# A Color-Caused Optical Illusion

#### Kevin Wright

#### 2019-12-04

Cleveland and McGill (1983) conducted experiments with different partitionings of colored-areas that were nearly the same size. In the example below, the two colored regions are less tha 1% different in area.

Using a map (similar to the one below left) with regions coded by two saturated colors, 49% of subjects said the red area was bigger, 22% said the green was bigger, and 31% said the areas were the same.

    library(maps)
    #library(mapproj)
    #nv <- map('county', 'nevada', fill=TRUE, col=1:12, projection="mollweide")
    reds <- c("nevada,carson city", "nevada,churchill", "nevada,clark",
              "nevada,douglas", "nevada,esmeralda", "nevada,lincoln",
              "nevada,nye", "nevada,storey", "nevada,white pine")
    grns <- c("nevada,elko", "nevada,eureka", "nevada,humboldt", "nevada,lander",
              "nevada,lyon", "nevada,mineral", "nevada,pershing", "nevada,washoe")
    nv.names <- c(reds,grns)

    # Draw the map and color it
    nv.names <- map('county', 'nevada', namesonly=TRUE, plot=FALSE)

    # green/red
    op <- par(mar=c(0,1,0,1), mfrow=c(1,2))
    nv <- map('county', 'nevada', fill=TRUE,
              col=ifelse(nv.names %in% reds,
                         rgb(206, 60, 17, max=255), # red
                         rgb(80,164,52, max=255)), # green
              projection="mollweide")
    # red/green
    nv <- map('county', 'nevada', fill=TRUE,
              col=ifelse(nv.names %in% reds,
                         rgb(80,164,52, max=255),
                         rgb(206, 60, 17, max=255)),
              projection="mollweide")

    par(op)

    # Area of red region = 55581
    sum(area.map(nv, regions=reds))

    ## [1] 55581.16

    # Area of green region = 55687
    sum(area.map(nv, regions=grns))

    ## [1] 55686.61

# Muted colors

When low-saturated, muted colors were used, the observers demonstrated no systematic biases.

    op <- par(mar=c(0,1,0,1), mfrow=c(1,2))
    # green/tan
    nv <- map('county', 'nevada', fill=TRUE,
              col=ifelse(nv.names %in% reds,
                         rgb(250, 229, 139, max=255),
                         rgb(204, 246, 186, max=255)),
              projection="mollweide")
    # tan/green
    nv <- map('county', 'nevada', fill=TRUE,
              col=ifelse(nv.names %in% reds,
                         rgb(204, 246, 186, max=255),
                         rgb(250, 229, 139, max=255)),
              projection="mollweide")

    par(op)

# Bibliography

Cleveland, William S., and Robert McGill. 1983. “A Color-Caused Optical Illusion on a Statistical Graph.” The American Statistcian 37: 101–5. https://doi.org/10.2307/2685868.