ws 4

*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: Sun, 25 Oct 2009 05:47:40 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw.htm/, Retrieved Sun, 25 Oct 2009 12:54:13 +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/Oct/25/t1256471652i1yb1sz4jwcc6xw.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.148646309 0.193804029 0.131910607 0.048982359 0.035920892 0.052430242 0.062010996 0.076835147 0.038935146 0.028633045 0.030047843 0.028588494 0.070373946 0.125599266 0.093117457 0.082838021 0.069228352 0.089461571 0.090135825 0.119156645 0.084594868 0.077924504 0.050993737 -0.012468929 0.014611083 0.064006082 0.060022728 0.027923409 0.015205745 0.021403349 0.021403349 0.047156409 0.036829054 0.005311826 -0.046777916 -0.085262281 -0.076011397 -0.078430257 -0.067808537 -0.084313313 -0.08589517 -0.055971412 -0.075210786 -0.11300426 -0.169796642 -0.220749887 -0.146468921 -0.052085939 0.003958635 -0.012954959 -0.100487052 -0.175181637 -0.163935918 -0.060773277 -0.019995189 0.019465346 -0.05531767 -0.094184475 -0.065037375 -0.049343114

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 5.00000004755775e-11 0.0113094944508857 4.42106415036630e-09 Geometric Mean NaN Harmonic Mean 0.0819855173246095 Quadratic Mean 0.0868698752119644 Winsorized Mean ( 1 / 20 ) 6.84221666666744e-06 0.0108829977696223 0.000628706980512861 Winsorized Mean ( 2 / 20 ) -0.000371514683333332 0.0107114438265894 -0.0346839034352313 Winsorized Mean ( 3 / 20 ) -0.000394045533333334 0.0105688157389198 -0.0372837925333731 Winsorized Mean ( 4 / 20 ) 0.000340912866666668 0.0101878545897116 0.0334626749591562 Winsorized Mean ( 5 / 20 ) 0.000959702283333336 0.00914916569279603 0.104895059894805 Winsorized Mean ( 6 / 20 ) 0.00191325988333333 0.0088433795057209 0.216349403765339 Winsorized Mean ( 7 / 20 ) 0.00256989756666667 0.00868849105252003 0.295781805049024 Winsorized Mean ( 8 / 20 ) 0.0030262445 0.00837608932226241 0.361295633746012 Winsorized Mean ( 9 / 20 ) 0.0028576508 0.00831579445729589 0.343641345956168 Winsorized Mean ( 10 / 20 ) 0.00219689263333333 0.00815616827213173 0.269353519941435 Winsorized Mean ( 11 / 20 ) 0.00307573745 0.00793382728392566 0.387673860285767 Winsorized Mean ( 12 / 20 ) 0.00226726925 0.00765037597645819 0.296360500056058 Winsorized Mean ( 13 / 20 ) 0.00219252293333334 0.00758300667162558 0.289136358212292 Winsorized Mean ( 14 / 20 ) 0.0027011847 0.00710783325208298 0.380029272522454 Winsorized Mean ( 15 / 20 ) 0.0028952037 0.00691936903208383 0.41842018926516 Winsorized Mean ( 16 / 20 ) 0.0035020917 0.00665510980660163 0.52622598300723 Winsorized Mean ( 17 / 20 ) 0.00271141575 0.00613037421045901 0.442292045626524 Winsorized Mean ( 18 / 20 ) 0.00247658685 0.00603959963259391 0.410058116540474 Winsorized Mean ( 19 / 20 ) 0.00286303196666667 0.00578787791378742 0.494660048002495 Winsorized Mean ( 20 / 20 ) 0.00316865696666667 0.00555920365356156 0.569983969671022 Trimmed Mean ( 1 / 20 ) 0.000464583810344828 0.0105286674062325 0.0441256041642853 Trimmed Mean ( 2 / 20 ) 0.000955021232142858 0.010091410004403 0.0946370459357187 Trimmed Mean ( 3 / 20 ) 0.00169198562962963 0.00966456580706825 0.175071044411761 Trimmed Mean ( 4 / 20 ) 0.00249430530769231 0.0092007663708342 0.271097559394518 Trimmed Mean ( 5 / 20 ) 0.00314032304 0.0087757008386191 0.357842991431570 Trimmed Mean ( 6 / 20 ) 0.00368547822916667 0.00860587875920357 0.428251237588634 Trimmed Mean ( 7 / 20 ) 0.00407074308695652 0.00847700915692451 0.480209825375888 Trimmed Mean ( 8 / 20 ) 0.00436311559090909 0.00834636378851322 0.522756460353894 Trimmed Mean ( 9 / 20 ) 0.00460184257142857 0.00825036577540714 0.557774369852285 Trimmed Mean ( 10 / 20 ) 0.0048925412 0.0081261755543649 0.602071806998069 Trimmed Mean ( 11 / 20 ) 0.00531816992105263 0.00798807527740344 0.665763620943408 Trimmed Mean ( 12 / 20 ) 0.00565793241666667 0.00784691368719937 0.721039206267353 Trimmed Mean ( 13 / 20 ) 0.00615655935294118 0.00771118671381755 0.79839324107006 Trimmed Mean ( 14 / 20 ) 0.006728295375 0.00752064746970328 0.894643101156483 Trimmed Mean ( 15 / 20 ) 0.0073035969 0.0073704320652019 0.990931988164242 Trimmed Mean ( 16 / 20 ) 0.00793336735714286 0.0071846418214233 1.10421195020286 Trimmed Mean ( 17 / 20 ) 0.00857249365384615 0.00697021112484786 1.22987575272812 Trimmed Mean ( 18 / 20 ) 0.009434416875 0.0067930391568881 1.38883593294668 Trimmed Mean ( 19 / 20 ) 0.0104886335454545 0.00650138018306766 1.61329337004031 Trimmed Mean ( 20 / 20 ) 0.0116926759 0.00609172257012562 1.91943670536508 Median 0.0204343475 Midrange -0.013472929 Midmean - Weighted Average at Xnp 0.00488062483870968 Midmean - Weighted Average at X(n+1)p 0.0073035969 Midmean - Empirical Distribution Function 0.00488062483870968 Midmean - Empirical Distribution Function - Averaging 0.0073035969 Midmean - Empirical Distribution Function - Interpolation 0.0073035969 Midmean - Closest Observation 0.00488062483870968 Midmean - True Basic - Statistics Graphics Toolkit 0.0073035969 Midmean - MS Excel (old versions) 0.006728295375 Number of observations 60 Variability - Ungrouped Data Absolute range 0.414553916 Relative range (unbiased) 4.7321903430951 Relative range (biased) 4.7721251468185 Variance (unbiased) 0.00767427988407688 Variance (biased) 0.00754637521934227 Standard Deviation (unbiased) 0.0876029673246111 Standard Deviation (biased) 0.0868698752119644 Coefficient of Variation (unbiased) 1752059329.82742 Coefficient of Variation (biased) 1737397487.71395 Mean Squared Error (MSE versus 0) 0.00754637521934227 Mean Squared Error (MSE versus Mean) 0.00754637521934227 Mean Absolute Deviation from Mean (MAD Mean) 0.0722488771416667 Mean Absolute Deviation from Median (MAD Median) 0.07029712265 Median Absolute Deviation from Mean 0.0645217285 Median Absolute Deviation from Median 0.065686392 Mean Squared Deviation from Mean 0.00754637521934227 Mean Squared Deviation from Median 0.00796393777504959 Interquartile Difference (Weighted Average at Xnp) 0.129819533 Interquartile Difference (Weighted Average at X(n+1)p) 0.130623057 Interquartile Difference (Empirical Distribution Function) 0.129819533 Interquartile Difference (Empirical Distribution Function - Averaging) 0.129431495 Interquartile Difference (Empirical Distribution Function - Interpolation) 0.128239933 Interquartile Difference (Closest Observation) 0.129819533 Interquartile Difference (True Basic - Statistics Graphics Toolkit) 0.128239933 Interquartile Difference (MS Excel (old versions)) 0.131814619 Semi Interquartile Difference (Weighted Average at Xnp) 0.0649097665 Semi Interquartile Difference (Weighted Average at X(n+1)p) 0.0653115285 Semi Interquartile Difference (Empirical Distribution Function) 0.0649097665 Semi Interquartile Difference (Empirical Distribution Function - Averaging) 0.0647157475 Semi Interquartile Difference (Empirical Distribution Function - Interpolation) 0.0641199665 Semi Interquartile Difference (Closest Observation) 0.0649097665 Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) 0.0641199665 Semi Interquartile Difference (MS Excel (old versions)) 0.0659073095 Coefficient of Quartile Variation (Weighted Average at Xnp) -22.3921716120679 Coefficient of Quartile Variation (Weighted Average at X(n+1)p) -36.1993553439772 Coefficient of Quartile Variation (Empirical Distribution Function) -22.3921716120679 Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) -37.9073484580237 Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) -39.8211441567162 Coefficient of Quartile Variation (Closest Observation) -22.3921716120679 Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) -39.8211441567162 Coefficient of Quartile Variation (MS Excel (old versions)) -34.6656617895544 Number of all Pairs of Observations 1770 Squared Differences between all Pairs of Observations 0.0153485597681537 Mean Absolute Differences between all Pairs of Observations 0.0994008712661017 Gini Mean Difference 0.0994008712661018 Leik Measure of Dispersion -994008702.413015 Index of Diversity -50309167192821240 Index of Qualitative Variation -51161864941852104 Coefficient of Dispersion 3.53565863268532 Observations 60 Percentiles - Ungrouped Data p Weighted Average at Xnp Weighted Average at X(n+1)p Empirical Distribution Function Empirical Distribution Function - Averaging Empirical Distribution Function - Interpolation Closest Observation True Basic - Statistics Graphics Toolkit MS Excel (old versions) 0.02 -0.211636 -0.210725 -0.175182 -0.175182 -0.174212 -0.22075 -0.185207 -0.22075 0.04 -0.173028 -0.172812 -0.169797 -0.169797 -0.167687 -0.175182 -0.172166 -0.175182 0.06 -0.16628 -0.165929 -0.163936 -0.163936 -0.154504 -0.163936 -0.167804 -0.163936 0.08 -0.149962 -0.148565 -0.146469 -0.146469 -0.122374 -0.146469 -0.16184 -0.146469 0.1 -0.113004 -0.111753 -0.113004 -0.106746 -0.101739 -0.113004 -0.101739 -0.113004 0.12 -0.099227 -0.09847 -0.094184 -0.094184 -0.093521 -0.100487 -0.096201 -0.100487 0.14 -0.090869 -0.089708 -0.085895 -0.085895 -0.085731 -0.094184 -0.090371 -0.085895 0.16 -0.085515 -0.085414 -0.085262 -0.085262 -0.084845 -0.085262 -0.085743 -0.085262 0.18 -0.084503 -0.084332 -0.084313 -0.084313 -0.080666 -0.084313 -0.085243 -0.084313 0.2 -0.07843 -0.077946 -0.07843 -0.077221 -0.076495 -0.07843 -0.076495 -0.07843 0.22 -0.075851 -0.075675 -0.075211 -0.075211 -0.075227 -0.076011 -0.075547 -0.076011 0.24 -0.07225 -0.070473 -0.067809 -0.067809 -0.067365 -0.075211 -0.072546 -0.067809 0.26 -0.066146 -0.065425 -0.065037 -0.065037 -0.063588 -0.065037 -0.067421 -0.065037 0.28 -0.061626 -0.060389 -0.060773 -0.060773 -0.058276 -0.060773 -0.056356 -0.060773 0.3 -0.055971 -0.055775 -0.055971 -0.055645 -0.055514 -0.055971 -0.055514 -0.055971 0.32 -0.054671 -0.053637 -0.052086 -0.052086 -0.052474 -0.055318 -0.053766 -0.052086 0.34 -0.050989 -0.050056 -0.049343 -0.049343 -0.049189 -0.052086 -0.051373 -0.049343 0.36 -0.047804 -0.046881 -0.046778 -0.046778 -0.04035 -0.046778 -0.049241 -0.046778 0.38 -0.025352 -0.018728 -0.019995 -0.019995 -0.017038 -0.019995 -0.014222 -0.019995 0.4 -0.012955 -0.012761 -0.012955 -0.012712 -0.012663 -0.012955 -0.012663 -0.012955 0.42 -0.009183 -0.002284 0.003959 0.003959 0.000345 -0.012469 -0.006226 0.003959 0.44 0.0045 0.005095 0.005312 0.005312 0.005258 0.003959 0.004175 0.005312 0.46 0.010891 0.014647 0.014611 0.014611 0.014694 0.014611 0.01517 0.014611 0.48 0.015087 0.016398 0.015206 0.015206 0.016569 0.015206 0.018273 0.015206 0.5 0.019465 0.020434 0.019465 0.020434 0.020434 0.019465 0.020434 0.020434 0.52 0.021403 0.021403 0.021403 0.021403 0.021403 0.021403 0.021403 0.021403 0.54 0.024011 0.027532 0.027923 0.027923 0.027011 0.021403 0.021795 0.027923 0.56 0.028322 0.028596 0.028588 0.028588 0.02859 0.028588 0.028626 0.028588 0.58 0.028624 0.029171 0.028633 0.028633 0.028944 0.028633 0.02951 0.028633 0.6 0.030048 0.033572 0.030048 0.032984 0.032397 0.030048 0.032397 0.035921 0.62 0.036103 0.036666 0.036829 0.036829 0.036448 0.035921 0.036084 0.036829 0.64 0.037671 0.039264 0.038935 0.038935 0.03843 0.036829 0.046828 0.038935 0.66 0.043868 0.047631 0.047156 0.047156 0.046663 0.047156 0.048508 0.047156 0.68 0.048617 0.049948 0.048982 0.048982 0.049224 0.048982 0.050028 0.048982 0.7 0.050994 0.051999 0.050994 0.051712 0.051425 0.050994 0.051425 0.05243 0.72 0.053949 0.059415 0.060023 0.060023 0.056075 0.05243 0.053038 0.060023 0.74 0.060818 0.06229 0.062011 0.062011 0.061335 0.060023 0.063727 0.062011 0.76 0.063208 0.065886 0.064006 0.064006 0.063687 0.064006 0.067348 0.064006 0.78 0.068184 0.069893 0.069228 0.069228 0.069251 0.069228 0.06971 0.070374 0.8 0.070374 0.075543 0.070374 0.073605 0.071666 0.070374 0.071666 0.076835 0.82 0.077053 0.078023 0.077925 0.077925 0.077249 0.076835 0.08274 0.077925 0.84 0.07989 0.08326 0.082838 0.082838 0.080676 0.077925 0.084173 0.082838 0.86 0.083892 0.086834 0.084595 0.084595 0.084138 0.084595 0.087223 0.084595 0.88 0.088488 0.08992 0.089462 0.089462 0.089072 0.089462 0.089677 0.090136 0.9 0.090136 0.092819 0.090136 0.091627 0.090434 0.090136 0.090434 0.093117 0.92 0.098325 0.11993 0.119157 0.119157 0.100408 0.093117 0.124826 0.119157 0.94 0.121734 0.127745 0.125599 0.125599 0.12212 0.119157 0.129765 0.125599 0.96 0.129386 0.141283 0.131911 0.131911 0.129639 0.131911 0.139274 0.148646 0.98 0.145299 0.183869 0.148646 0.148646 0.145634 0.148646 0.158581 0.193804 Frequency Table (Histogram) Bins Midpoint Abs. Frequency Rel. Frequency Cumul. Rel. Freq. Density [-0.25,-0.2[ -0.225 1 0.016667 0.016667 0.333333 [-0.2,-0.15[ -0.175 3 0.05 0.066667 1 [-0.15,-0.1[ -0.125 3 0.05 0.116667 1 [-0.1,-0.05[ -0.075 13 0.216667 0.333333 4.333333 [-0.05,0[ -0.025 5 0.083333 0.416667 1.666667 [0,0.05[ 0.025 16 0.266667 0.683333 5.333333 [0.05,0.1[ 0.075 14 0.233333 0.916667 4.666667 [0.1,0.15[ 0.125 4 0.066667 0.983333 1.333333 [0.15,0.2] 0.175 1 0.016667 1 0.333333 Properties of Density Trace Bandwidth 0.0347641068737323 #Observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/1oswd1256471250.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/1oswd1256471250.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/2grbd1256471250.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/2grbd1256471250.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/5pj9f1256471251.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/5pj9f1256471251.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/7fz7c1256471251.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/7fz7c1256471251.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/9tjuq1256471251.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/25/t1256471652i1yb1sz4jwcc6xw/9tjuq1256471251.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 36 ;

Parameters (R input):

par1 = 0 ; par2 = 36 ;

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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