview,2 - Zoom,NoOverview,2 => Rm vs. Zm in far
NoZoom,NoOverview,2 - NoZoom,Overview,2 => Rm vs. RmO in far
NoZoom,NoOverview,2 - Zoom,Overview,2 => Rm vs. ZmO in far
Zoom,NoOverview,2 - NoZoom,Overview,2 => Zm vs. RmO in far

NoZoom,Overview,2 - Zoom,Overview,2 => RmO vs. ZmO in far
NoZoom,NoOverview,1 - NoZoom,NoOverview,2 => Rm in close vs. far

2.1.2 Count task
We use the linear mixed modeling.
baseline
zoomModel
overviewModelinterModel

Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
3 512.31 523.46 -253.16
506.31
4 334.26 349.13 -163.13
326.26 180.0494
1<2e-16 ***5 334.53 353.12 -162.26
324.531.729510.1885
6 336.05 358.36 -162.03
324.050.476210.4901

We can see with/without zooming significantly affects the camera moving distance. The highest
level of interaction model is not significant. The pair-wise comparisons reveal the same
information: whether being able to zoom significantly affects the camera moving distance.
$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview - Zoom,NoOverview
0.7634 0.0654 282 11.674 <.0001
NoZoom,NoOverview - NoZoom,Overview -0.0289 0.0654 282 -0.442 0.9712
NoZoom,NoOverview - Zoom,Overview
0.6710 0.0654 282 10.261 <.0001
Zoom,NoOverview - NoZoom,Overview-0.7923 0.0654 282 -12.115 <.0001
Zoom,NoOverview - Zoom,Overview-0.0924 0.0654 282 -1.413 0.4924
NoZoom,Overview - Zoom,Overview
0.6999 0.0654 282 10.702 <.0001

We have significant comparisons within:

NoZoom,NoOverview - Zoom,NoOverview => Rm vs. Zm
NoZoom,NoOverview - Zoom,Overview => Rm vs. ZmO
Zoom,NoOverview - NoZoom,Overview => Zm vs. RmO
NoZoom,Overview - Zoom,Overview => RmO vs. ZmO

2.2 Number of interactions
2.2.1 Number of interactions
For the Distance task, we use the linear mixed modeling:
Df
AIC
BIC logLik deviance Chisq Chi Df Pr(>Chisq)
baseline
3 1151.1 1163.5 -572.57
1145.1
zoomModel
4 1150.0 1166.5 -571.01
1142.0 3.1204
1
0.07732 .
overviewModel 5 1148.3 1168.9 -569.15
1138.3 3.7233
1
0.05366 .
diffModel
6 1149.9 1174.6 -568.93
1137.9 0.4341
1
0.51001
zoomOverview
7 1145.6 1174.5 -565.81
1131.6 6.2452
1
0.01245 *zoomDiff
8 1142.1 1175.1 -563.06
1126.1 5.4935
1
0.01909 *overviewDiff
9 1144.1 1181.2 -563.06
1126.1 0.0001
1
0.99219
interModel
10 1142.1 1183.3 -561.06
1122.1 4.0109
1
0.04521 *We then conducted post-hoc test:$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview,1 - Zoom,NoOverview,1-0.00174 0.149 430 -0.012 1.0000
NoZoom,NoOverview,1 - NoZoom,Overview,10.18517 0.149 430 1.244 0.9183
NoZoom,NoOverview,1 - Zoom,Overview,10.10544 0.149 430 0.708 0.9967
NoZoom,NoOverview,1 - NoZoom,NoOverview,2 -0.37144 0.149 430 -2.495 0.2003
NoZoom,NoOverview,1 - Zoom,NoOverview,20.27207 0.149 430 1.828 0.6016
NoZoom,NoOverview,1 - NoZoom,Overview,20.10871 0.149 430 0.730 0.9961
NoZoom,NoOverview,1 - Zoom,Overview,20.08136 0.149 430 0.547 0.9994
Zoom,NoOverview,1 - NoZoom,Overview,10.18691 0.149 430 1.255 0.9144
Zoom,NoOverview,1 - Zoom,Overview,10.10718 0.149 430 0.720 0.9964
Zoom,NoOverview,1 - NoZoom,NoOverview,2-0.36970 0.149 430 -2.483 0.2053
Zoom,NoOverview,1 - Zoom,NoOverview,20.27381 0.149 430 1.839 0.5936
Zoom,NoOverview,1 - NoZoom,Overview,20.11045 0.149 430 0.742 0.9956
Zoom,NoOverview,1 - Zoom,Overview,20.08310 0.149 430 0.558 0.9993
NoZoom,Overview,1 - Zoom,Overview,1-0.07972 0.149 430 -0.536 0.9995
NoZoom,Overview,1 - NoZoom,NoOverview,2-0.55661 0.149 430 -3.739 0.0051
NoZoom,Overview,1 - Zoom,NoOverview,20.08690 0.149 430 0.584 0.9991
NoZoom,Overview,1 - NoZoom,Overview,2-0.07646 0.149 430 -0.514 0.9996
NoZoom,Overview,1 - Zoom,Overview,2-0.10381 0.149 430 -0.697 0.9970
Zoom,Overview,1 - NoZoom,NoOverview,2-0.47689 0.149 430 -3.203 0.0313
Zoom,Overview,1 - Zoom,NoOverview,20.16663 0.149 430 1.119 0.9524
Zoom,Overview,1 - NoZoom,Overview,20.00327 0.149 430 0.022 1.0000

Zoom,Overview,1 - Zoom,Overview,2NoZoom,NoOverview,2 - Zoom,NoOverview,2NoZoom,NoOverview,2 - NoZoom,Overview,2NoZoom,NoOverview,2 - Zoom,Overview,2Zoom,NoOverview,2 - NoZoom,Overview,2Zoom,NoOverview,2 - Zoom,Overview,2NoZoom,Overview,2 - Zoom,Overview,2-0.02408 0.149 430 -0.162
0.64351 0.149 430 4.323
0.48015 0.149 430 3.225
0.45281 0.149 430 3.042-0.16336 0.149 430 -1.097-0.19071 0.149 430 -1.281-0.02735 0.149 430 -0.184

1.00000.00050.02930.0506
0.95720.90561.0000We have significant comparisons within:

NoZoom,NoOverview,2 - Zoom,NoOverview,2 => Rm vs. Zm in far.
NoZoom,NoOverview,2 - NoZoom,Overview,2 => Rm vs. RmO in far.

For the Count task.
baseline
zoomModel
overviewModelinterModel

Df
AIC
BIC logLik deviance
Chisq Chi Df
3 847.24 858.39 -420.62
841.244 744.79 759.66 -368.39
736.79 104.446
1
5 746.05 764.64 -368.03
736.050.736
1
6 724.92 747.22 -356.46
712.92 23.131
1

Pr(>Chisq)< 2.2e-16 ***0.39090.000001513 ***Pair-wise comparisons:$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview - Zoom,NoOverview-1.395 0.119 282 -11.691 <.0001
NoZoom,NoOverview - NoZoom,Overview-0.337 0.119 282 -2.824 0.0560
NoZoom,NoOverview - Zoom,Overview-0.908 0.119 282 -7.609 <.0001
Zoom,NoOverview - NoZoom,Overview
1.058 0.119 282
8.867 <.0001
Zoom,NoOverview - Zoom,Overview
0.487 0.119 282
4.082 0.0003
NoZoom,Overview - Zoom,Overview-0.571 0.119 282 -4.785 <.0001

We have significant comparisons within:

NoZoom,NoOverview - Zoom,NoOverview => Rm vs. Zm
NoZoom,NoOverview - Zoom,Overview => Rm vs. ZmO
Zoom,NoOverview - NoZoom,Overview => Zm vs. RmO
Zoom,NoOverview - Zoom,Overview => Zm vs. ZmO
NoZoom,Overview - Zoom,Overview => RmO vs. ZmO

2.2.2 Number of teleportation
For the Distance task, we use linear mixed modeling:
Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
baseline
3 1207.90 1220.27 -600.95 1201.90
zoomModel
4 982.11 998.60 -487.06
974.11 227.7892
1 < 2.2e-16 ***overviewModel 5 984.09 1004.70 -487.04
974.090.0275
1
0.86826
diffModel
6 984.63 1009.37 -486.32
972.631.4551
10.22771
zoomOverview
7 955.62 984.47 -470.81
941.62 31.0157
1 2.559e-08 ***zoomDiff
8 951.57 984.55 -467.79
935.57
6.043910.01395 *overviewDiff
9 951.12 988.22 -466.56
933.122.45281
0.11732
interModel
10 952.32 993.55 -466.16
932.32
0.797910.37173If we check the zoomOverview model with pair-wise comparisons:$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview - Zoom,NoOverview
1.429 0.086 433 16.622 <.0001
NoZoom,NoOverview - NoZoom,Overview
0.333 0.086 433
3.869 0.0007
NoZoom,NoOverview - Zoom,Overview
1.076 0.086 433 12.510 <.0001
Zoom,NoOverview - NoZoom,Overview-1.096 0.086 433 -12.753 <.0001
Zoom,NoOverview - Zoom,Overview-0.353 0.086 433 -4.112 0.0003
NoZoom,Overview - Zoom,Overview
0.743 0.086 433
8.641 <.0001

We have significant comparisons within:
NoZoom,NoOverview - Zoom,NoOverview => Rm vs. Zm
NoZoom,NoOverview - NoZoom,Overview => Rm vs. RmO
NoZoom,NoOverview - Zoom,Overview => Rm vs. ZmO
Zoom,NoOverview - NoZoom,Overview => Zm vs. RmO
Zoom,NoOverview - Zoom,Overview => Zm vs. ZmO
NoZoom,Overview - Zoom,Overview => RmO vs. ZmOFor the Count task, we use linear mixed modeling:baseline
zoomModel
overviewModelinterModel

Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
3 686.35 697.50 -340.17
680.35
4 609.72 624.59 -300.86
601.72 78.6232
1 < 2.2e-16 ***5 582.27 600.85 -286.13
572.27 29.4565
1 5.718e-08 ***6 584.07 606.37 -286.03
572.07 0.1988
1
0.6557

We can see both with/without overview and with/without zooming affect the number of
teleportation. Pair-wise comparisons also confirm:$contrasts
contrast
estimate
SE df t.ratio p.value
NoZoom,NoOverview - Zoom,NoOverview
0.688 0.0934 282
7.364 <.0001
NoZoom,NoOverview - NoZoom,Overview-0.337 0.0934 282 -3.606 0.0021
NoZoom,NoOverview - Zoom,Overview
0.292 0.0934 282
3.130 0.0103
Zoom,NoOverview - NoZoom,Overview-1.025 0.0934 282 -10.970 <.0001
Zoom,NoOverview - Zoom,Overview-0.396 0.0934 282 -4.233 0.0002
NoZoom,Overview - Zoom,Overview
0.629 0.0934 282
6.736 <.0001

We have significant comparisons within:
NoZoom,NoOverview - Zoom,NoOverview => Rm vs. Zm
NoZoom,NoOverview - NoZoom,Overview => Rm vs. RmO
NoZoom,NoOverview - Zoom,Overview => Rm vs. ZmO
Zoom,NoOverview - NoZoom,Overview => Zm vs. RmO
Zoom,NoOverview - Zoom,Overview => Zm vs. ZmO
NoZoom,Overview - Zoom,Overview => RmO vs. ZmO

2.2.3 Number of zooming interactions
For the Distance task, we use linear mixed modeling:baseline
overviewModel
diffModelinterModel

Df
AIC
BIC logLik deviance Chisq Chi Df Pr(>Chisq)
3 582.45 592.74 -288.23
576.45
4 583.76 597.48 -287.88
575.76 0.6920
10.4055
5 585.11 602.26 -287.56
575.11 0.6464
1
0.4214
6 585.08 605.66 -286.54
573.08 2.0308
1
0.1541For the Count task, we use linear mixed modeling as well:baseline
overviewModel

Df
AIC
BIC logLik deviance Chisq Chi Df
Pr(>Chisq)
3 413.75 422.82 -203.87
407.75
4 388.58 400.67 -190.29
380.58 27.169
1 0.0000001864 ***There is a significant difference between ZmO and Zm.

2.3 Overview usage
2.3.1 Percentage of time looking at the overview
For the Distance task, we use linear mixed modeling:baseline
visModeldiffModelinterModel

Df
AIC
BIC logLik deviance
Chisq Chi Df Pr(>Chisq)
3 79.985 90.273 -36.992
73.985
4 -52.453 -38.736 30.226 -60.453 134.4376
1< 2e-16 ***5 -51.865 -34.719 30.933 -61.865
1.41231
0.23467
6 -55.437 -34.861 33.719 -67.437
5.571810.01825 *Pairwise comparisons reveal:$contrasts
contrast
estimate
SE df t.ratio p.value
RmO,1 - ZmO,1
0.2997 0.0368 206
8.136 <.0001
RmO,1 - RmO,2 -0.0926 0.0368 206 -2.515 0.0605
RmO,1 - ZmO,20.3299 0.0368 206
8.958 <.0001
ZmO,1 - RmO,2 -0.3923 0.0368 206 -10.652 <.0001
ZmO,1 - ZmO,20.0302 0.0368 206
0.821 0.8444
RmO,2 - ZmO,20.4226 0.0368 206 11.473 <.0001

For the Count task, we also use the linear mixed modeling:baseline
visModelDf
AIC
BIC logLik deviance Chisq Chi Df Pr(>Chisq)
3 -203.64 -194.57 104.82 -209.64
4 -240.01 -227.91 124.00 -248.01 38.368
1 5.859e-10 ***The result indicates a significant difference between RmO and ZmO.

3 User rankings and ratings
3.1 Ranking
For the Distance task, we use the Friedman test:
Asymptotic Friedman Testdata:

rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 12.06, df = 3, p-value = 0.00718

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.049722415
Zm - Rm
0.005363617
ZmO - Rm 0.203561935
Zm - RmO 0.883087957
ZmO - RmO 0.928187875
ZmO - Zm 0.532752114

For the Count task, we again use the Friedman test:
Asymptotic Friedman Testdata:

rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 15.66, df = 3, p-value = 0.001331

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.6110631288
Zm - Rm
0.0008571373
ZmO - Rm 0.0419198741
Zm - RmO 0.0496862951
ZmO - RmO 0.6881364555
ZmO - Zm 0.4559519472

3.2 Overall usability
We use Friedman test:
Asymptotic Friedman Testdata:

rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 19.732, df = 3, p-value = 0.0001929

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.002310403
Zm - Rm
0.000212506
ZmO - Rm 0.026041899
Zm - RmO 0.950659143
ZmO - RmO 0.883035785
ZmO - Zm 0.582421851

3.3 Ratings
3.3.1 Confidence
For the Distance task, we use the Friedman test:
Asymptotic Friedman Test
data: rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 11.265, df = 3, p-value = 0.01038

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.008155308
Zm - Rm
0.092222825
ZmO - Rm 0.078024309
Zm - RmO 0.832565609
ZmO - RmO 0.865691589
ZmO - Zm 0.999874506

For the Count task, we again use Friedman test:
Asymptotic Friedman Test
data: rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 5.3636, df = 3, p-value = 0.147

3.3.2 Physical demanding
For the Distance task, we use the Friedman test:
Asymptotic Friedman Test
data: rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 17.891, df = 3, p-value = 0.0004633

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.0160951833
Zm - Rm
0.0005098434
ZmO - Rm 0.0079289380
Zm - RmO 0.7711237171
ZmO - RmO 0.9961436807
ZmO - Zm 0.8809787869

For the Count task, we again use Friedman test:
Asymptotic Friedman Test
data: rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 32.419, df = 3, p-value = 0.0000004271

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.193350052196
Zm - Rm
0.000044940036
ZmO - Rm 0.000004655783
Zm - RmO 0.045553502612
ZmO - RmO 0.017381216517
ZmO - Zm 0.986207801596

3.3.3 Mental demanding
For the Distance task, we use the Friedman test:
Asymptotic Friedman Test
data: rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 3.8466, df = 3, p-value = 0.2785

For the Count task, we again use Friedman test:
Asymptotic Friedman Test
data: rank by vis (Rm, RmO, Zm, ZmO)
stratified by user
chi-squared = 8.6978, df = 3, p-value = 0.03359

Post-hoc comparisons:$PostHoc.Test
RmO - Rm 0.64250194
Zm - Rm
0.04961030
ZmO - Rm 0.04249676
Zm - RmO 0.59571749
ZmO - RmO 0.50203770
ZmO - Zm 0.99887033