Adjusted mean for an ANCOVA

ANCOVAadjmean

# My attempt to make Cohen's example into a formula (the correct calculations for the example in the textbook start on line 40)

adjmeans <- function(IV, DV, CV, data){
  ano1 <- lm(formula = getElement(object = data, name = DV) ~ getElement(object = data, name = CV))
  ano2 <- lm(formula = getElement(object = data, name = IV) ~ getElement(object = data, name = CV))
  
  SSYer <- anova(ano1)$"Sum Sq"[2]
  SSXer <- anova(ano2)$"Sum Sq"[2]
  
  scpw <- sum(sapply(X = levels(data$CV), FUN = function(condition){
    n <- length(data[data$condition == condition, IV]) - 1
    sdx <- sd(data[data$condition == condition, IV])
    sdy <- sd(data[data$condition == condition, DV])
    r <- cor(data[data$condition == condition, DV], data[data$condition == condition, IV])
    n * sdx * sdy * r})) 
  
  r_pooled <- scpw / sqrt(SSXer * SSYer)
  
  bp <- r_pooled * sqrt(SSYer / SSXer)
  
  # adusted means
  return(sapply(X = levels(data$CV), FUN = function(condition){mean(data[data$condition == condition, DV]) - bp * (mean(data[data$condition == condition, "initial"]) - mean(data$initial))}))
} # made to work with a model with a linear model; 1 continuous outcome, 1 continuous predictor, 1 categorical predictor (treatment, control variable)
adjmeans(IV = "initial", DV = "final", CV = "condition", data = dat)














# data from p.645 Explaining Psychological Statistics
dat <- data.frame(initial = c(1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 1, 2, 2, 3, 3, 4, 5, 6, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7), final = c(3, 4, 3, 5, 7, 7, 6, 9, 6, 8, 2, 6, 5, 8, 6, 9, 8, 6, 2, 4, 3, 5, 3, 7, 5, 7, 4, 9, 8, 6), condition = factor(x = c(rep(x = "psycho", times = 10), rep(x = "behav", times = 8), rep(x = "cont", times = 12)), levels = c("cont", "behav", "psycho")))

# the computations to verify my numbers
ano1 <- lm(formula = final ~ condition, data = dat)
ano2 <- lm(formula = initial ~ condition, data = dat)
anova(ano1)
anova(ano2)

SSYer <- anova(ano1)$"Sum Sq"[2]
SSXer <- anova(ano2)$"Sum Sq"[2]
sum(anova(ano)$"Sum Sq") * (1 - cor(dat$initial, dat$final)^2) # SSAtotal p. 646

scpw <- sum(sapply(X = levels(dat$condition), FUN = function(condition, x = "initial", y = "final"){{
  n <- length(dat[dat$condition == condition, x]) - 1
  sdx <- sd(dat[dat$condition == condition, x])
  sdy <- sd(dat[dat$condition == condition, y])
  r <- cor(dat[dat$condition == condition, y], dat[dat$condition == condition, x])
  n * sdx * sdy * r}})) 

r_pooled <- scpw / sqrt(SSXer * SSYer)

bp <- r_pooled * sqrt(SSYer / SSXer)

sapply(X = levels(dat$condition), FUN = function(condition){mean(dat[dat$condition == condition, "final"]) - bp * (mean(dat[dat$condition == condition, "initial"]) - mean(dat$initial))})

Update1:

Adjusted Means

adjmeans <- function(IV, DV, CV, data){

compute the sums of squares for the covariate and the outcome variable

ano1 <- lm(formula = getElement(object = data, name = DV) ~ getElement(object = data, name = CV))
ano2 <- lm(formula = getElement(object = data, name = IV) ~ getElement(object = data, name = CV))
SSYer <- anova(ano1)$"Sum Sq"[2]
SSXer <- anova(ano2)$"Sum Sq"[2]

compute the "Within-Group Sum of Cross Products"

scpw <- sum(sapply(X = levels(getElement(object = data, name = CV)), FUN = function(con, x = IV, y = DV){
n <- length(data[getElement(object = data, name = CV) == con, x]) - 1
sdx <- sd(data[getElement(object = data, name = CV) == con, x])
sdy <- sd(data[getElement(object = data, name = CV) == con, y])
r <- cor(data[getElement(object = data, name = CV) == con, y], data[getElement(object = data, name = CV) == con, x])
n * sdx * sdy * r}))

pooled r

r_pooled <- scpw / sqrt(SSXer * SSYer)

pooled within-group regression slope

bp <- r_pooled * sqrt(SSYer / SSXer)

adusted means

adjmeans <- sapply(X = levels(getElement(object = data, name = CV)), FUN = function(condition){mean(data[getElement(object = data, name = CV) == condition, DV]) - bp * (mean(data[getElement(object = data, name = CV) == condition, CV]) - mean(getElement(object = data, name = IV)))})
return(adjmeans)
} # made to work with a model with a linear model; 1 continuous outcome, 1 continuous predictor, 1 categorical predictor (treatment, control variable)