Summary
This analysis is looking at six different timers GSI is using over a 7 week sample. The six categories are Break, Breakdown, Fuel Timer, Loading/Unloading, Lunch, and Restroom. We will be using an alpha level of 0.05 for significance.
I have broken these down by department, and as you know, each department has a different number of routes.
Each department has two different plots. The first plot is ploting each route over the 7 weeks we are analyzing. The second is a boxplot of each route in which you will see seven dots corresponding to the seven weeks we are analyzing.
If you’ve never seen a boxplot before here is the breakdown: the middle line of the box is the ‘median’, the ends of the boxes are the 25th and 75th percentile (or 1 standard deviation away from the mean), and the lines extending from the box are within 1.5 standard deviations away from the mean. If there are dots not attached to the box these are known as ‘outliers’.
Finally I ran an Analysis of Variance (ANOVA) within each department which is comparing each route’s average and seeing if one route differs significantly from the other routes. The ‘Levenes’ Test is checking if the variances come from the same population, so if this fails we cannot run an ANOVA. If there is a significant difference within the department, I ran a Tukey HSD (Honest Significant Test) which is doing multiple comparisons between each route and seeing which ones are significantly different from each other.
From there we can deduce which routes are taking more or less time than the other routes. I will now go through each department and explain the results.
Timer Summary
CF
Df Sum Sq Mean Sq F value Pr(>F)
group 3 898.2 299.4 2.558 0.0789 .
Residuals 24 2809.6 117.1
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
As you can see from the plots there is not a big difference between groups and the ANOVA supports this producting a p-value of 0.08 which is not significant at a level of 0.05
CR
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 7 0.4639 0.8557
48
Df Sum Sq Mean Sq F value Pr(>F)
group 7 13075 1867.9 12.47 5.67e-09 ***
Residuals 48 7191 149.8
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = response ~ group, data = dati)
$group
diff lwr upr p adj
2-1 -27.1690476 -47.897926 -6.440169 0.0031292
3-1 -0.7166667 -21.445545 20.012212 1.0000000
4-1 -26.0857143 -46.814593 -5.356836 0.0051719
5-1 -23.8714286 -44.600307 -3.142550 0.0138612
6-1 -0.9642857 -21.693164 19.764593 0.9999999
7-1 -27.8714286 -48.600307 -7.142550 0.0022453
8-1 13.5833333 -7.145545 34.312212 0.4443406
3-2 26.4523810 5.723503 47.181259 0.0043690
4-2 1.0833333 -19.645545 21.812212 0.9999998
5-2 3.2976190 -17.431259 24.026497 0.9995890
6-2 26.2047619 5.475883 46.933640 0.0048970
7-2 -0.7023810 -21.431259 20.026497 1.0000000
8-2 40.7523810 20.023503 61.481259 0.0000030
4-3 -25.3690476 -46.097926 -4.640169 0.0071615
5-3 -23.1547619 -43.883640 -2.425883 0.0188168
6-3 -0.2476190 -20.976497 20.481259 1.0000000
7-3 -27.1547619 -47.883640 -6.425883 0.0031503
8-3 14.3000000 -6.428878 35.028878 0.3782561
5-4 2.2142857 -18.514593 22.943164 0.9999716
6-4 25.1214286 4.392550 45.850307 0.0080029
7-4 -1.7857143 -22.514593 18.943164 0.9999935
8-4 39.6690476 18.940169 60.397926 0.0000054
6-5 22.9071429 2.178264 43.636021 0.0208776
7-5 -4.0000000 -24.728878 16.728878 0.9985585
8-5 37.4547619 16.725883 58.183640 0.0000174
7-6 -26.9071429 -47.636021 -6.178264 0.0035373
8-6 14.5476190 -6.181259 35.276497 0.3565664
8-7 41.4547619 20.725883 62.183640 0.0000021
Levene’s test passes, and the ANOVA was definitely significant with a p-value almost at zero. From the multiple comparisons it looks like routes 1,3,6, and 8 are all similar with 2,4,5, and 7 being a lot lower than the rest.
DEL
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.6358 0.4407
12
Df Sum Sq Mean Sq F value Pr(>F)
group 1 377463 377463 47.97 1.59e-05 ***
Residuals 12 94430 7869
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = response ~ group, data = dati)
$group
diff lwr upr p adj
2-1 -328.4 -431.7121 -225.0879 1.59e-05
From the boxplot you can see Delc2 is significantly higher than the other two. Levene’s test failed because delc1 is extremely low compared to the other two. I took out delc1 and Levene’s test passed which is what you’re seeing. From the comparisons you can see delc2 and delc3 are significantly different from each other.
My guess here is that delc1 is not using it’s timers correctly because it is so much different than the other two.
PT
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 3 1.5508 0.2272
24
Df Sum Sq Mean Sq F value Pr(>F)
group 3 5459 1819.8 7.531 0.00102 **
Residuals 24 5800 241.7
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = response ~ group, data = dati)
$group
diff lwr upr p adj
2-1 26.066667 3.144788 48.988546 0.0216722
3-1 -4.195238 -27.117117 18.726641 0.9571302
4-1 -10.683333 -33.605212 12.238546 0.5804971
3-2 -30.261905 -53.183784 -7.340026 0.0066263
4-2 -36.750000 -59.671879 -13.828121 0.0009710
4-3 -6.488095 -29.409974 16.433784 0.8623675
Levene’s Test passed, and from the multiple comparisons we see that pt2 is significantly different than pt1, pt3, and pt4.
RA
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 6 1.5359 0.1902
42
Df Sum Sq Mean Sq F value Pr(>F)
group 6 102944 17157 25.43 1.66e-12 ***
Residuals 42 28339 675
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = response ~ group, data = dati)
$group
diff lwr upr p adj
2-1 -125.5833333 -168.56363542 -82.603031 0.0000000
3-1 -115.3952381 -158.37554018 -72.414936 0.0000000
4-1 -115.2690476 -158.24934971 -72.288746 0.0000000
5-1 -45.9595238 -88.93982590 -2.979222 0.0292128
6-1 -133.3047619 -176.28506399 -90.324460 0.0000000
7-1 -72.3380952 -115.31839733 -29.357793 0.0001036
3-2 10.1880952 -32.79220685 53.168397 0.9895923
4-2 10.3142857 -32.66601638 53.294588 0.9888981
5-2 79.6238095 36.64350743 122.604112 0.0000189
6-2 -7.7214286 -50.70173066 35.258874 0.9976837
7-2 53.2452381 10.26493601 96.225540 0.0070203
4-3 0.1261905 -42.85411161 43.106493 1.0000000
5-3 69.4357143 26.45541220 112.416016 0.0002024
6-3 -17.9095238 -60.88982590 25.070778 0.8526825
7-3 43.0571429 0.07684077 86.037445 0.0493307
5-4 69.3095238 26.32922172 112.289826 0.0002083
6-4 -18.0357143 -61.01601638 24.944588 0.8485481
7-4 42.9309524 -0.04934971 85.911254 0.0504341
6-5 -87.3452381 -130.32554018 -44.364936 0.0000030
7-5 -26.3785714 -69.35887352 16.601731 0.4916998
7-6 60.9666667 17.98636458 103.946969 0.0013590
Levene’s test passed, and from the multiple comparisons we see that ra1 is significantly different than all the other groups, ra5 is significantly different than all other groups except ra7, ra7 is different than ra2, ra3 (barely), and ra6. All other comparisons failed.
RC
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 14 1.4662 0.1404
90
Df Sum Sq Mean Sq F value Pr(>F)
group 14 135635 9688 15.47 <2e-16 ***
Residuals 90 56344 626
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = response ~ group, data = dati)
$group
diff lwr upr p adj
2-1 -15.8857143 -62.528991 30.757563 0.9970108
3-1 -14.6285714 -61.271849 32.014706 0.9987435
4-1 -3.5523810 -50.195658 43.090896 1.0000000
5-1 22.2500000 -24.393277 68.893277 0.9383744
6-1 86.1642857 39.521009 132.807563 0.0000006
7-1 -33.2452381 -79.888515 13.398039 0.4609591
8-1 -20.2000000 -66.843277 26.443277 0.9715026
9-1 -9.3738095 -56.017087 37.269468 0.9999934
10-1 -39.2333333 -85.876611 7.409944 0.2016079
11-1 -11.5190476 -58.162325 35.124230 0.9999169
12-1 -0.1285714 -46.771849 46.514706 1.0000000
13-1 61.7642857 15.121009 108.407563 0.0011598
14-1 -20.9571429 -67.600420 25.686134 0.9613866
15-1 60.9119048 14.268628 107.555182 0.0014703
3-2 1.2571429 -45.386134 47.900420 1.0000000
4-2 12.3333333 -34.309944 58.976611 0.9998144
5-2 38.1357143 -8.507563 84.778991 0.2397987
6-2 102.0500000 55.406723 148.693277 0.0000000
7-2 -17.3595238 -64.002801 29.283753 0.9927698
8-2 -4.3142857 -50.957563 42.328991 1.0000000
9-2 6.5119048 -40.131372 53.155182 0.9999999
10-2 -23.3476190 -69.990896 23.295658 0.9124739
11-2 4.3666667 -42.276611 51.009944 1.0000000
12-2 15.7571429 -30.886134 62.400420 0.9972504
13-2 77.6500000 31.006723 124.293277 0.0000095
14-2 -5.0714286 -51.714706 41.571849 1.0000000
15-2 76.7976190 30.154342 123.440896 0.0000125
4-3 11.0761905 -35.567087 57.719468 0.9999480
5-3 36.8785714 -9.764706 83.521849 0.2891152
6-3 100.7928571 54.149580 147.436134 0.0000000
7-3 -18.6166667 -65.259944 28.026611 0.9860703
8-3 -5.5714286 -52.214706 41.071849 1.0000000
9-3 5.2547619 -41.388515 51.898039 1.0000000
10-3 -24.6047619 -71.248039 22.038515 0.8751215
11-3 3.1095238 -43.533753 49.752801 1.0000000
12-3 14.5000000 -32.143277 61.143277 0.9988576
13-3 76.3928571 29.749580 123.036134 0.0000142
14-3 -6.3285714 -52.971849 40.314706 1.0000000
15-3 75.5404762 28.897199 122.183753 0.0000186
5-4 25.8023810 -20.840896 72.445658 0.8319141
6-4 89.7166667 43.073389 136.359944 0.0000002
7-4 -29.6928571 -76.336134 16.950420 0.6498835
8-4 -16.6476190 -63.290896 29.995658 0.9952022
9-4 -5.8214286 -52.464706 40.821849 1.0000000
10-4 -35.6809524 -82.324230 10.962325 0.3413816
11-4 -7.9666667 -54.609944 38.676611 0.9999992
12-4 3.4238095 -43.219468 50.067087 1.0000000
13-4 65.3166667 18.673389 111.959944 0.0004205
14-4 -17.4047619 -64.048039 29.238515 0.9925863
15-4 64.4642857 17.821009 111.107563 0.0005383
6-5 63.9142857 17.271009 110.557563 0.0006306
7-5 -55.4952381 -102.138515 -8.851961 0.0062373
8-5 -42.4500000 -89.093277 4.193277 0.1151737
9-5 -31.6238095 -78.267087 15.019468 0.5468737
10-5 -61.4833333 -108.126611 -14.840056 0.0012544
11-5 -33.7690476 -80.412325 12.874230 0.4340190
12-5 -22.3785714 -69.021849 24.264706 0.9356546
13-5 39.5142857 -7.128991 86.157563 0.1925655
14-5 -43.2071429 -89.850420 3.436134 0.0998950
15-5 38.6619048 -7.981372 85.305182 0.2209198
7-6 -119.4095238 -166.052801 -72.766247 0.0000000
8-6 -106.3642857 -153.007563 -59.721009 0.0000000
9-6 -95.5380952 -142.181372 -48.894818 0.0000000
10-6 -125.3976190 -172.040896 -78.754342 0.0000000
11-6 -97.6833333 -144.326611 -51.040056 0.0000000
12-6 -86.2928571 -132.936134 -39.649580 0.0000006
13-6 -24.4000000 -71.043277 22.243277 0.8817715
14-6 -107.1214286 -153.764706 -60.478151 0.0000000
15-6 -25.2523810 -71.895658 21.390896 0.8526580
8-7 13.0452381 -33.598039 59.688515 0.9996464
9-7 23.8714286 -22.771849 70.514706 0.8979201
10-7 -5.9880952 -52.631372 40.655182 1.0000000
11-7 21.7261905 -24.917087 68.369468 0.9486277
12-7 33.1166667 -13.526611 79.759944 0.4676497
13-7 95.0095238 48.366247 141.652801 0.0000000
14-7 12.2880952 -34.355182 58.931372 0.9998222
15-7 94.1571429 47.513866 140.800420 0.0000000
9-8 10.8261905 -35.817087 57.469468 0.9999606
10-8 -19.0333333 -65.676611 27.609944 0.9829929
11-8 8.6809524 -37.962325 55.324230 0.9999975
12-8 20.0714286 -26.571849 66.714706 0.9729991
13-8 81.9642857 35.321009 128.607563 0.0000023
14-8 -0.7571429 -47.400420 45.886134 1.0000000
15-8 81.1119048 34.468628 127.755182 0.0000031
10-9 -29.8595238 -76.502801 16.783753 0.6411279
11-9 -2.1452381 -48.788515 44.498039 1.0000000
12-9 9.2452381 -37.398039 55.888515 0.9999944
13-9 71.1380952 24.494818 117.781372 0.0000736
14-9 -11.5833333 -58.226611 35.059944 0.9999112
15-9 70.2857143 23.642437 116.928991 0.0000956
11-10 27.7142857 -18.928991 74.357563 0.7490464
12-10 39.1047619 -7.538515 85.748039 0.2058452
13-10 100.9976190 54.354342 147.640896 0.0000000
14-10 18.2761905 -28.367087 64.919468 0.9882416
15-10 100.1452381 53.501961 146.788515 0.0000000
12-11 11.3904762 -35.252801 58.033753 0.9999273
13-11 73.2833333 26.640056 119.926611 0.0000379
14-11 -9.4380952 -56.081372 37.205182 0.9999928
15-11 72.4309524 25.787675 119.074230 0.0000494
13-12 61.8928571 15.249580 108.536134 0.0011187
14-12 -20.8285714 -67.471849 25.814706 0.9632680
15-12 61.0404762 14.397199 107.683753 0.0014188
14-13 -82.7214286 -129.364706 -36.078151 0.0000018
15-13 -0.8523810 -47.495658 45.790896 1.0000000
15-14 81.8690476 35.225770 128.512325 0.0000024
Levene’s test passed. Rc50 is different than all others execpt Rc90, Rc90 is different than all others except Rc50 and Rc5, Rc92 is different than all others except Rc5, and Rc50. Therefore I would look at Rc5, Rc50, Rc90, and Rc92 since they are much higher than the rest and see what could be causing this.
RM
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 3 0.6629 0.5829
24
Df Sum Sq Mean Sq F value Pr(>F)
group 3 1500 500.1 1.791 0.176
Residuals 24 6701 279.2
There is no difference in the RM routes.
RR
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 4 2.3929 0.07269 .
30
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)
group 4 38456 9614 12.09 5.7e-06 ***
Residuals 30 23854 795
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = response ~ group, data = dati)
$group
diff lwr upr p adj
2-1 -26.38571 -70.105405 17.333977 0.4199401
3-1 -42.00952 -85.729215 1.710167 0.0643250
5-1 -59.53095 -103.250643 -15.811261 0.0037277
6-1 34.91429 -8.805405 78.633977 0.1676783
3-2 -15.62381 -59.343501 28.095881 0.8363960
5-2 -33.14524 -76.864929 10.574453 0.2076176
6-2 61.30000 17.580309 105.019691 0.0027292
5-3 -17.52143 -61.241120 26.198262 0.7721004
6-3 76.92381 33.204119 120.643501 0.0001593
6-5 94.44524 50.725547 138.164929 0.0000063
Levene’s test barely passed here, I’m guessing because of RR3 which has some weeks very close to 0 minutes of break. RR6 is different than all others except RR1, and RR5 is different than RR1.