Luke Brzozowski September 9th 2025
#Results
Are Men bigger than women?: Men have both a greater mean and standard deviation value for stature, sitting height, weight in kg, and bmi than women. This means that on average, men are larger than women strictly based on these four variables.
Rank the variables for women from closest to normally distributed to most different from normal: The variable that is closest to normally distributed is stature, followed by sitting height, followed by weight in kg, and finally BMI.
What percentage of men in the dataset have both knee height and buttock knee length less than the respective 95th percentiles?: 92.7 percent of men have both knee height and buttock knee length less than the respective 95th percentiles.
What percentage of women in the dataset have both buttock popliteal length > than the 5th percentile and hip breadth sitting < than the 95th percentile? 89.5 percent of women have both buttock popliteal length greater than the 5th percentile and hip breadth sitting less than the 95th percentile.
On which dimension is the ANSUR II dataset is the difference in means between men and women largest as a fraction of the mean of the male and female standard deviations? Smallest? The dimension where the difference in means between men and women is the largest as a fraction of the mean of male and female standard deviations is the largest is the neck circumference. The dimension where the it is the smallest is buttock circumference.
#Questions to be Answered
##Parametric Summary Statistics
Make a table of the means and standard deviations for stature, sittingheight, weightkg (make sure to convert to kg), and BMI for men and women. Are men bigger than women?
A2M\(BMI <- round(A2M\)weightkg / (A2M\(stature/1000)^2, 1) A2F\)BMI <- round(A2F\(weightkg / (A2F\)stature/1000)^2, 1)
measurement <- c(“Stature”, “SittingHeight”, “Weightkg”, “BMI”)
malemeans <- c(1756.2, 918.3, 855.2, 276.8)
malestddevs <- c(68.6, 35.7, 142.2, 40.4)
femalemeans <- c(1628.5, 856.6, 677.6, 255.0)
femalestddevs <- c(64.2, 33.1, 109.8, 34.9)
data <- data.frame(Measurement = measurement, MaleMeans = malemeans, MaleStdDevs = malestddevs, FemaleMeans = femalemeans, FemaleStdDevs = femalestddevs)
kable(data, caption = “Male and Female Means and StdDevs of Measurements”)
##Quantiles vs Normal Approximations
Compute the following quantiles for stature, sittingheight, weightkg, BMI for women. Compare under normality using qnorm and then plot estimated vs actual with a 1:1 line using abline(0,1). Rank variables from closest to normally distributed to most different from normal based on plots
prcs <- c(0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99)
plot(quantile(A2F\(stature, prcs), qnorm(prcs, mean = mean(A2F\)stature), sd = sd(A2F$stature))) abline(0,1, col = “red”)
plot(quantile(A2F\(sittingheight, prcs), qnorm(prcs, mean = mean(A2F\)sittingheight), sd = sd(A2F$sittingheight))) abline(0,1, col = “red”)
plot(quantile(A2F\(weightkg, prcs), qnorm(prcs, mean = mean(A2F\)weightkg), sd = sd(A2F$weightkg))) abline(0,1, col = “red”)
plot(quantile(A2F\(BMI, prcs), qnorm(prcs, mean = mean(A2F\)BMI), sd = sd(A2F$BMI))) abline(0,1, col =“red”)
##Bivariate Accomodation
Plot knee height sitting vs buttock knee length for men. Add lines for 95th percentile of each variable. What percentage of men in this dataset have both knee height and buttock knee length less than the respective 95th percentiles? Repeat analysis for buttock popliteal length and hip breadth sitting for women but assess number of women who have buttock popliteal length > than the 5th percentile and hip breadth sitting < than the 95th percentile
x95 <- quantile(A2M\(kneeheightsitting, 0.95) y95 <- quantile(A2M\)buttockkneelength, 0.95) x295 <- quantile(A2F\(buttockpopliteallength, 0.05) y295 <- quantile(A2F\)hipbreadthsitting, 0.95)
plot(A2M\(kneeheightsitting, A2M\)buttockkneelength) abline(v = x95, col = “red”) abline(h = y95, col = “red”)
sum((A2M\(kneeheightsitting < x95) & (A2M\)buttockkneelength < y95)) / nrow(A2M)
plot(A2F\(buttockpopliteallength, A2F\)hipbreadthsitting) abline(v = x295, col = “red”) abline(h = y295, col = “red”)
sum((A2F\(buttockpopliteallength > x295) & (A2F\)hipbreadthsitting < y295)) / nrow(A2F)
##Male Female Differences by Variable On which of the dimensions is the difference between men and women the largest as a fraction of the mean of the male and female standard deviations? Smallest?
num_cols <- intersect(names(A2F)[sapply(A2F, is.numeric)], names(A2M)[sapply(A2M, is.numeric)])
smd <- function(x_male, x_female) { mean_diff <- abs(mean(x_male, na.rm = TRUE) - mean(x_female, na.rm = TRUE)) pooled_sd <- (sd(x_male, na.rm = TRUE) + sd(x_female, na.rm = TRUE)) / 2 return(mean_diff / pooled_sd)}
results <- sapply(num_cols, function(col) {smd(A2M[[col]], A2F[[col]])})
results_df <- data.frame(dimension = names(results), score = results)
results_df <- results_df[order(-results_df$score), ]
head(results_df, 1)
tail(results_df, 1)