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contingency_tables [2008/11/24 11:33]
steko old revision restored
contingency_tables [2018/08/04 00:01]
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-====== Contingency Tables ====== 
  
-A contingency is obtained when by crossing two qualitatives nominal variables, typically artifacts type and archaeological assemblage. 
- 
-Let's assume we have a data.frame object named ''​MyData''​. Each line corresponds to an artifact. The first column contains a label, the second the assemblage and the last the artifact type : 
- 
- 
-<​file>​label assemblage type 
-CLXIV-001 CL XIV 5+6 t 
-CLXIV-002 CL XIV 3+4 plh 
-... ... ... </​file>​ 
- 
-**''​R''​** provides two functions for computing contingency table, here assemblage against type: 
- 
-<code C>​MyCrossTable <- table(MyData[,​2],​ MyData[,3]) 
-</​code>​ 
- 
-an alternative : 
-<code C>​MyCrossTable2 <- xtabs(~., NMB_2006[,​c(1,​6)] ) 
-</​code>​ 
- 
-The latter can be used as argument to the ''​corresp()''​ function from the MASS package which computes correspondence analysis, a factorial data reduction method suitable for contingency tables. 
- 
-==== Frequency Tables ==== 
- 
-The ''​prop.table()''​ function calculates the frequency table (percentages). Its first argument is an objet of class table. The second is the margin : 1 for row, 2 for columns. 
- 
-<code C>​MyCrosFreq <- prop.table(MyCrossTable,​ 1) 
-</​code>​ 
- 
-Here is an example : 
-<​file>​ 
-     ​TYPE_REC_ 
-PHASE     type 1    type 2    type 3    type 4 
-    1 0.29242348 0.2506487 0.1904153 0.2665125 
-    2 0.44952914 0.2752219 0.1045417 0.1707073 
-    3 0.00000000 0.5199755 0.1823170 0.2977075 
-    4 0.13439854 0.5759938 0.1875329 0.1020748 
-    5 0.07930212 0.1942093 0.1844235 0.5420651 
-    6 0.14209591 0.2609925 0.1652278 0.4316838 
-</​file>​ 
-==== Plotting ​ ==== 
- 
-Now we can plot our frequency table. A graphical representation allows us to have a feel of the trends, even if there are many artifacts types and assemblages. 
- 
-A common and popular way to represent a frequency table is Ford's Battleship diagram. Is is derived from the barplot. 
- 
-Here is a code that implements it (Jammet-Reynal,​ 2006): 
-<code C>ford <- function(x, cex.row.labels=1) { 
-#################################################​ 
-##  FORD'S "​BATTLESHIP"​ DIAGRAM ​               ## 
-##  Loic JAMMET-REYNAL,​ may 2006               ## 
-##  Departement d'​Anthropologie et d'​Ecologie ​ ## 
-##  University of Geneva ​                      ## 
-##  jammetr1[at]etu.unige.ch ​                  ## 
-#################################################​ 
- 
-    dim(x)[2] -> jmax # colonnes j 
-    dim(x)[1] -> imax # lignes i 
-    ​ 
-    set.up <- function(xlim,​ ylim) { 
-        # setting up coord. system 
-        plot(    xlim,    # x 
-                ylim,     # y 
-                type="​n",​ # no plotting 
-                axes = FALSE, 
-                asp = NA, 
-                xlab = "",​ 
-                ylab = ""​) 
-    } 
-    ​ 
-    ## initialisation du device 
-    ## on divise par le nombre de colonnes + 1 
-    ## 1ere colonne : labels 
-    op <- par(mfrow=c(1,​ jmax+1), mar=c(5,​0,​2,​0)) 
-    ​ 
-    # labels des lignes (colonne 1) 
-    set.up(c(0,​1), ​            # x 
-           ​c(0.9,​ imax+1.10) ) # y 
-    ​ 
-    for (i in 1:imax) { 
-        text(0.5, 
-               ​i+0.5,​ 
-              row.names(x)[i],​ 
-              font = 2, # boldface 
-              cex = cex.row.labels) 
-    } 
- 
-    for (j in 1:jmax) { # colonnes j 
-        set.up(xlim = c(-60,​60)*max(x), ​  # x 
-               ylim = c(0.9, imax+1.10) ) # y 
-        ​ 
-        title(sub=colnames(x)[j],​ 
-              font.sub=2, # boldface 
-              cex.sub = 1.5) 
-        ​ 
-        for (i in 1: imax) { # lignes i 
-            # le plus important. boite multipliee 
-            # par les parametres 
-            X <- c(-50,​+50,​+50,​-50,​-50)*x[i,​j] 
-            Y <- c(i,​i,​i+1,​i+1,​i) 
-            polygon(X, 
-                    Y, 
-                    xpd=FALSE, ​ 
-                    col="​black",​ 
-                    mar=c(0,​0,​0,​0) ) 
-        } 
-    } 
-} 
-</​code>​ 
- 
-You first have to run the above code. A new function called ''​ford()''​ will be available. Its argument is a frequency table. 
- 
-In order to represent a chronological hypothesis, you have to rearrange the order of rows and columns. A way to do it is giving two a vector of indices between brackets right after the frequency table object: 
-<code C>​ford(MyCrosFreq[c(1,​2,​4,​3),​ c(2,​4,​5,​3,​1,​6)]) 
-</​code>​ 
- 
-This is an output example : 
- 
-{{ford.png?​600|Ford diagram}} 
- 
-==== Reference ==== 
-**Jammet-Reynal,​ L. (2006).-** //La céramique de Clairvaux VII (Jura, France) : typologie, étude quantitative et sériation.//​ Genève : Département d'​anthropologie et d'​écologie de l'​Université. Unpublished Master thesis. 
contingency_tables.txt · Last modified: 2018/08/04 00:01 (external edit)