Clothing and Intelligence Rating of Children

Schoolboys were classified according to their clothing and to their teachers rating of "dullness" (lack of intelligence), in a 5 x 7 table originally from Gilby (1911). Anscombe (1981) presents a slightly collapsed 4 x 6 table, used here, where the last two categories of clothing were pooled as were the first two categories of dullness due to small counts.

Both Dullness and Clothing are ordered categories, so models and methods that examine their association in terms of ordinal categories are profitable.

Usage

data(Gilby)

Format

A 2-dimensional array resulting from cross-tabulating 2 variables for 1725 observations. The variable names and their levels are:

No	Name	Levels
1	Dullness	"Ment. defective", "Slow", "Slow Intell", "Fairly Intell", "Capable", "V.Able"
2	Clothing	"V.Well clad", "Well clad", "Passable", "Insufficient"

Source

Anscombe, F. J. (1981). Computing in Statistical Science Through APL. New York: Springer-Verlag, p. 302

References

Gilby, W. H. (1911). On the significance of the teacher's appreciation of general intelligence. Biometrika, 8, 93-108 (esp. p. 94). [Quoted by Kendall (1943,..., 1953) Table 13.1, p 320.]

Examples

data(Gilby)

# CMH tests treating row/column variables as ordinal
CMHtest(Gilby)
#> Cochran-Mantel-Haenszel Statistics for Dullness by Clothing 
#> 
#>                  AltHypothesis  Chisq Df       Prob
#> cor        Nonzero correlation 133.21  1 8.1410e-31
#> rmeans  Row mean scores differ 134.79  5 2.2915e-27
#> cmeans  Col mean scores differ 135.22  3 4.0462e-29
#> general    General association 174.72 15 2.7516e-29
#> 

mosaic(Gilby, shade=TRUE)


# correspondence analysis to see relations among categories
if(require(ca)){
  ca(Gilby)
  plot(ca(Gilby), lines=TRUE)

}