This document provides screenshots of each task, full analysis output, information about display metrics, and Figure 1 depicting confidence ratings.

1. Highest Point

2. Highest Point in Region

3. Locate 275m

4. Compare Heights

11. Average Height Comparison

12. Steepest at 355

Display Metrics

Figure 1

1. Highest Point Task

Screen shot of task

Analysis

R Code: Aov(Error ~ Binning + Banding + Darkness + White.test)


		Df	Sum Sq		Mean Sq		F value		Pr(>F)    
Binning		4	146		36.54		2.419 		0.04780 *  
Banding		1	189		189.36		12.536 		0.00044 ***
Darkness	1	8		8.29		0.548 		0.45931    
White.test	1	44		44.47		2.944 		0.08686 .  
Residuals	463	699		415.11                    

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Post hoc Tukey HSD comparisons were used to test significant differences
between binning techniques for each task, correcting for multiple comparisons.

    Tukey multiple comparisons of means 95% family-wise confidence level

  Binning
               diff        lwr       upr     p adj
  20-10  -0.2151799 -1.7810105 1.3506506 0.9957291
  30-10   0.2295243 -1.3448823 1.8039309 0.9946352
  40-10  -0.6343781 -2.1919456 0.9231895 0.7984387
  Con-10  1.0433345 -0.5267438 2.6134129 0.3633378
  30-20   0.4447043 -1.1378774 2.0272860 0.9392431
  40-20  -0.4191982 -1.9850287 1.1466324 0.9486942
  Con-20  1.2585145 -0.3197614 2.8367903 0.1876749
  40-30  -0.8639024 -2.4383090 0.7105042 0.5612559
  Con-30  0.8138102 -0.7729744 2.4005948 0.6250806
  Con-40  1.6777126  0.1076343 3.2477910 0.0294656

Means

    Binning     Mean       SD
  1      10 3.890910 3.607527
  2      20 3.675730 3.938769
  3      30 4.120434 4.393573
  4      40 3.256531 3.069140
  5     Con 4.934244 4.550895

2. Highest Point in Region

Screen shot of task

Analysis

Aov(Error ~ Binning + Banding + Darkness + White.test)

               Df Sum Sq Mean Sq F value Pr(>F)  
  Binning       4   40.2  10.052   2.744  0.028 *
  Banding       1    7.5   7.506   2.049  0.153  
  Darkness      1    3.7   3.712   1.013  0.315  
  White.test    1    0.5   0.504   0.137  0.711  
  Residuals   472 1729.3   3.664                 
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD

    Tukey multiple comparisons of means 95% family-wise confidence level
  
  Binning
               diff          lwr       upr     p adj
  20-10  -0.1045969 -0.863343128 0.6541493 0.9956784
  30-10   0.6508950 -0.111771784 1.4135617 0.1351026
  40-10   0.4933186 -0.263519998 1.2501573 0.3836093
  Con-10  0.3806236 -0.380064990 1.1413122 0.6471353
  30-20   0.7554919 -0.001223538 1.5122073 0.0506033
  40-20   0.5979156 -0.152925560 1.3487567 0.1888309
  Con-20  0.4852205 -0.269501146 1.2399422 0.3980755
  40-30  -0.1575763 -0.912379062 0.5972264 0.9791264
  Con-30 -0.2702714 -1.028934386 0.4883916 0.8661960
  Con-40 -0.1126950 -0.865498932 0.6401089 0.9940613

Means

    Binning     Mean       SD
  1      10 2.212050 1.871169
  2      20 2.107453 2.045616
  3      30 2.862945 1.895512
  4      40 2.705368 1.632463
  5     Con 2.592673 2.096149

3. Locate 275m

Screen shot of task

Analysis

Aov(Error ~ Binning + Banding + Darkness + White.test)

               Df Sum Sq Mean Sq F value Pr(>F)  
  Binning       4   1866   466.4   2.763 0.0271 *
  Banding       1     54    54.0   0.320 0.5719  
  Darkness      1    297   296.8   1.758 0.1854  
  White.test    1     27    26.6   0.157 0.6918  
  Residuals   491  82877   168.8                 
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD

    Tukey multiple comparisons of means 95% family-wise confidence level
  
  Binning
               diff        lwr        upr     p adj
  20-10   0.3230288  -4.716181  5.3622385 0.9997873
  30-10   0.7656448  -4.273565  5.8048545 0.9937175
  40-10  -4.5867374  -9.613270  0.4397951 0.0926278
  Con-10 -0.6982762  -5.712351  4.3157989 0.9955084
  30-20   0.4426160  -4.609239  5.4944712 0.9992669
  40-20  -4.9097662  -9.948976  0.1294436 0.0603384
  Con-20 -1.0213050  -6.048089  4.0054788 0.9811382
  40-30  -5.3523821 -10.391592 -0.3131724 0.0310014
  Con-30 -1.4639209  -6.490705  3.5628629 0.9313323
  Con-40  3.8884612  -1.125614  8.9025363 0.2117911

Means

    Binning     Mean       SD
  1      10 23.36416 10.57737
  2      20 23.68719 11.32612
  3      30 24.12981 12.87705
  4      40 18.77742 12.46810
  5     Con 22.66589 16.72308

4. Compare Heights

Screen shot of task

Analysis

Logistic regression in R: glm(Comparison ~ Binning + Darkness + White.test + Banding, family = "binomial")

*The 10m binning was the reference group.

   
  Deviance Residuals: 
      Min       1Q   Median       3Q      Max  
  -1.0172  -0.8204  -0.7420   1.4600   1.9378  
  
  Coefficients:
               Estimate Std. Error z value Pr(>|z|)  
  (Intercept) -0.630984   0.540695  -1.167   0.2432  
  Binning20   -0.005596   0.336441  -0.017   0.9867  
  Binning30    0.418361   0.322363   1.298   0.1944  
  Binning40    0.035405   0.328768   0.108   0.9142  
  BinningCon   0.243549   0.318826   0.764   0.4449  
  Darkness     0.003913   0.019450   0.201   0.8406  
  White.test  -0.096997   0.046049  -2.106   0.0352 *
  Banding     -0.083564   0.164830  -0.507   0.6122  
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  
  (Dispersion parameter for binomial family taken to be 1)
  
      Null deviance: 580.63  on 498  degrees of freedom
  Residual deviance: 573.45  on 491  degrees of freedom
  AIC: 589.45
  
  Number of Fisher Scoring iterations: 4

Chisq test comparing full to reduced model 

model1.reduced <- glm(comp_h ~ 1,data=total, family=binomial)
anova(model1.reduced,model1, test="Chisq")

  Analysis of Deviance Table
  
  1: Reduced Model
  2: Full Model 
    Resid. Df Resid. Dev Df Deviance Pr(>Chi)
  1       498     580.63                     
  2       491     573.45  7    7.189   0.4095

5. Rank Heights

Screen shot of task

Analysis

 Ordinal Logistic Regression in R: polr(Rank ~ Binning+ Region + Darkness + White.test + Banding, Hess=TRUE)

*The 10m binning was the reference group.

                     Value  Std. Error      t value    p value
  Binning20  -5.083827e-03 0.152375023 -0.033363915 0.97338438
  Binning30  -7.529816e-03 0.152490000 -0.049379081 0.96061720
  Binning40  -8.458467e-04 0.150651234 -0.005614602 0.99552022
  BinningCon -3.427779e-03 0.149996129 -0.022852449 0.98176797
  RegionB     3.537331e-01 0.116174565  3.044841442 0.00232803
  RegionC     3.846758e-02 0.114319302  0.336492404 0.73649958
  Darkness   -7.435453e-05 0.009082492 -0.008186578 0.99346813
  White.test -9.755997e-04 0.020235653 -0.048211922 0.96154735
  Banding     2.360426e-03 0.077838094  0.030324817 0.97580800
  1|2        -5.792320e-01 0.263271652 -2.200130487 0.02779764
  2|3         8.150850e-01 0.263719496  3.090727112 0.00199667
  
  Residual Deviance: 3278.609 
  AIC: 3300.609

Anova comparing full and reduced models 
anova(Reduced, Full, test="Chisq")
1: Reduced 
2: Full

  Likelihood ratio tests of ordinal regression models
  
  Response: Rank
                                                 Model Resid. df Resid. Dev
  1                                                  1      1495   3289.245
  2 Binning + Region + Darkness + White.test + Banding      1486   3278.609
      Test    Df LR stat.   Pr(Chi)
  1                                
  2 1 vs 2     9 10.63635 0.3014609

6. Steepest

Screen shot of tasks 6 and 7

7. Lookup

Analysis

Anova for upper value: Aov(Upper Value Error ~ Binning + Lower Value Errorr + Darkness + White.test + Banding)

                          Df  Sum Sq Mean Sq F value Pr(>F)    
  Binning                  4   81568   20392   2.602 0.0354 *  
  IdentifyDirectLowError   1  762409  762409  97.294 <2e-16 ***
  Darkness                 1   41771   41771   5.331 0.0214 *  
  White.test               1   45314   45314   5.783 0.0166 *  
  Banding                  1   10677   10677   1.363 0.2437    
  Residuals              479 3753498    7836                   
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD

  Tukey multiple comparisons of means 95% family-wise confidence level

  Binning
               diff        lwr       upr     p adj
  20-10   -9.019592 -47.545943 29.506759 0.9682429
  30-10  -29.311284 -67.639544  9.016977 0.2243061
  40-10  -18.365407 -56.597254 19.866439 0.6818236
  Con-10   6.993858 -31.334402 45.322118 0.9873803
  30-20  -20.291692 -58.720146 18.136763 0.5982700
  40-20   -9.345816 -47.678108 28.986477 0.9632323
  Con-20  16.013450 -22.415005 54.441904 0.7846240
  40-30   10.945876 -27.187318 49.079070 0.9346411
  Con-30  36.305141  -1.924715 74.534998 0.0718755
  Con-40  25.359265 -12.773929 63.492459 0.3626387

Anova for lower value: Aov(Lower Value Error ~ Binning Contrast Codes+ Upper Value Errorr + Darkness + White.test + Banding)

                          Df  Sum Sq Mean Sq F value Pr(>F)    
  BinningConBin            1   35338   35338   4.426 0.0359 *  
  IdentifyDirectLowError   1  723662  723662  90.634 <2e-16 ***
  Darkness                 1   44895   44895   5.623 0.0181 *  
  White.test               1   35157   35157   4.403 0.0364 *  
  Banding                  1    7678    7678   0.962 0.3273    
  Residuals              482 3848509    7984                   
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Means

    BinningConBin     Mean        SD
  1        Binned 107.3659  97.16117
  2    Continuous 128.6074 100.90448

8. Steepness Compare

Screen shot of task

Analysis

Logistic regression
glm(Comparison ~ Binning + Darkness + White.test + Banding, family = "binomial")
anova(Reduced Model, Full Model, test="Chisq")

  Analysis of Deviance Table
  
  Model 1: Comparison ~ 1
  Model 2: Comparison ~ Binning + Darkness + White.test + Banding
    Resid. Df Resid. Dev Df Deviance Pr(>Chi)
  1       498     661.13                     
  2       491     659.78  7   1.3501    0.987

9. Steepness Rank

Screen shot of task

Analysis

Ordinal Logistic 
 polr(Rank ~ Binning + Region + Darkness + White.test + Banding, Hess=TRUE)

*The 10m binning was the reference group.

   
  Binning20   0.0002925308 0.154395633  0.001894683
  Binning30  -0.0031053928 0.153850799 -0.020184444
  Binning40  -0.0181773346 0.152994257 -0.118810568
  BinningCon -0.0225647760 0.153024646 -0.147458443
  RegionB    -0.0705973907 0.114015426 -0.619191572
  RegionC     1.2246834330 0.123820758  9.890776418
  Darkness    0.0015326991 0.009241387  0.165851622
  White.test  0.0020395608 0.020580812  0.099100113
  Banding    -0.0138311857 0.079650264 -0.173648962
  1|2        -0.4416820007 0.267225768 -1.652842101
  2|3         1.0528579936 0.268550953  3.920514835
  
  Residual Deviance: 3151.449 
  AIC: 3173.449

Anova comparing full and reduced models 
anova(Reduced, Full, test="Chisq")
1: Reduced 
2: Full

  Likelihood ratio tests of ordinal regression models
  
  Response: Rank
                                                 Model Resid. df Resid. Dev
  1                                                  1      1495   3289.245
  2 Binning + Region + Darkness + White.test + Banding      1486   3151.449
      Test    Df LR stat. Pr(Chi)
  1                              
  2 1 vs 2     9 137.7962       0

10. Average Height

Screen shot of task

Analysis

Aov(Error ~ Binning + Banding + Darkness +White.test)

               Df  Sum Sq Mean Sq F value Pr(>F)
  Binning       4   11146    2787   1.241  0.293
  Banding       1    6037    6037   2.688  0.102
  Darkness      1     884     884   0.394  0.531
  White.test    1       7       7   0.003  0.957
  Residuals   474 1064590    2246

11. Average Height Comparison

Screen shot of task

Logistic regression
glm(Comparison ~ Binning + Darkness + White.test + Banding, family = "binomial")
*The 40m binning was the reference group.   

  Deviance Residuals: 
      Min       1Q   Median       3Q      Max  
  -1.0013  -0.6591  -0.5524  -0.4994   2.0909  
  
  Coefficients:
                 Estimate Std. Error z value Pr(>|z|)    
  (Intercept)   -0.755361   0.626605  -1.205 0.228017    
  Binning10 -0.974691   0.333563  -2.922 0.003477 ** 
  Binning20 -0.854097   0.326668  -2.615 0.008934 ** 
  Binning30 -1.454919   0.372835  -3.902 9.53e-05 ***
  BinningCon -1.289935   0.355186  -3.632 0.000282 ***
  Darkness       0.007435   0.022236   0.334 0.738103    
  White.test     0.012246   0.048050   0.255 0.798830    
  Banding        0.037186   0.189888   0.196 0.844743    
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  
  (Dispersion parameter for binomial family taken to be 1)
  
      Null deviance: 502.71  on 498  degrees of freedom
  Residual deviance: 479.91  on 491  degrees of freedom
  AIC: 495.91
  
  Number of Fisher Scoring iterations: 4

12. Identify and Relation-seeking

Screen shot of task

Display Parameter Metrics

Screen of each question

Darkness measure

Darkness measure

Lightness measure

Banding measure

images from. http://www.lagom.nl/lcd-test/

Figure 1

Confidence rating. Error bars (95% CI)

(a) Locate 275m

(b) Compare Heights

(c) Steepness Compare

To Bin or Not to Bin? Evaluating the Impact of Binning Continuous Data: Supplementary Materials

1. Highest Point Task

Screen shot of task

Analysis

2. Highest Point in Region

Screen shot of task

Analysis

3. Locate 275m

Screen shot of task

Analysis

4. Compare Heights

Screen shot of task

Analysis

5. Rank Heights

Screen shot of task

Analysis

6. Steepest

Screen shot of tasks 6 and 7

7. Lookup

Analysis

8. Steepness Compare

Screen shot of task

Analysis

9. Steepness Rank

Screen shot of task

Analysis

10. Average Height

Screen shot of task

Analysis

11. Average Height Comparison

Screen shot of task

12. Identify and Relation-seeking

Screen shot of task

Display Parameter Metrics

Screen of each question

Darkness measure

Darkness measure

Lightness measure

Banding measure

Figure 1

Confidence rating. Error bars (95% CI)

(a) Locate 275m

(b) Compare Heights

(c) Steepness Compare

(d) Average Height Compare