Nutrition data

This observational dataset involves three factors, but where several factor combinations are missing. It is used as a case study in Milliken and Johnson, Chapter 17, p.202. (You may also find it in the second edition, p.278.)

nutrition

Format

A data frame with 107 observations and 4 variables:

age

a factor with levels 1, 2, 3, 4. Mother's age group.

group

a factor with levels FoodStamps, NoAid. Whether or not the family receives food stamp assistance.

race

a factor with levels Black, Hispanic, White. Mother's race.

gain

a numeric vector (the response variable). Gain score (posttest minus pretest) on knowledge of nutrition.

Source

Milliken, G. A. and Johnson, D. E. (1984) Analysis of Messy Data – Volume I: Designed Experiments. Van Nostrand, ISBN 0-534-02713-7.

Details

A survey was conducted by home economists “to study how much lower-socioeconomic-level mothers knew about nutrition and to judge the effect of a training program designed to increase their knowledge of nutrition.” This is a messy dataset with several empty cells.

Examples

nutr.aov <- aov(gain ~ (group + age + race)^2, data = nutrition)

# Summarize predictions for age group 3
nutr.emm <- emmeans(nutr.aov, ~ race * group, at = list(age="3"))
                   
emmip(nutr.emm, race ~ group)


# Hispanics seem exceptional; but this doesn't test out due to very sparse data
pairs(nutr.emm, by = "group")
#> group = FoodStamps:
#>  contrast         estimate    SE df t.ratio p.value
#>  Black - Hispanic     7.50  5.97 92   1.255  0.4241
#>  Black - White        2.08  2.84 92   0.733  0.7447
#>  Hispanic - White    -5.42  5.43 92  -0.998  0.5799
#> 
#> group = NoAid:
#>  contrast         estimate    SE df t.ratio p.value
#>  Black - Hispanic    -6.17  8.49 92  -0.726  0.7486
#>  Black - White       -3.47  5.02 92  -0.691  0.7693
#>  Hispanic - White     2.70 10.70 92   0.253  0.9655
#> 
#> P value adjustment: tukey method for comparing a family of 3 estimates 
pairs(nutr.emm, by = "race")
#> race = Black:
#>  contrast           estimate   SE df t.ratio p.value
#>  FoodStamps - NoAid    11.17 7.41 92   1.508  0.1350
#> 
#> race = Hispanic:
#>  contrast           estimate   SE df t.ratio p.value
#>  FoodStamps - NoAid    -2.50 9.75 92  -0.256  0.7983
#> 
#> race = White:
#>  contrast           estimate   SE df t.ratio p.value
#>  FoodStamps - NoAid     5.62 9.68 92   0.580  0.5631
#>