This is an R Markdown document. Markdown is a simple formatting syntax for authoring web pages (click the MD toolbar button for help on Markdown).
When you click the Knit HTML button a web page will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:
as of August 28, 2014, superceding the version of August 24. Always use the most recent version.
In this study, we conduct an experiment to investigate the influencing factors of diamond stone prices in Singapore. To do so, the dataset “Diamond” under the “Ecdat” package in R was used and we examed the effect of “Color” and “Clarity” factors in this study.
install.packages("Ecdat")
## Installing package into 'C:/Users/wei/Documents/R/win-library/3.1'
## (as 'lib' is unspecified)
## Error: trying to use CRAN without setting a mirror
library("Ecdat", lib.loc="C:/Users/wei/Documents/R/win-library/3.1")
## Loading required package: Ecfun
##
## Attaching package: 'Ecdat'
##
## The following object is masked from 'package:datasets':
##
## Orange
data1<-data.frame(Diamond)
head(data1)
## carat colour clarity certification price
## 1 0.30 D VS2 GIA 1302
## 2 0.30 E VS1 GIA 1510
## 3 0.30 G VVS1 GIA 1510
## 4 0.30 G VS1 GIA 1260
## 5 0.31 D VS1 GIA 1641
## 6 0.31 E VS1 GIA 1555
In this multi-factor, multi-level experiment, we exam the effects of two factors: “colour” with 6 levels and “clarity” with 5 levels.
data1$colour<-as.factor(data1$colour)
nlevels(data1$colour)
## [1] 6
data1$clarity<-as.factor(data1$clarity)
nlevels(data1$clarity)
## [1] 5
In this study, the continuous variable is the response variable: “price” indicating the price of the diamond.
The response variable is the “price” mentioned above.
Singfat Chu at the National University of Singapore used data pertaining to 308 diamond stones listed in an advertisement to conduct his study on the pricing of the C's of Diamond Stones. The dataset has information on the price of the diamond stone and 4Cs (Carat, Clarity, Colour and Cut) that charaterize the quality of a diamond stone. In this study, we focus on two of them: Colour and Clarity.
The dataset was selected from an advertisement and thus the data were not collected under a well designed random experiment, we may conclude that the data are not random.
To test the effect of colour and clarity on diamond pricing, we conduct a multi-factor, multi-level analysis of variance on the two factors and also investigate their interaction effect.
Traditionally, 4C's are the factors that characterize the quality (and thus influence the price) of a diamond stone. Therefore, it is interesting for us to conduct this experiment to test the validity of thiscommon rule.
Since the data were not collected in a pre-designed experiment, they are not random.
No, there are no replicated or repeated measures.
No, since there's no obvious nuisance variable and the data size is relatively small.
For the first boxplot (by colour), the median of diamond price doesn't show much variance in different levels (different colors), indicating that the variation in diamond pricing might simply due to the sample randomization. For the second boxplot (by clarity), we can see that the median of the diamond price does show some variability among different clarity levels, indicating that the variation in the diamond pricing might have something to do with the clarity level.
boxplot(price~colour, data1)
boxplot(price~clarity, data1)
In this section we estimate three models to conduct the analysis of variance: the first two are used to test the effect of colour/clarity on diamond pricing separately and the third one is to test whehter there is an interaction effect between the diamond colour and clarity.
model_colour=aov(price~colour,data=data1)
model_clarity=aov(price~clarity,data=data1)
model_colour_clarity=aov(price~colour*clarity,data=data1)
According to the estimation results, we may conclude that the variation in diamond pricing may due the variation in diamond clarity levels and/or the interaction effect between the diamond colour and clarity. The first model estimation result shows that diamond colour itself might not be able to explain the variation in the pricing, in other words, the variation in pricing might simply due to the randomization of the sample.
summary(model_colour)
## Df Sum Sq Mean Sq F value Pr(>F)
## colour 5 1.08e+08 21645956 1.9 0.095 .
## Residuals 302 3.45e+09 11414561
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(model_clarity)
## Df Sum Sq Mean Sq F value Pr(>F)
## clarity 4 3.00e+08 74917212 6.97 2.2e-05 ***
## Residuals 303 3.26e+09 10745078
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(model_colour_clarity)
## Df Sum Sq Mean Sq F value Pr(>F)
## colour 5 1.08e+08 21645956 2.16 0.058 .
## clarity 4 2.96e+08 74015430 7.40 1.1e-05 ***
## colour:clarity 20 3.71e+08 18537589 1.85 0.016 *
## Residuals 278 2.78e+09 10001382
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The qqplot and fitted Y vs. residuals plot show that our data generally follows the normal distribution assumption.
qqnorm(residuals(model_colour))
qqline(residuals(model_colour))
qqnorm(residuals(model_clarity))
qqline(residuals(model_clarity))
qqnorm(residuals(model_colour_clarity))
qqline(residuals(model_colour_clarity))
plot(fitted(model_colour),residuals(model_colour))
plot(fitted(model_clarity),residuals(model_clarity))
plot(fitted(model_colour_clarity),residuals(model_colour_clarity))
###Interaction Plot The interaction plot shows that the interaction effect does exist, which is consistent with our analysis of variance result.
interaction.plot(data1$colour,data1$clarity,data1$price, xlab= "Colour", ylab="Price", main ="Interaction plot", trace.label="Clarity")
###Post-Hoc Test The purpose of Tukey's HSD test is to determine which groups in the sample differ. While ANOVA can tell the researcher whether groups in the sample differ, it cannot tell the researcher which groups differ.
TukeyHSD(model_colour_clarity)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = price ~ colour * clarity, data = data1)
##
## $colour
## diff lwr upr p adj
## E-D -1591.9 -4241 1057.5 0.5169
## F-D -2313.5 -4794 166.9 0.0832
## G-D -2673.7 -5206 -140.9 0.0318
## H-D -2134.9 -4684 414.2 0.1586
## I-D -1924.8 -4609 759.7 0.3128
## F-E -721.5 -2418 974.4 0.8264
## G-E -1081.7 -2853 690.0 0.4986
## H-E -542.9 -2338 1252.1 0.9538
## I-E -332.9 -2316 1649.8 0.9968
## G-F -360.2 -1867 1147.0 0.9834
## H-F 178.6 -1356 1713.1 0.9994
## I-F 388.6 -1362 2138.9 0.9881
## H-G 538.8 -1079 2156.7 0.9313
## I-G 748.8 -1075 2572.6 0.8469
## I-H 210.0 -1636 2056.4 0.9995
##
## $clarity
## diff lwr upr p adj
## VS1-IF 2152.6 526.3 3779 0.0030
## VS2-IF 3103.3 1332.3 4874 0.0000
## VVS1-IF 2885.7 1107.1 4664 0.0001
## VVS2-IF 2622.6 985.4 4260 0.0002
## VS2-VS1 950.7 -583.4 2485 0.4346
## VVS1-VS1 733.2 -809.8 2276 0.6885
## VVS2-VS1 470.0 -907.5 1848 0.8823
## VVS1-VS2 -217.5 -1912.5 1477 0.9967
## VVS2-VS2 -480.7 -2026.5 1065 0.9132
## VVS2-VVS1 -263.2 -1817.8 1291 0.9904
##
## $`colour:clarity`
## diff lwr upr p adj
## E:IF-D:IF -7653.600 -20779.7 5472.5 0.9264
## F:IF-D:IF -6095.750 -18805.1 6613.6 0.9937
## G:IF-D:IF -8039.909 -20555.2 4475.4 0.8192
## H:IF-D:IF -7431.909 -19947.2 5083.4 0.9113
## I:IF-D:IF -7393.250 -20102.6 5316.1 0.9282
## D:VS1-D:IF -5411.857 -18221.7 7397.9 0.9992
## E:VS1-D:IF -4362.611 -16673.4 7948.2 1.0000
## F:VS1-D:IF -4916.440 -17136.2 7303.3 0.9997
## G:VS1-D:IF -5631.750 -18103.5 6840.0 0.9975
## H:VS1-D:IF -4445.182 -16960.5 8070.1 1.0000
## I:VS1-D:IF -4408.250 -17117.6 8301.1 1.0000
## D:VS2-D:IF -7489.000 -22164.5 7186.5 0.9850
## E:VS2-D:IF -3575.714 -16385.5 9234.1 1.0000
## F:VS2-D:IF -3969.857 -16372.9 8433.2 1.0000
## G:VS2-D:IF -3980.444 -16611.1 8650.2 1.0000
## H:VS2-D:IF -3649.071 -16052.1 8754.0 1.0000
## I:VS2-D:IF -4417.857 -17227.7 8391.9 1.0000
## D:VVS1-D:IF 5910.000 -8765.5 20585.5 0.9997
## E:VVS1-D:IF -1823.200 -14949.3 11302.9 1.0000
## F:VVS1-D:IF -5395.278 -17706.1 6915.5 0.9985
## G:VVS1-D:IF -5316.500 -17788.3 7155.3 0.9990
## H:VVS1-D:IF -4974.600 -17541.9 7592.7 0.9997
## I:VVS1-D:IF -3309.600 -16435.7 9816.5 1.0000
## D:VVS2-D:IF -880.250 -14277.1 12516.6 1.0000
## E:VVS2-D:IF -4627.778 -17258.4 8002.9 0.9999
## F:VVS2-D:IF -5512.647 -17842.5 6817.2 0.9979
## G:VVS2-D:IF -4722.905 -16987.4 7541.5 0.9998
## H:VVS2-D:IF -4575.867 -16951.3 7799.6 0.9999
## I:VVS2-D:IF -3876.167 -16347.9 8595.6 1.0000
## F:IF-E:IF 1557.850 -5273.2 8388.9 1.0000
## G:IF-E:IF -386.309 -6849.2 6076.6 1.0000
## H:IF-E:IF 221.691 -6241.2 6684.6 1.0000
## I:IF-E:IF 260.350 -6570.7 7091.4 1.0000
## D:VS1-E:IF 2241.743 -4774.5 9258.0 1.0000
## E:VS1-E:IF 3290.989 -2766.5 9348.4 0.9667
## F:VS1-E:IF 2737.160 -3133.0 8607.3 0.9959
## G:VS1-E:IF 2021.850 -4356.3 8400.0 1.0000
## H:VS1-E:IF 3208.418 -3254.4 9671.3 0.9897
## I:VS1-E:IF 3245.350 -3585.7 10076.4 0.9946
## D:VS2-E:IF 164.600 -9860.7 10189.9 1.0000
## E:VS2-E:IF 4077.886 -2938.3 11094.1 0.9288
## F:VS2-E:IF 3683.743 -2559.0 9926.5 0.9168
## G:VS2-E:IF 3673.156 -3010.3 10356.7 0.9618
## H:VS2-E:IF 4004.529 -2238.2 10247.3 0.8214
## I:VS2-E:IF 3235.743 -3780.5 10252.0 0.9966
## D:VVS1-E:IF 13563.600 3538.3 23588.9 0.0002
## E:VVS1-E:IF 5830.400 -1748.0 13408.8 0.4561
## F:VVS1-E:IF 2258.322 -3799.1 8315.8 0.9999
## G:VVS1-E:IF 2337.100 -4041.1 8715.3 0.9999
## H:VVS1-E:IF 2679.000 -3884.1 9242.1 0.9996
## I:VVS1-E:IF 4344.000 -3234.4 11922.4 0.9386
## D:VVS2-E:IF 6773.350 -1264.7 14811.4 0.2622
## E:VVS2-E:IF 3025.822 -3657.7 9709.3 0.9974
## F:VVS2-E:IF 2140.953 -3955.1 8237.0 1.0000
## G:VVS2-E:IF 2930.695 -3031.9 8893.3 0.9911
## H:VVS2-E:IF 3077.733 -3110.0 9265.5 0.9895
## I:VVS2-E:IF 3777.433 -2600.7 10155.6 0.9137
## G:IF-F:IF -1944.159 -7511.9 3623.6 1.0000
## H:IF-F:IF -1336.159 -6903.9 4231.6 1.0000
## I:IF-F:IF -1297.500 -7288.7 4693.7 1.0000
## D:VS1-F:IF 683.893 -5517.6 6885.4 1.0000
## E:VS1-F:IF 1733.139 -3358.4 6824.7 1.0000
## F:VS1-F:IF 1179.310 -3688.0 6046.6 1.0000
## G:VS1-F:IF 464.000 -5005.2 5933.2 1.0000
## H:VS1-F:IF 1650.568 -3917.2 7218.3 1.0000
## I:VS1-F:IF 1687.500 -4303.7 7678.7 1.0000
## D:VS2-F:IF -1393.250 -10866.2 8079.7 1.0000
## E:VS2-F:IF 2520.036 -3681.5 8721.6 0.9996
## F:VS2-F:IF 2125.893 -3184.8 7436.6 0.9997
## G:VS2-F:IF 2115.306 -3707.1 7937.7 1.0000
## H:VS2-F:IF 2446.679 -2864.0 7757.3 0.9966
## I:VS2-F:IF 1677.893 -4523.6 7879.4 1.0000
## D:VVS1-F:IF 12005.750 2532.8 21478.7 0.0010
## E:VVS1-F:IF 4272.550 -2558.5 11103.6 0.8558
## F:VVS1-F:IF 700.472 -4391.1 5792.0 1.0000
## G:VVS1-F:IF 779.250 -4690.0 6248.5 1.0000
## H:VVS1-F:IF 1121.150 -4562.6 6804.9 1.0000
## I:VVS1-F:IF 2786.150 -4044.9 9617.2 0.9996
## D:VVS2-F:IF 5215.500 -2122.2 12553.2 0.6339
## E:VVS2-F:IF 1467.972 -4354.5 7290.4 1.0000
## F:VVS2-F:IF 583.103 -4554.3 5720.5 1.0000
## G:VVS2-F:IF 1372.845 -3605.6 6351.3 1.0000
## H:VVS2-F:IF 1519.883 -3726.0 6765.8 1.0000
## I:VVS2-F:IF 2219.583 -3249.6 7688.8 0.9996
## H:IF-G:IF 608.000 -4501.3 5717.3 1.0000
## I:IF-G:IF 646.659 -4921.1 6214.4 1.0000
## D:VS1-G:IF 2628.052 -3165.4 8421.5 0.9973
## E:VS1-G:IF 3677.298 -908.5 8263.1 0.3635
## F:VS1-G:IF 3123.469 -1212.0 7458.9 0.6046
## G:VS1-G:IF 2408.159 -2593.6 7409.9 0.9934
## H:VS1-G:IF 3594.727 -1514.6 8704.1 0.6555
## I:VS1-G:IF 3631.659 -1936.1 9199.4 0.7960
## D:VS2-G:IF 550.909 -8660.1 9761.9 1.0000
## E:VS2-G:IF 4464.195 -1329.3 10257.6 0.4525
## F:VS2-G:IF 4070.052 -757.8 8897.9 0.2613
## G:VS2-G:IF 4059.465 -1326.3 9445.2 0.5029
## H:VS2-G:IF 4390.838 -437.0 9218.7 0.1394
## I:VS2-G:IF 3622.052 -2171.4 9415.5 0.8563
## D:VVS1-G:IF 13949.909 4738.9 23160.9 0.0000
## E:VVS1-G:IF 6216.709 -246.2 12679.6 0.0787
## F:VVS1-G:IF 2644.631 -1941.1 7230.4 0.9344
## G:VVS1-G:IF 2723.409 -2278.4 7725.2 0.9658
## H:VVS1-G:IF 3065.309 -2170.2 8300.8 0.9232
## I:VVS1-G:IF 4730.309 -1732.6 11193.2 0.5696
## D:VVS2-G:IF 7159.659 163.4 14155.9 0.0373
## E:VVS2-G:IF 3412.131 -1973.6 8797.9 0.8389
## F:VVS2-G:IF 2527.262 -2109.4 7163.9 0.9654
## G:VVS2-G:IF 3317.004 -1142.8 7776.8 0.5333
## H:VVS2-G:IF 3464.042 -1292.5 8220.6 0.5808
## I:VVS2-G:IF 4163.742 -838.0 9165.5 0.2858
## I:IF-H:IF 38.659 -5529.1 5606.4 1.0000
## D:VS1-H:IF 2020.052 -3773.4 7813.5 1.0000
## E:VS1-H:IF 3069.298 -1516.5 7655.1 0.7525
## F:VS1-H:IF 2515.469 -1820.0 6850.9 0.9301
## G:VS1-H:IF 1800.159 -3201.6 6801.9 1.0000
## H:VS1-H:IF 2986.727 -2122.6 8096.1 0.9244
## I:VS1-H:IF 3023.659 -2544.1 8591.4 0.9669
## D:VS2-H:IF -57.091 -9268.1 9153.9 1.0000
## E:VS2-H:IF 3856.195 -1937.3 9649.6 0.7622
## F:VS2-H:IF 3462.052 -1365.8 8289.9 0.6148
## G:VS2-H:IF 3451.465 -1934.3 8837.2 0.8228
## H:VS2-H:IF 3782.838 -1045.0 8610.7 0.4147
## I:VS2-H:IF 3014.052 -2779.4 8807.5 0.9806
## D:VVS1-H:IF 13341.909 4130.9 22552.9 0.0000
## E:VVS1-H:IF 5608.709 -854.2 12071.6 0.2095
## F:VVS1-H:IF 2036.631 -2549.1 6622.4 0.9981
## G:VVS1-H:IF 2115.409 -2886.4 7117.2 0.9992
## H:VVS1-H:IF 2457.309 -2778.2 7692.8 0.9955
## I:VVS1-H:IF 4122.309 -2340.6 10585.2 0.8295
## D:VVS2-H:IF 6551.659 -444.6 13547.9 0.1047
## E:VVS2-H:IF 2804.131 -2581.6 8189.9 0.9805
## F:VVS2-H:IF 1919.262 -2717.4 6555.9 0.9994
## G:VVS2-H:IF 2709.004 -1750.8 7168.8 0.8895
## H:VVS2-H:IF 2856.042 -1900.5 7612.6 0.9011
## I:VVS2-H:IF 3555.742 -1446.0 8557.5 0.6336
## D:VS1-I:IF 1981.393 -4220.1 8182.9 1.0000
## E:VS1-I:IF 3030.639 -2060.9 8122.2 0.9092
## F:VS1-I:IF 2476.810 -2390.5 7344.1 0.9856
## G:VS1-I:IF 1761.500 -3707.7 7230.7 1.0000
## H:VS1-I:IF 2948.068 -2619.7 8515.8 0.9758
## I:VS1-I:IF 2985.000 -3006.2 8976.2 0.9892
## D:VS2-I:IF -95.750 -9568.7 9377.2 1.0000
## E:VS2-I:IF 3817.536 -2384.0 10019.1 0.8749
## F:VS2-I:IF 3423.393 -1887.3 8734.1 0.8141
## G:VS2-I:IF 3412.806 -2409.6 9235.2 0.9223
## H:VS2-I:IF 3744.179 -1566.5 9054.8 0.6511
## I:VS2-I:IF 2975.393 -3226.1 9176.9 0.9937
## D:VVS1-I:IF 13303.250 3830.3 22776.2 0.0001
## E:VVS1-I:IF 5570.050 -1261.0 12401.1 0.3279
## F:VVS1-I:IF 1997.972 -3093.6 7089.5 0.9998
## G:VVS1-I:IF 2076.750 -3392.5 7546.0 0.9999
## H:VVS1-I:IF 2418.650 -3265.1 8102.4 0.9991
## I:VVS1-I:IF 4083.650 -2747.4 10914.7 0.9053
## D:VVS2-I:IF 6513.000 -824.7 13850.7 0.1736
## E:VVS2-I:IF 2765.472 -3057.0 8587.9 0.9946
## F:VVS2-I:IF 1880.603 -3256.8 7018.0 0.9999
## G:VVS2-I:IF 2670.345 -2308.1 7648.8 0.9715
## H:VVS2-I:IF 2817.383 -2428.5 8063.3 0.9711
## I:VVS2-I:IF 3517.083 -1952.1 8986.3 0.8177
## E:VS1-D:VS1 1049.246 -4288.2 6386.7 1.0000
## F:VS1-D:VS1 495.417 -4628.5 5619.3 1.0000
## G:VS1-D:VS1 -219.893 -5918.7 5478.9 1.0000
## H:VS1-D:VS1 966.675 -4826.8 6760.1 1.0000
## I:VS1-D:VS1 1003.607 -5197.9 7205.1 1.0000
## D:VS2-D:VS1 -2077.143 -11684.5 7530.2 1.0000
## E:VS2-D:VS1 1836.143 -4568.8 8241.0 1.0000
## F:VS2-D:VS1 1442.000 -4104.8 6988.8 1.0000
## G:VS2-D:VS1 1431.413 -4607.2 7470.0 1.0000
## H:VS2-D:VS1 1762.786 -3784.0 7309.6 1.0000
## I:VS2-D:VS1 994.000 -5410.9 7398.9 1.0000
## D:VVS1-D:VS1 11321.857 1714.5 20929.2 0.0041
## E:VVS1-D:VS1 3588.657 -3427.6 10604.9 0.9845
## F:VVS1-D:VS1 16.579 -5320.8 5354.0 1.0000
## G:VVS1-D:VS1 95.357 -5603.4 5794.2 1.0000
## H:VVS1-D:VS1 437.257 -5467.8 6342.3 1.0000
## I:VVS1-D:VS1 2102.257 -4914.0 9118.5 1.0000
## D:VVS2-D:VS1 4531.607 -2978.8 12042.0 0.8963
## E:VVS2-D:VS1 784.079 -5254.5 6822.7 1.0000
## F:VVS2-D:VS1 -100.790 -5482.0 5280.4 1.0000
## G:VVS2-D:VS1 688.952 -4540.6 5918.5 1.0000
## H:VVS2-D:VS1 835.990 -4648.8 6320.8 1.0000
## I:VVS2-D:VS1 1535.690 -4163.1 7234.5 1.0000
## F:VS1-E:VS1 -553.829 -4257.9 3150.2 1.0000
## G:VS1-E:VS1 -1269.139 -5734.7 3196.5 1.0000
## H:VS1-E:VS1 -82.571 -4668.3 4503.2 1.0000
## I:VS1-E:VS1 -45.639 -5137.2 5045.9 1.0000
## D:VS2-E:VS1 -3126.389 -12057.6 5804.8 1.0000
## E:VS2-E:VS1 786.897 -4550.5 6124.3 1.0000
## F:VS2-E:VS1 392.754 -3877.2 4662.7 1.0000
## G:VS2-E:VS1 382.167 -4509.7 5274.0 1.0000
## H:VS2-E:VS1 713.540 -3556.4 4983.5 1.0000
## I:VS2-E:VS1 -55.246 -5392.7 5282.2 1.0000
## D:VVS1-E:VS1 10272.611 1341.4 19203.8 0.0064
## E:VVS1-E:VS1 2539.411 -3518.0 8596.9 0.9993
## F:VVS1-E:VS1 -1032.667 -5026.8 2961.5 1.0000
## G:VVS1-E:VS1 -953.889 -5419.5 3511.7 1.0000
## H:VVS1-E:VS1 -611.989 -5337.9 4114.0 1.0000
## I:VVS1-E:VS1 1053.011 -5004.4 7110.5 1.0000
## D:VVS2-E:VS1 3482.361 -3141.2 10105.9 0.9778
## E:VVS2-E:VS1 -265.167 -5157.0 4626.7 1.0000
## F:VVS2-E:VS1 -1150.036 -5202.5 2902.4 1.0000
## G:VVS2-E:VS1 -360.294 -4209.2 3488.6 1.0000
## H:VVS2-E:VS1 -213.256 -4402.4 3975.9 1.0000
## I:VVS2-E:VS1 486.444 -3979.2 4952.0 1.0000
## G:VS1-F:VS1 -715.310 -4923.4 3492.8 1.0000
## H:VS1-F:VS1 471.258 -3864.2 4806.7 1.0000
## I:VS1-F:VS1 508.190 -4359.1 5375.5 1.0000
## D:VS2-F:VS1 -2572.560 -11377.8 6232.7 1.0000
## E:VS2-F:VS1 1340.726 -3783.2 6464.6 1.0000
## F:VS2-F:VS1 946.583 -3053.3 4946.4 1.0000
## G:VS2-F:VS1 935.996 -3722.0 5593.9 1.0000
## H:VS2-F:VS1 1267.369 -2732.5 5267.2 1.0000
## I:VS2-F:VS1 498.583 -4625.3 5622.5 1.0000
## D:VVS1-F:VS1 10826.440 2021.2 19631.7 0.0018
## E:VVS1-F:VS1 3093.240 -2776.9 8963.4 0.9772
## F:VVS1-F:VS1 -478.838 -4182.9 3225.2 1.0000
## G:VVS1-F:VS1 -400.060 -4608.2 3808.0 1.0000
## H:VVS1-F:VS1 -58.160 -4541.6 4425.3 1.0000
## I:VVS1-F:VS1 1606.840 -4263.3 7477.0 1.0000
## D:VVS2-F:VS1 4036.190 -2416.6 10488.9 0.8557
## E:VVS2-F:VS1 288.662 -4369.3 4946.6 1.0000
## F:VVS2-F:VS1 -596.207 -4363.0 3170.6 1.0000
## G:VVS2-F:VS1 193.535 -3353.3 3740.4 1.0000
## H:VVS2-F:VS1 340.573 -3572.9 4254.0 1.0000
## I:VVS2-F:VS1 1040.273 -3167.8 5248.4 1.0000
## H:VS1-G:VS1 1186.568 -3815.2 6188.3 1.0000
## I:VS1-G:VS1 1223.500 -4245.7 6692.7 1.0000
## D:VS2-G:VS1 -1857.250 -11009.0 7294.5 1.0000
## E:VS2-G:VS1 2056.036 -3642.8 7754.8 1.0000
## F:VS2-G:VS1 1661.893 -3052.0 6375.8 1.0000
## G:VS2-G:VS1 1651.306 -3632.5 6935.1 1.0000
## H:VS2-G:VS1 1982.679 -2731.2 6696.6 0.9992
## I:VS2-G:VS1 1213.893 -4484.9 6912.7 1.0000
## D:VVS1-G:VS1 11541.750 2390.0 20693.5 0.0011
## E:VVS1-G:VS1 3808.550 -2569.6 10186.7 0.9063
## F:VVS1-G:VS1 236.472 -4229.1 4702.1 1.0000
## G:VVS1-G:VS1 315.250 -4576.6 5207.1 1.0000
## H:VVS1-G:VS1 657.150 -4473.4 5787.7 1.0000
## I:VVS1-G:VS1 2322.150 -4056.0 8700.3 0.9999
## D:VVS2-G:VS1 4751.500 -2166.6 11669.6 0.7042
## E:VVS2-G:VS1 1003.972 -4279.8 6287.7 1.0000
## F:VVS2-G:VS1 119.103 -4398.7 4636.9 1.0000
## G:VVS2-G:VS1 908.845 -3427.3 5245.0 1.0000
## H:VVS2-G:VS1 1055.883 -3584.9 5696.7 1.0000
## I:VVS2-G:VS1 1755.583 -3136.2 6647.4 1.0000
## I:VS1-H:VS1 36.932 -5530.8 5604.7 1.0000
## D:VS2-H:VS1 -3043.818 -12254.8 6167.2 1.0000
## E:VS2-H:VS1 869.468 -4924.0 6662.9 1.0000
## F:VS2-H:VS1 475.325 -4352.6 5303.2 1.0000
## G:VS2-H:VS1 464.737 -4921.0 5850.5 1.0000
## H:VS2-H:VS1 796.110 -4031.8 5624.0 1.0000
## I:VS2-H:VS1 27.325 -5766.1 5820.8 1.0000
## D:VVS1-H:VS1 10355.182 1144.2 19566.2 0.0093
## E:VVS1-H:VS1 2621.982 -3840.9 9084.8 0.9996
## F:VVS1-H:VS1 -950.096 -5535.9 3635.7 1.0000
## G:VVS1-H:VS1 -871.318 -5873.1 4130.4 1.0000
## H:VVS1-H:VS1 -529.418 -5764.9 4706.1 1.0000
## I:VVS1-H:VS1 1135.582 -5327.3 7598.4 1.0000
## D:VVS2-H:VS1 3564.932 -3431.3 10561.2 0.9853
## E:VVS2-H:VS1 -182.596 -5568.3 5203.1 1.0000
## F:VVS2-H:VS1 -1067.465 -5704.1 3569.2 1.0000
## G:VVS2-H:VS1 -277.723 -4737.5 4182.1 1.0000
## H:VVS2-H:VS1 -130.685 -4887.2 4625.9 1.0000
## I:VVS2-H:VS1 569.015 -4432.8 5570.8 1.0000
## D:VS2-I:VS1 -3080.750 -12553.7 6392.2 1.0000
## E:VS2-I:VS1 832.536 -5369.0 7034.1 1.0000
## F:VS2-I:VS1 438.393 -4872.3 5749.1 1.0000
## G:VS2-I:VS1 427.806 -5394.6 6250.2 1.0000
## H:VS2-I:VS1 759.179 -4551.5 6069.8 1.0000
## I:VS2-I:VS1 -9.607 -6211.1 6191.9 1.0000
## D:VVS1-I:VS1 10318.250 845.3 19791.2 0.0154
## E:VVS1-I:VS1 2585.050 -4246.0 9416.1 0.9999
## F:VVS1-I:VS1 -987.028 -6078.6 4104.5 1.0000
## G:VVS1-I:VS1 -908.250 -6377.5 4561.0 1.0000
## H:VVS1-I:VS1 -566.350 -6250.1 5117.4 1.0000
## I:VVS1-I:VS1 1098.650 -5732.4 7929.7 1.0000
## D:VVS2-I:VS1 3528.000 -3809.7 10865.7 0.9935
## E:VVS2-I:VS1 -219.528 -6042.0 5602.9 1.0000
## F:VVS2-I:VS1 -1104.397 -6241.8 4033.0 1.0000
## G:VVS2-I:VS1 -314.655 -5293.1 4663.8 1.0000
## H:VVS2-I:VS1 -167.617 -5413.5 5078.3 1.0000
## I:VVS2-I:VS1 532.083 -4937.1 6001.3 1.0000
## E:VS2-D:VS2 3913.286 -5694.1 13520.6 0.9996
## F:VS2-D:VS2 3519.143 -5538.8 12577.0 0.9998
## G:VS2-D:VS2 3508.556 -5858.6 12875.7 0.9999
## H:VS2-D:VS2 3839.929 -5218.0 12897.8 0.9991
## I:VS2-D:VS2 3071.143 -6536.2 12678.5 1.0000
## D:VVS1-D:VS2 13399.000 1416.5 25381.5 0.0102
## E:VVS1-D:VS2 5665.800 -4359.5 15691.1 0.9474
## F:VVS1-D:VS2 2093.722 -6837.5 11024.9 1.0000
## G:VVS1-D:VS2 2172.500 -6979.3 11324.3 1.0000
## H:VVS1-D:VS2 2514.400 -6767.2 11796.0 1.0000
## I:VVS1-D:VS2 4179.400 -5845.9 14204.7 0.9994
## D:VVS2-D:VS2 6608.750 -3768.4 16985.9 0.8317
## E:VVS2-D:VS2 2861.222 -6505.9 12228.4 1.0000
## F:VVS2-D:VS2 1976.353 -6981.1 10933.8 1.0000
## G:VVS2-D:VS2 2766.095 -6101.1 11633.3 1.0000
## H:VVS2-D:VS2 2913.133 -6106.9 11933.2 1.0000
## I:VVS2-D:VS2 3612.833 -5538.9 12764.6 0.9998
## F:VS2-E:VS2 -394.143 -5941.0 5152.7 1.0000
## G:VS2-E:VS2 -404.730 -6443.3 5633.9 1.0000
## H:VS2-E:VS2 -73.357 -5620.2 5473.5 1.0000
## I:VS2-E:VS2 -842.143 -7247.0 5562.8 1.0000
## D:VVS1-E:VS2 9485.714 -121.6 19093.1 0.0583
## E:VVS1-E:VS2 1752.514 -5263.7 8768.7 1.0000
## F:VVS1-E:VS2 -1819.563 -7157.0 3517.9 1.0000
## G:VVS1-E:VS2 -1740.786 -7439.6 3958.0 1.0000
## H:VVS1-E:VS2 -1398.886 -7303.9 4506.1 1.0000
## I:VVS1-E:VS2 266.114 -6750.1 7282.3 1.0000
## D:VVS2-E:VS2 2695.464 -4814.9 10205.9 1.0000
## E:VVS2-E:VS2 -1052.063 -7090.7 4986.5 1.0000
## F:VVS2-E:VS2 -1936.933 -7318.1 3444.3 1.0000
## G:VVS2-E:VS2 -1147.190 -6376.8 4082.4 1.0000
## H:VVS2-E:VS2 -1000.152 -6485.0 4484.7 1.0000
## I:VVS2-E:VS2 -300.452 -5999.3 5398.4 1.0000
## G:VS2-F:VS2 -10.587 -5130.1 5108.9 1.0000
## H:VS2-F:VS2 320.786 -4208.2 4849.7 1.0000
## I:VS2-F:VS2 -448.000 -5994.8 5098.8 1.0000
## D:VVS1-F:VS2 9879.857 822.0 18937.8 0.0151
## E:VVS1-F:VS2 2146.657 -4096.1 8389.4 1.0000
## F:VVS1-F:VS2 -1425.421 -5695.4 2844.5 1.0000
## G:VVS1-F:VS2 -1346.643 -6060.5 3367.2 1.0000
## H:VVS1-F:VS2 -1004.743 -5966.0 3956.5 1.0000
## I:VVS1-F:VS2 660.257 -5582.5 6903.0 1.0000
## D:VVS2-F:VS2 3089.607 -3703.8 9883.0 0.9972
## E:VVS2-F:VS2 -657.921 -5777.4 4461.6 1.0000
## F:VVS2-F:VS2 -1542.790 -5867.3 2781.7 1.0000
## G:VVS2-F:VS2 -753.048 -4887.4 3381.3 1.0000
## H:VVS2-F:VS2 -606.010 -5058.8 3846.8 1.0000
## I:VVS2-F:VS2 93.690 -4620.2 4807.6 1.0000
## H:VS2-G:VS2 331.373 -4788.1 5450.8 1.0000
## I:VS2-G:VS2 -437.413 -6476.0 5601.2 1.0000
## D:VVS1-G:VS2 9890.444 523.3 19257.6 0.0244
## E:VVS1-G:VS2 2157.244 -4526.3 8840.7 1.0000
## F:VVS1-G:VS2 -1414.833 -6306.7 3477.0 1.0000
## G:VVS1-G:VS2 -1336.056 -6619.8 3947.7 1.0000
## H:VVS1-G:VS2 -994.156 -6499.7 4511.4 1.0000
## I:VVS1-G:VS2 670.844 -6012.7 7354.3 1.0000
## D:VVS2-G:VS2 3100.194 -4100.4 10300.8 0.9989
## E:VVS2-G:VS2 -647.333 -6295.9 5001.3 1.0000
## F:VVS2-G:VS2 -1532.203 -6471.8 3407.3 1.0000
## G:VVS2-G:VS2 -742.460 -5516.4 4031.5 1.0000
## H:VVS2-G:VS2 -595.422 -5647.7 4456.8 1.0000
## I:VVS2-G:VS2 104.278 -5179.5 5388.1 1.0000
## I:VS2-H:VS2 -768.786 -6315.6 4778.0 1.0000
## D:VVS1-H:VS2 9559.071 501.2 18617.0 0.0245
## E:VVS1-H:VS2 1825.871 -4416.9 8068.6 1.0000
## F:VVS1-H:VS2 -1746.206 -6016.1 2523.7 0.9995
## G:VVS1-H:VS2 -1667.429 -6381.3 3046.5 1.0000
## H:VVS1-H:VS2 -1325.529 -6286.7 3635.7 1.0000
## I:VVS1-H:VS2 339.471 -5903.3 6582.2 1.0000
## D:VVS2-H:VS2 2768.821 -4024.6 9562.2 0.9996
## E:VVS2-H:VS2 -978.706 -6098.2 4140.8 1.0000
## F:VVS2-H:VS2 -1863.576 -6188.1 2461.0 0.9989
## G:VVS2-H:VS2 -1073.833 -5208.2 3060.5 1.0000
## H:VVS2-H:VS2 -926.795 -5379.6 3526.0 1.0000
## I:VVS2-H:VS2 -227.095 -4941.0 4486.8 1.0000
## D:VVS1-I:VS2 10327.857 720.5 19935.2 0.0188
## E:VVS1-I:VS2 2594.657 -4421.6 9610.9 0.9999
## F:VVS1-I:VS2 -977.421 -6314.8 4360.0 1.0000
## G:VVS1-I:VS2 -898.643 -6597.4 4800.2 1.0000
## H:VVS1-I:VS2 -556.743 -6461.8 5348.3 1.0000
## I:VVS1-I:VS2 1108.257 -5908.0 8124.5 1.0000
## D:VVS2-I:VS2 3537.607 -3972.8 11048.0 0.9952
## E:VVS2-I:VS2 -209.921 -6248.5 5828.7 1.0000
## F:VVS2-I:VS2 -1094.790 -6476.0 4286.4 1.0000
## G:VVS2-I:VS2 -305.048 -5534.6 4924.5 1.0000
## H:VVS2-I:VS2 -158.010 -5642.8 5326.8 1.0000
## I:VVS2-I:VS2 541.690 -5157.1 6240.5 1.0000
## E:VVS1-D:VVS1 -7733.200 -17758.5 2292.1 0.4501
## F:VVS1-D:VVS1 -11305.278 -20236.5 -2374.1 0.0010
## G:VVS1-D:VVS1 -11226.500 -20378.3 -2074.7 0.0019
## H:VVS1-D:VVS1 -10884.600 -20166.2 -1603.0 0.0045
## I:VVS1-D:VVS1 -9219.600 -19244.9 805.7 0.1254
## D:VVS2-D:VVS1 -6790.250 -17167.4 3586.9 0.7908
## E:VVS2-D:VVS1 -10537.778 -19904.9 -1170.6 0.0092
## F:VVS2-D:VVS1 -11422.647 -20380.1 -2465.2 0.0009
## G:VVS2-D:VVS1 -10632.905 -19500.1 -1765.7 0.0030
## H:VVS2-D:VVS1 -10485.867 -19505.9 -1465.8 0.0053
## I:VVS2-D:VVS1 -9786.167 -18937.9 -634.4 0.0203
## F:VVS1-E:VVS1 -3572.078 -9629.5 2485.4 0.9173
## G:VVS1-E:VVS1 -3493.300 -9871.5 2884.9 0.9633
## H:VVS1-E:VVS1 -3151.400 -9714.5 3411.7 0.9936
## I:VVS1-E:VVS1 -1486.400 -9064.8 6092.0 1.0000
## D:VVS2-E:VVS1 942.950 -7095.1 8981.0 1.0000
## E:VVS2-E:VVS1 -2804.578 -9488.1 3878.9 0.9993
## F:VVS2-E:VVS1 -3689.447 -9785.5 2406.6 0.8933
## G:VVS2-E:VVS1 -2899.705 -8862.3 3062.9 0.9923
## H:VVS2-E:VVS1 -2752.667 -8940.4 3435.1 0.9981
## I:VVS2-E:VVS1 -2052.967 -8431.1 4325.2 1.0000
## G:VVS1-F:VVS1 78.778 -4386.8 4544.4 1.0000
## H:VVS1-F:VVS1 420.678 -4305.3 5146.6 1.0000
## I:VVS1-F:VVS1 2085.678 -3971.8 8143.1 1.0000
## D:VVS2-F:VVS1 4515.028 -2108.5 11138.6 0.7188
## E:VVS2-F:VVS1 767.500 -4124.3 5659.3 1.0000
## F:VVS2-F:VVS1 -117.369 -4169.8 3935.1 1.0000
## G:VVS2-F:VVS1 672.373 -3176.5 4521.2 1.0000
## H:VVS2-F:VVS1 819.411 -3369.7 5008.5 1.0000
## I:VVS2-F:VVS1 1519.111 -2946.5 5984.7 1.0000
## H:VVS1-G:VVS1 341.900 -4788.7 5472.5 1.0000
## I:VVS1-G:VVS1 2006.900 -4371.3 8385.1 1.0000
## D:VVS2-G:VVS1 4436.250 -2481.8 11354.3 0.8219
## E:VVS2-G:VVS1 688.722 -4595.1 5972.5 1.0000
## F:VVS2-G:VVS1 -196.147 -4714.0 4321.7 1.0000
## G:VVS2-G:VVS1 593.595 -3742.5 4929.7 1.0000
## H:VVS2-G:VVS1 740.633 -3900.2 5381.4 1.0000
## I:VVS2-G:VVS1 1440.333 -3451.5 6332.2 1.0000
## I:VVS1-H:VVS1 1665.000 -4898.1 8228.1 1.0000
## D:VVS2-H:VVS1 4094.350 -2994.6 11183.3 0.9334
## E:VVS2-H:VVS1 346.822 -5158.7 5852.4 1.0000
## F:VVS2-H:VVS1 -538.047 -5313.4 4237.3 1.0000
## G:VVS2-H:VVS1 251.695 -4352.1 4855.5 1.0000
## H:VVS2-H:VVS1 398.733 -4493.1 5290.6 1.0000
## I:VVS2-H:VVS1 1098.433 -4032.2 6229.0 1.0000
## D:VVS2-I:VVS1 2429.350 -5608.7 10467.4 1.0000
## E:VVS2-I:VVS1 -1318.178 -8001.7 5365.3 1.0000
## F:VVS2-I:VVS1 -2203.047 -8299.1 3893.0 1.0000
## G:VVS2-I:VVS1 -1413.305 -7375.9 4549.3 1.0000
## H:VVS2-I:VVS1 -1266.267 -7454.0 4921.5 1.0000
## I:VVS2-I:VVS1 -566.567 -6944.7 5811.6 1.0000
## E:VVS2-D:VVS2 -3747.528 -10948.1 3453.0 0.9806
## F:VVS2-D:VVS2 -4632.397 -11291.3 2026.5 0.6787
## G:VVS2-D:VVS2 -3842.655 -10379.6 2694.3 0.9200
## H:VVS2-D:VVS2 -3695.617 -10438.5 3047.3 0.9630
## I:VVS2-D:VVS2 -2995.917 -9914.0 3922.2 0.9988
## F:VVS2-E:VVS2 -884.869 -5824.4 4054.7 1.0000
## G:VVS2-E:VVS2 -95.127 -4869.1 4678.8 1.0000
## H:VVS2-E:VVS2 51.911 -5000.3 5104.2 1.0000
## I:VVS2-E:VVS2 751.611 -4532.2 6035.4 1.0000
## G:VVS2-F:VVS2 789.742 -3119.6 4699.1 1.0000
## H:VVS2-F:VVS2 936.780 -3308.0 5181.5 1.0000
## I:VVS2-F:VVS2 1636.480 -2881.4 6154.3 1.0000
## H:VVS2-G:VVS2 147.038 -3903.8 4197.9 1.0000
## I:VVS2-G:VVS2 846.738 -3489.4 5182.9 1.0000
## I:VVS2-H:VVS2 699.700 -3941.1 5340.5 1.0000
plot(TukeyHSD(model_colour_clarity))
http://cran.r-project.org/web/packages/Ecdat/Ecdat.pdf http://www.amstat.org/publications/jse/v9n2/datasets.chu.html