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EXERCISE 1 ANOVA

*The author of this computation has been verified*
R Software Module: Ian.Holliday/rwasp_One Factor ANOVA.wasp (opens new window with default values)
Title produced by software: One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)
Date of computation: Tue, 30 Nov 2010 12:46:34 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291121152j52umgyilm77egx.htm/, Retrieved Tue, 30 Nov 2010 13:45:53 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291121152j52umgyilm77egx.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1 36 88 3 56 94 3 48 90 3 32 73 1 44 68 2 39 80 3 34 86 3 41 86 2 50 91 1 39 79 1 62 96 3 52 92 3 37 72 3 50 96 1 41 70 3 55 86 3 41 87 3 56 88 2 39 79 2 52 90 1 46 95 1 44 85 3 41 90 1 50 115 1 50 84 3 44 79 1 52 94 2 54 97 3 44 86 2 52 111 2 37 87 3 52 98 1 50 87 3 36 68 3 50 88 1 52 82 2 55 111 1 31 75 1 36 94 2 49 95 1 42 80 1 37 95 3 41 68 2 30 94 2 52 88 1 30 84 1 44 101 1 66 98 2 48 78 3 43 109 3 57 102 3 46 81 3 54 97 2 48 75 2 48 97 3 62 101 3 58 101 2 58 95 2 62 95 3 46 95 2 34 90 3 66 107 3 52 92 2 55 86 2 55 70 3 57 95 3 56 96 2 55 91 1 56 87 2 54 92 2 55 97 2 46 102 2 52 91 3 32 68 2 44 88 3 46 97 1 59 90 3 46 101 3 46 94 1 54 101 1 66 109 2 56 100 1 59 103 3 57 94 1 52 97 3 48 85 2 44 75 3 41 77 1 50 87 1 48 78 2 48 108 3 59 97 1 34 105 3 46 106 1 54 107 2 55 95 2 54 107 3 59 115 3 44 101 1 54 85 3 52 90 3 66 115 3 44 95 2 57 97 3 39 112 3 60 97 3 45 77 3 41 90 1 50 94 3 39 103 1 43 77 etc...
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


ANOVA Model
MOMAGE ~ MC30VRB
means1.5-0.51.50.750.50.90.91.056-0.510.61.51.10.70.50.3331.50.6670.3750.8330.6431.11.1670.6431.50.50.5


ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
MC30VRB2618.2910.7031.0580.4
Residuals12683.7620.665


Tukey Honest Significant Difference Comparisons
difflwruprp adj
31-30-0.5-3.9482.9481
32-301.5-1.1714.1710.927
34-300.75-1.4312.9311
36-300.5-1.6812.6811
37-300.9-1.1692.9690.997
39-300.9-0.9242.7240.982
41-301.056-0.7982.9090.916
42-30-0.5-3.9482.9481
43-301-0.9912.9910.978
44-300.6-1.2242.4241
45-301.5-1.9484.9480.997
46-301.1-0.7242.9240.861
48-300.7-1.1242.5241
49-300.5-2.9483.9481
50-300.333-1.4472.1141
51-301.5-1.9484.9480.997
52-300.667-1.1142.4471
54-300.375-1.5132.2631
55-300.833-1.022.6860.995
56-300.643-1.292.5761
57-301.1-0.9693.1690.958
58-301.167-1.1893.5220.981
59-300.643-1.292.5761
60-301.5-0.6813.6810.653
62-300.5-1.8552.8551
66-300.5-1.6812.6811
32-312-1.7775.7770.96
34-311.25-2.1984.6981
36-311-2.4484.4481
37-311.4-1.9784.7780.998
39-311.4-1.8344.6340.997
41-311.556-1.6954.8060.988
42-310-4.3614.3611
43-311.5-1.8314.8310.995
44-311.1-2.1344.3341
45-312-2.3616.3610.993
46-311.6-1.6344.8340.982
48-311.2-2.0344.4341
49-311-3.3615.3611
50-310.833-2.3764.0431
51-312-2.3616.3610.993
52-311.167-2.0434.3761
54-310.875-2.3964.1461
55-311.333-1.9174.5840.999
56-311.143-2.1544.441
57-311.6-1.7784.9780.989
58-311.667-1.8945.2280.991
59-311.143-2.1544.441
60-312-1.4485.4480.901
62-311-2.5614.5611
66-311-2.4484.4481
34-32-0.75-3.4211.9211
36-32-1-3.6711.6711
37-32-0.6-3.181.981
39-32-0.6-2.9891.7891
41-32-0.444-2.8551.9661
42-32-2-5.7771.7770.96
43-32-0.5-3.0182.0181
44-32-0.9-3.2891.4891
45-320-3.7773.7771
46-32-0.4-2.7891.9891
48-32-0.8-3.1891.5891
49-32-1-4.7772.7771
50-32-1.167-3.5221.1890.981
51-320-3.7773.7771
52-32-0.833-3.1891.5221
54-32-1.125-3.5631.3130.993
55-32-0.667-3.0771.7441
56-32-0.857-3.331.6151
57-32-0.4-2.982.181
58-32-0.333-3.1482.4821
59-32-0.857-3.331.6151
60-320-2.6712.6711
62-32-1-3.8151.8151
66-32-1-3.6711.6711
36-34-0.25-2.4311.9311
37-340.15-1.9192.2191
39-340.15-1.6741.9741
41-340.306-1.5482.1591
42-34-1.25-4.6982.1981
43-340.25-1.7412.2411
44-34-0.15-1.9741.6741
45-340.75-2.6984.1981
46-340.35-1.4742.1741
48-34-0.05-1.8741.7741
49-34-0.25-3.6983.1981
50-34-0.417-2.1971.3641
51-340.75-2.6984.1981
52-34-0.083-1.8641.6971
54-34-0.375-2.2631.5131
55-340.083-1.771.9361
56-34-0.107-2.041.8261
57-340.35-1.7192.4191
58-340.417-1.9392.7721
59-34-0.107-2.041.8261
60-340.75-1.4312.9311
62-34-0.25-2.6052.1051
66-34-0.25-2.4311.9311
37-360.4-1.6692.4691
39-360.4-1.4242.2241
41-360.556-1.2982.4091
42-36-1-4.4482.4481
43-360.5-1.4912.4911
44-360.1-1.7241.9241
45-361-2.4484.4481
46-360.6-1.2242.4241
48-360.2-1.6242.0241
49-360-3.4483.4481
50-36-0.167-1.9471.6141
51-361-2.4484.4481
52-360.167-1.6141.9471
54-36-0.125-2.0131.7631
55-360.333-1.522.1861
56-360.143-1.792.0761
57-360.6-1.4692.6691
58-360.667-1.6893.0221
59-360.143-1.792.0761
60-361-1.1813.1810.993
62-360-2.3552.3551
66-360-2.1812.1811
39-370-1.6891.6891
41-370.156-1.5651.8761
42-37-1.4-4.7781.9780.998
43-370.1-1.7671.9671
44-37-0.3-1.9891.3891
45-370.6-2.7783.9781
46-370.2-1.4891.8891
48-37-0.2-1.8891.4891
49-37-0.4-3.7782.9781
50-37-0.567-2.2081.0751
51-370.6-2.7783.9781
52-37-0.233-1.8751.4081
54-37-0.525-2.2831.2331
55-37-0.067-1.7871.6531
56-37-0.257-2.0631.5491
57-370.2-1.752.151
58-370.267-1.9852.5191
59-37-0.257-2.0631.5491
60-370.6-1.4692.6691
62-37-0.4-2.6521.8521
66-37-0.4-2.4691.6691
41-390.156-1.2611.5721
42-39-1.4-4.6341.8340.997
43-390.1-1.4921.6921
44-39-0.3-1.6791.0791
45-390.6-2.6343.8341
46-390.2-1.1791.5791
48-39-0.2-1.5791.1791
49-39-0.4-3.6342.8341
50-39-0.567-1.8870.7540.997
51-390.6-2.6343.8341
52-39-0.233-1.5541.0871
54-39-0.525-1.9880.9381
55-39-0.067-1.4841.351
56-39-0.257-1.7771.2631
57-390.2-1.4891.8891
58-390.267-1.7632.2971
59-39-0.257-1.7771.2631
60-390.6-1.2242.4241
62-39-0.4-2.431.631
66-39-0.4-2.2241.4241
42-41-1.556-4.8061.6950.988
43-41-0.056-1.6811.571
44-41-0.456-1.8720.9611
45-410.444-2.8063.6951
46-410.044-1.3721.4611
48-41-0.356-1.7721.0611
49-41-0.556-3.8062.6951
50-41-0.722-2.0820.6380.959
51-410.444-2.8063.6951
52-41-0.389-1.7490.9711
54-41-0.681-2.1790.8180.994
55-41-0.222-1.6761.2321
56-41-0.413-1.9671.1411
57-410.044-1.6761.7651
58-410.111-1.9452.1671
59-41-0.413-1.9671.1411
60-410.444-1.4092.2981
62-41-0.556-2.6111.51
66-41-0.556-2.4091.2981
43-421.5-1.8314.8310.995
44-421.1-2.1344.3341
45-422-2.3616.3610.993
46-421.6-1.6344.8340.982
48-421.2-2.0344.4341
49-421-3.3615.3611
50-420.833-2.3764.0431
51-422-2.3616.3610.993
52-421.167-2.0434.3761
54-420.875-2.3964.1461
55-421.333-1.9174.5840.999
56-421.143-2.1544.441
57-421.6-1.7784.9780.989
58-421.667-1.8945.2280.991
59-421.143-2.1544.441
60-422-1.4485.4480.901
62-421-2.5614.5611
66-421-2.4484.4481
44-43-0.4-1.9921.1921
45-430.5-2.8313.8311
46-430.1-1.4921.6921
48-43-0.3-1.8921.2921
49-43-0.5-3.8312.8311
50-43-0.667-2.2090.8750.997
51-430.5-2.8313.8311
52-43-0.333-1.8751.2091
54-43-0.625-2.291.041
55-43-0.167-1.7921.4591
56-43-0.357-2.0731.3591
57-430.1-1.7671.9671
58-430.167-2.0142.3471
59-43-0.357-2.0731.3591
60-430.5-1.4912.4911
62-43-0.5-2.6811.6811
66-43-0.5-2.4911.4911
45-440.9-2.3344.1341
46-440.5-0.8791.8791
48-440.1-1.2791.4791
49-44-0.1-3.3343.1341
50-44-0.267-1.5871.0541
51-440.9-2.3344.1341
52-440.067-1.2541.3871
54-44-0.225-1.6881.2381
55-440.233-1.1841.651
56-440.043-1.4771.5631
57-440.5-1.1892.1891
58-440.567-1.4632.5971
59-440.043-1.4771.5631
60-440.9-0.9242.7240.982
62-44-0.1-2.131.931
66-44-0.1-1.9241.7241
46-45-0.4-3.6342.8341
48-45-0.8-4.0342.4341
49-45-1-5.3613.3611
50-45-1.167-4.3762.0431
51-450-4.3614.3611
52-45-0.833-4.0432.3761
54-45-1.125-4.3962.1461
55-45-0.667-3.9172.5841
56-45-0.857-4.1542.441
57-45-0.4-3.7782.9781
58-45-0.333-3.8943.2281
59-45-0.857-4.1542.441
60-450-3.4483.4481
62-45-1-4.5612.5611
66-45-1-4.4482.4481
48-46-0.4-1.7790.9791
49-46-0.6-3.8342.6341
50-46-0.767-2.0870.5540.9
51-460.4-2.8343.6341
52-46-0.433-1.7540.8871
54-46-0.725-2.1880.7380.981
55-46-0.267-1.6841.151
56-46-0.457-1.9771.0631
57-460-1.6891.6891
58-460.067-1.9632.0971
59-46-0.457-1.9771.0631
60-460.4-1.4242.2241
62-46-0.6-2.631.431
66-46-0.6-2.4241.2241
49-48-0.2-3.4343.0341
50-48-0.367-1.6870.9541
51-480.8-2.4344.0341
52-48-0.033-1.3541.2871
54-48-0.325-1.7881.1381
55-480.133-1.2841.551
56-48-0.057-1.5771.4631
57-480.4-1.2892.0891
58-480.467-1.5632.4971
59-48-0.057-1.5771.4631
60-480.8-1.0242.6240.996
62-48-0.2-2.231.831
66-48-0.2-2.0241.6241
50-49-0.167-3.3763.0431
51-491-3.3615.3611
52-490.167-3.0433.3761
54-49-0.125-3.3963.1461
55-490.333-2.9173.5841
56-490.143-3.1543.441
57-490.6-2.7783.9781
58-490.667-2.8944.2281
59-490.143-3.1543.441
60-491-2.4484.4481
62-490-3.5613.5611
66-490-3.4483.4481
51-501.167-2.0434.3761
52-500.333-0.9261.5921
54-500.042-1.3661.4491
55-500.5-0.861.861
56-500.31-1.1571.7761
57-500.767-0.8752.4080.991
58-500.833-1.1572.8240.998
59-500.31-1.1571.7761
60-501.167-0.6142.9470.743
62-500.167-1.8242.1571
66-500.167-1.6141.9471
52-51-0.833-4.0432.3761
54-51-1.125-4.3962.1461
55-51-0.667-3.9172.5841
56-51-0.857-4.1542.441
57-51-0.4-3.7782.9781
58-51-0.333-3.8943.2281
59-51-0.857-4.1542.441
60-510-3.4483.4481
62-51-1-4.5612.5611
66-51-1-4.4482.4481
54-52-0.292-1.6991.1161
55-520.167-1.1931.5271
56-52-0.024-1.491.4431
57-520.433-1.2082.0751
58-520.5-1.4912.4911
59-52-0.024-1.491.4431
60-520.833-0.9472.6140.991
62-52-0.167-2.1571.8241
66-52-0.167-1.9471.6141
55-540.458-1.041.9571
56-540.268-1.3281.8641
57-540.725-1.0332.4830.999
58-540.792-1.2962.8791
59-540.268-1.3281.8641
60-541.125-0.7633.0130.875
62-540.125-1.9632.2131
66-540.125-1.7632.0131
56-55-0.19-1.7451.3641
57-550.267-1.4531.9871
58-550.333-1.7232.3891
59-55-0.19-1.7451.3641
60-550.667-1.1862.521
62-55-0.333-2.3891.7231
66-55-0.333-2.1861.521
57-560.457-1.3492.2631
58-560.524-1.6042.6521
59-560-1.6481.6481
60-560.857-1.0762.790.996
62-56-0.143-2.2711.9851
66-56-0.143-2.0761.791
58-570.067-2.1852.3191
59-57-0.457-2.2631.3491
60-570.4-1.6692.4691
62-57-0.6-2.8521.6521
66-57-0.6-2.6691.4691
59-58-0.524-2.6521.6041
60-580.333-2.0222.6891
62-58-0.667-3.1851.8511
66-58-0.667-3.0221.6891
60-590.857-1.0762.790.996
62-59-0.143-2.2711.9851
66-59-0.143-2.0761.791
62-60-1-3.3551.3550.998
66-60-1-3.1811.1810.993
66-620-2.3552.3551


Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group260.9650.52
126
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291121152j52umgyilm77egx/3ddje1291121186.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291121152j52umgyilm77egx/3ddje1291121186.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291121152j52umgyilm77egx/4ddje1291121186.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291121152j52umgyilm77egx/4ddje1291121186.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
 
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
 
R code (references can be found in the software module):
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
intercept<-as.logical(par3)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
xdf<-data.frame(x1,f1)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
names(xdf)<-c('Response', 'Treatment')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment - 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment, data = xdf) )
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, paste(V1, ' ~ ', V2), length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmxdf$coefficients)){
a<-table.element(a, round(lmxdf$coefficients[i], digits=3),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3),,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$Df[2],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='anovaplot.png')
boxplot(Response ~ Treatment, data=xdf, xlab=V2, ylab=V1)
dev.off()
if(intercept==TRUE){
thsd<-TukeyHSD(aov.xdf)
bitmap(file='TukeyHSDPlot.png')
plot(thsd)
dev.off()
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Honest Significant Difference Comparisons', 5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1, TRUE)
for(i in 1:4){
a<-table.element(a,colnames(thsd[[1]])[i], 1, TRUE)
}
a<-table.row.end(a)
for(i in 1:length(rownames(thsd[[1]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[1]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[1]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
if(intercept==FALSE){
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'TukeyHSD Message', 1,TRUE)
a<-table.row.end(a)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Must Include Intercept to use Tukey Test ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
library(car)
lt.lmxdf<-levene.test(lmxdf)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Levenes Test for Homogeneity of Variance', 4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
for (i in 1:3){
a<-table.element(a,names(lt.lmxdf)[i], 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Group', 1, TRUE)
for (i in 1:3){
a<-table.element(a,round(lt.lmxdf[[i]][1], digits=3), 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
a<-table.element(a,lt.lmxdf[[1]][2], 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
 





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