Home » date » 2009 » Nov » 04 »

*The author of this computation has been verified*
R Software Module: /rwasp_summary1.wasp (opens new window with default values)
Title produced by software: Univariate Summary Statistics
Date of computation: Wed, 04 Nov 2009 07:54:00 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw.htm/, Retrieved Wed, 04 Nov 2009 15:57:00 +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/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw.htm/},
    year = {2009},
}
@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 = {2009},
    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:
WS5,inflatie4
 
Dataseries X:
» Textbox « » Textfile « » CSV «
-1,666073923 -1,908115119 -2,079135718 -0,995053325 -1,637094521 -1,280563624 -2,050156316 -1,808115119 -1,637094521 -2,151584222 -2,12260482 -2,22260482 -1,851584222 -1,866073923 -1,766073923 -2,42260482 -2,751584222 -3,208115119 -2,566073923 -2,251584222 -1,966073923 -1,537094521 -1,180563624 -0,666073923 -1,008115119 -1,064646017 -0,893625419 -0,893625419 -0,42260482 0,333926077 0,548415778 0,348415778 0,07739518 0,17739518 0,191884881 0,149843684 1,335353983 2,149843684 3,67739518 4,149843684 4,349843684 4,291884881 3,607802488 4,149843684 4,862905479 5,033926077 5,090456974 4,746987872 4,103518769 2,903518769 1,51800847 0,632498171 0,289029068 -0,624032727 -0,254440035 -1,18199153 -1,824032727 -2,209543026 -2,751584222
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.69491804801408e-110.3180551993790915.3290059440088e-11
Geometric MeanNaN
Harmonic Mean3.01809736413357
Quadratic Mean2.42223623361147
Winsorized Mean ( 1 / 19 )0.006779661033898330.3165374818456560.0214181934928139
Winsorized Mean ( 2 / 19 )0.0009823526271186770.3149722676345120.00311885435024578
Winsorized Mean ( 3 / 19 )0.004520964084745790.3120349060253530.0144886485372199
Winsorized Mean ( 4 / 19 )-0.01267734676271190.303815369812946-0.0417271409623454
Winsorized Mean ( 5 / 19 )-0.003095838711864350.300676819806819-0.0102962333905666
Winsorized Mean ( 6 / 19 )-0.01459364837288130.296771454021630-0.0491747038844838
Winsorized Mean ( 7 / 19 )-0.01304394399999990.296573113468583-0.043982220260778
Winsorized Mean ( 8 / 19 )-0.01146646752542370.294060415130665-0.0389935772903287
Winsorized Mean ( 9 / 19 )-0.07204778418644060.278097618857664-0.259073718366917
Winsorized Mean ( 10 / 19 )-0.07647551130508470.274429640555757-0.278670741069411
Winsorized Mean ( 11 / 19 )-0.2023797060.244091281418683-0.829114849263557
Winsorized Mean ( 12 / 19 )-0.3385680501355930.209213988618750-1.61828591085544
Winsorized Mean ( 13 / 19 )-0.4650153947118640.179893223498846-2.58495226038821
Winsorized Mean ( 14 / 19 )-0.4983812603728810.170370086901524-2.92528617808919
Winsorized Mean ( 15 / 19 )-0.6733895936779660.138533044621637-4.86085897784991
Winsorized Mean ( 16 / 19 )-0.6887200066949150.133767028574624-5.1486529530758
Winsorized Mean ( 17 / 19 )-0.7417606959152540.124125614179629-5.97588741709515
Winsorized Mean ( 18 / 19 )-0.7333551550677970.121567034155998-6.03251662886448
Winsorized Mean ( 19 / 19 )-0.7156101240677970.114721083784794-6.23782569392573
Trimmed Mean ( 1 / 19 )-0.03302354129824560.311586789734838-0.105985049386557
Trimmed Mean ( 2 / 19 )-0.07572152198181820.305248552157221-0.248065130683461
Trimmed Mean ( 3 / 19 )-0.1184151880377360.298209370564713-0.397087414837084
Trimmed Mean ( 4 / 19 )-0.1658219395098040.290577554868466-0.570663276400909
Trimmed Mean ( 5 / 19 )-0.2119215873265310.284013999997068-0.746165989453755
Trimmed Mean ( 6 / 19 )-0.2643501795319150.276381340748773-0.956468981645927
Trimmed Mean ( 7 / 19 )-0.3189266067111110.267511939232795-1.19219578619844
Trimmed Mean ( 8 / 19 )-0.3788836734883720.255607223961160-1.48228859739091
Trimmed Mean ( 9 / 19 )-0.4449739635853660.240149371373157-1.85290496927406
Trimmed Mean ( 10 / 19 )-0.5076595606923080.224390010161651-2.26239822497708
Trimmed Mean ( 11 / 19 )-0.5764159361351350.203273729955576-2.83566369476817
Trimmed Mean ( 12 / 19 )-0.6337357740.184804388479787-3.42922470193025
Trimmed Mean ( 13 / 19 )-0.6777127833636360.171486391220422-3.95199163350828
Trimmed Mean ( 14 / 19 )-0.7088521032903230.162934335616233-4.35053851976244
Trimmed Mean ( 15 / 19 )-0.7394377676551720.153546722786820-4.81571833142793
Trimmed Mean ( 16 / 19 )-0.7490596004074070.151076943138496-4.95813315285793
Trimmed Mean ( 17 / 19 )-0.757959690480.148220716830197-5.11372301179952
Trimmed Mean ( 18 / 19 )-0.7604040400434780.146464243878502-5.19173840595706
Trimmed Mean ( 19 / 19 )-0.7646259559523810.143471362508782-5.32946744619909
Median-0.893625419
Midrange0.9411709275
Midmean - Weighted Average at Xnp-0.776992306166667
Midmean - Weighted Average at X(n+1)p-0.708852103290322
Midmean - Empirical Distribution Function-0.708852103290322
Midmean - Empirical Distribution Function - Averaging-0.708852103290322
Midmean - Empirical Distribution Function - Interpolation-0.739437767655172
Midmean - Closest Observation-0.776992306166667
Midmean - True Basic - Statistics Graphics Toolkit-0.708852103290322
Midmean - MS Excel (old versions)-0.708852103290322
Number of observations59


Variability - Ungrouped Data
Absolute range8.298572093
Relative range (unbiased)3.39683823937685
Relative range (biased)3.42599618395896
Variance (unbiased)5.96838748127234
Variance (biased)5.86722837142027
Standard Deviation (unbiased)2.44302834229821
Standard Deviation (biased)2.42223623361147
Coefficient of Variation (unbiased)144138434608.132
Coefficient of Variation (biased)142911702217.672
Mean Squared Error (MSE versus 0)5.86722837142027
Mean Squared Error (MSE versus Mean)5.86722837142027
Mean Absolute Deviation from Mean (MAD Mean)1.99050635507096
Mean Absolute Deviation from Median (MAD Median)1.87838467257627
Median Absolute Deviation from Mean1.82403272701695
Median Absolute Deviation from Median1.185510299
Mean Squared Deviation from Mean5.86722837142027
Mean Squared Deviation from Median6.66579476093349
Interquartile Difference (Weighted Average at Xnp)2.684796346
Interquartile Difference (Weighted Average at X(n+1)p)3.201427906
Interquartile Difference (Empirical Distribution Function)3.201427906
Interquartile Difference (Empirical Distribution Function - Averaging)3.201427906
Interquartile Difference (Empirical Distribution Function - Interpolation)2.8427551495
Interquartile Difference (Closest Observation)2.498572094
Interquartile Difference (True Basic - Statistics Graphics Toolkit)3.201427906
Interquartile Difference (MS Excel (old versions))3.201427906
Semi Interquartile Difference (Weighted Average at Xnp)1.342398173
Semi Interquartile Difference (Weighted Average at X(n+1)p)1.600713953
Semi Interquartile Difference (Empirical Distribution Function)1.600713953
Semi Interquartile Difference (Empirical Distribution Function - Averaging)1.600713953
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)1.42137757475
Semi Interquartile Difference (Closest Observation)1.249286047
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)1.600713953
Semi Interquartile Difference (MS Excel (old versions))1.600713953
Coefficient of Quartile Variation (Weighted Average at Xnp)-2.51297871876845
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)-6.03223595857356
Coefficient of Quartile Variation (Empirical Distribution Function)-6.03223595857356
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)-6.03223595857356
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)-3.24922324431566
Coefficient of Quartile Variation (Closest Observation)-2.02547114755544
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)-6.03223595857356
Coefficient of Quartile Variation (MS Excel (old versions))-6.03223595857356
Number of all Pairs of Observations1711
Squared Differences between all Pairs of Observations11.9367749625447
Mean Absolute Differences between all Pairs of Observations2.66447050569608
Gini Mean Difference2.66447050569608
Leik Measure of Dispersion-78601747969.383
Index of Diversity-3.46165311707117e+20
Index of Qualitative Variation-3.52133679150343e+20
Coefficient of Dispersion-2.22745046498163
Observations59


Percentiles - Ungrouped Data
pWeighted Average at XnpWeighted Average at X(n+1)pEmpirical Distribution FunctionEmpirical Distribution Function - AveragingEmpirical Distribution Function - InterpolationClosest ObservationTrue Basic - Statistics Graphics ToolkitMS Excel (old versions)
0.02-3.12594-3.116809-2.751584-2.751584-2.751584-3.208115-2.84289-3.208115
0.04-2.751584-2.751584-2.751584-2.751584-2.692221-2.751584-2.751584-2.751584
0.06-2.651409-2.640278-2.566074-2.566074-2.497209-2.566074-2.67738-2.566074
0.08-2.462776-2.451299-2.422605-2.422605-2.313152-2.422605-2.53738-2.422605
0.1-2.268686-2.251584-2.251584-2.251584-2.228401-2.251584-2.251584-2.251584
0.12-2.22156-2.219992-2.209543-2.209543-2.210065-2.222605-2.212155-2.222605
0.14-2.194474-2.18636-2.151584-2.151584-2.148107-2.209543-2.174768-2.209543
0.16-2.138833-2.134197-2.122605-2.122605-2.110433-2.151584-2.139992-2.122605
0.18-2.095654-2.08783-2.079136-2.079136-2.066385-2.079136-2.113911-2.079136
0.2-2.055952-2.050156-2.050156-2.050156-1.999707-2.050156-2.050156-2.050156
0.22-1.967756-1.954482-1.966074-1.966074-1.922025-1.966074-1.919707-1.966074
0.24-1.901389-1.891299-1.866074-1.866074-1.869437-1.908115-1.88289-1.908115
0.26-1.861147-1.85738-1.851584-1.851584-1.84938-1.866074-1.860278-1.851584
0.28-1.837257-1.829543-1.824033-1.824033-1.820213-1.824033-1.846074-1.824033
0.3-1.81289-1.808115-1.808115-1.808115-1.791299-1.808115-1.808115-1.808115
0.32-1.771119-1.746074-1.766074-1.766074-1.710074-1.766074-1.686074-1.766074
0.34-1.664335-1.654482-1.637095-1.637095-1.645209-1.666074-1.648686-1.666074
0.36-1.637095-1.637095-1.637095-1.637095-1.637095-1.637095-1.637095-1.637095
0.38-1.595095-1.557095-1.537095-1.537095-1.526833-1.637095-1.617095-1.537095
0.4-1.383176-1.280564-1.280564-1.280564-1.260849-1.280564-1.280564-1.280564
0.42-1.203677-1.181706-1.181992-1.181992-1.181477-1.181992-1.180849-1.181992
0.44-1.180621-1.134197-1.180564-1.180564-1.120286-1.180564-1.111013-1.180564
0.46-1.056732-1.030727-1.008115-1.008115-1.026205-1.064646-1.042034-1.008115
0.48-1.003935-0.997666-0.995053-0.995053-0.997143-1.008115-1.005503-0.995053
0.5-0.944339-0.893625-0.893625-0.893625-0.893625-0.893625-0.893625-0.893625
0.52-0.893625-0.848115-0.893625-0.893625-0.857217-0.893625-0.711584-0.893625
0.54-0.697931-0.649257-0.666074-0.666074-0.652621-0.666074-0.640849-0.666074
0.56-0.615976-0.503176-0.422605-0.422605-0.527347-0.624033-0.543462-0.422605
0.58-0.385609-0.288073-0.25444-0.25444-0.314979-0.422605-0.388972-0.25444
0.6-0.1217060.0773950.0773950.0773950.011028-0.254440.0773950.077395
0.620.1194150.1553540.1498440.1498440.1469460.1498440.1718850.149844
0.640.1707830.1831910.1773950.1773950.1791340.1773950.1860890.177395
0.660.1910150.2501710.1918850.1918850.2190850.1918850.2307430.289029
0.680.2944170.3249470.3339260.3339260.3087840.2890290.2980080.333926
0.70.3382730.3484160.3484160.3484160.342620.3339260.3484160.348416
0.720.4444160.5652320.5484160.5484160.5004160.3484160.6156820.548416
0.740.603910.913640.6324980.6324980.6257720.6324981.0542120.632498
0.761.2228971.4449471.3353541.3353541.3499661.3353541.4084161.518008
0.781.5306452.0234772.1498442.1498441.6696491.5180081.6443762.149844
0.82.3005792.9035192.9035192.9035192.4513142.1498442.9035192.903519
0.823.1711473.6217213.6078023.6078023.2979182.9035193.6634773.607802
0.843.6467743.8478453.6773953.6773953.6579093.6773953.9330693.677395
0.863.9927274.1313144.1035194.1035194.0523844.1035194.1220494.149844
0.884.1461384.1498444.1498444.1498444.1498444.1498444.1498444.149844
0.94.1640484.2918854.2918854.2918854.1782524.1498444.2918854.291885
0.924.3081134.4292734.3498444.3498444.312754.2918854.6675594.349844
0.944.532534.7933554.7469884.7469884.5563594.3498444.8165384.746988
0.964.8211754.9655184.8629054.8629054.8258124.8629054.9313145.033926
0.985.0031425.0791515.0339265.0339265.0065635.0339265.0452325.090457


Frequency Table (Histogram)
BinsMidpointAbs. FrequencyRel. FrequencyCumul. Rel. Freq.Density
[-4,-3[-3.510.0169490.0169490.016949
[-3,-2[-2.5110.1864410.203390.186441
[-2,-1[-1.5160.2711860.4745760.271186
[-1,0[-0.570.1186440.593220.118644
[0,1[0.590.1525420.7457630.152542
[1,2[1.520.0338980.7796610.033898
[2,3[2.520.0338980.8135590.033898
[3,4[3.520.0338980.8474580.033898
[4,5[4.570.1186440.9661020.118644
[5,6]5.520.03389810.033898


Properties of Density Trace
Bandwidth0.844708304132893
#Observations59
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/128if1257346432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/128if1257346432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/20fnd1257346432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/20fnd1257346432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/52ls51257346432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/52ls51257346432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/7xy7g1257346432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/7xy7g1257346432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/9lyrs1257346432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/04/t1257346620c6tfg3tfn3pcvmw/9lyrs1257346432.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
load(file='createtable')
x <-sort(x[!is.na(x)])
num <- 50
res <- array(NA,dim=c(num,3))
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
iqd <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','http://www.xycoon.com/absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','http://www.xycoon.com/relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','http://www.xycoon.com/relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','http://www.xycoon.com/unbiased.htm', varx)
res[5,] <- c('Variance (biased)','http://www.xycoon.com/biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','http://www.xycoon.com/unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','http://www.xycoon.com/biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','http://www.xycoon.com/variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','http://www.xycoon.com/variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','http://www.xycoon.com/mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','http://www.xycoon.com/mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'http://www.xycoon.com/mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'http://www.xycoon.com/median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'http://www.xycoon.com/mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'http://www.xycoon.com/median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'http://www.xycoon.com/mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'http://www.xycoon.com/median.htm', msemed)
mylink1 <- hyperlink('http://www.xycoon.com/difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('http://www.xycoon.com/deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('http://www.xycoon.com/variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'http://www.xycoon.com/pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'http://www.xycoon.com/squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'http://www.xycoon.com/mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'http://www.xycoon.com/gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'http://www.xycoon.com/leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'http://www.xycoon.com/diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'http://www.xycoon.com/qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'http://www.xycoon.com/dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main='Robustness of Central Tendency', xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main='Robustness of Central Tendency', xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main='Robustness of Central Tendency', xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main='Robustness of Central Tendency', xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
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,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
lx <- length(x)
qval <- array(NA,dim=c(99,8))
mystep <- 25
mystart <- 25
if (lx>10){
mystep=10
mystart=10
}
if (lx>20){
mystep=5
mystart=5
}
if (lx>50){
mystep=2
mystart=2
}
if (lx>=100){
mystep=1
mystart=1
}
for (perc in seq(mystart,99,mystep)) {
qval[perc,1] <- q1(x,lx,perc/100,i,f)
qval[perc,2] <- q2(x,lx,perc/100,i,f)
qval[perc,3] <- q3(x,lx,perc/100,i,f)
qval[perc,4] <- q4(x,lx,perc/100,i,f)
qval[perc,5] <- q5(x,lx,perc/100,i,f)
qval[perc,6] <- q6(x,lx,perc/100,i,f)
qval[perc,7] <- q7(x,lx,perc/100,i,f)
qval[perc,8] <- q8(x,lx,perc/100,i,f)
}
bitmap(file='test3.png')
myqqnorm <- qqnorm(x,col=2)
qqline(x)
grid()
dev.off()
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Percentiles - Ungrouped Data',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p',1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_1.htm', 'Weighted Average at Xnp',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),1,TRUE)
a<-table.row.end(a)
for (perc in seq(mystart,99,mystep)) {
a<-table.row.start(a)
a<-table.element(a,round(perc/100,2),1,TRUE)
for (j in 1:8) {
a<-table.element(a,round(qval[perc,j],6))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
bitmap(file='histogram1.png')
myhist<-hist(x)
dev.off()
myhist
n <- length(x)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/histogram.htm','Frequency Table (Histogram)',''),6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bins',header=TRUE)
a<-table.element(a,'Midpoint',header=TRUE)
a<-table.element(a,'Abs. Frequency',header=TRUE)
a<-table.element(a,'Rel. Frequency',header=TRUE)
a<-table.element(a,'Cumul. Rel. Freq.',header=TRUE)
a<-table.element(a,'Density',header=TRUE)
a<-table.row.end(a)
crf <- 0
mybracket <- '['
mynumrows <- (length(myhist$breaks)-1)
for (i in 1:mynumrows) {
a<-table.row.start(a)
if (i == 1)
dum <- paste('[',myhist$breaks[i],sep='')
else
dum <- paste(mybracket,myhist$breaks[i],sep='')
dum <- paste(dum,myhist$breaks[i+1],sep=',')
if (i==mynumrows)
dum <- paste(dum,']',sep='')
else
dum <- paste(dum,mybracket,sep='')
a<-table.element(a,dum,header=TRUE)
a<-table.element(a,myhist$mids[i])
a<-table.element(a,myhist$counts[i])
rf <- myhist$counts[i]/n
crf <- crf + rf
a<-table.element(a,round(rf,6))
a<-table.element(a,round(crf,6))
a<-table.element(a,round(myhist$density[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
bitmap(file='density1.png')
mydensity1<-density(x,kernel='gaussian',na.rm=TRUE)
plot(mydensity1,main='Gaussian Kernel')
grid()
dev.off()
mydensity1
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Properties of Density Trace',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bandwidth',header=TRUE)
a<-table.element(a,mydensity1$bw)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Observations',header=TRUE)
a<-table.element(a,mydensity1$n)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable4.tab')
 





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