Example of two one-sided t tests (to test equivalence)

tost_ex.R

# Load libraries
library("tidyverse")
library("TOSTER")

# Set seed for reproducibility
set.seed(10)

# Working memory means for 3 groups
wm_n   <- rnorm(mean = 8.67, sd = 1.15, n = 12)
wm_nin <- rnorm(mean = 9.04, sd = 2.11, n = 26)
wm_m   <- rnorm(mean = 9.16, sd = 1.93, n = 25)

# Create DF
my_df <- c(
  rep("n", 12), 
  rep("nin", 26), 
  rep("m", 25)) %>% 
  as_data_frame(.) %>% 
  rename(., group = value) %>% 
  bind_cols(., 
  wm = c(rnorm(mean = 8.67, sd = 1.15, n = 12), # in
         rnorm(mean = 9.04, sd = 2.11, n = 26), # nin
         rnorm(mean = 9.16, sd = 1.93, n = 25)  # m
     ), 
  dele = c(rnorm(mean = 49.17, sd = 4.43, n = 12), # in
           rnorm(mean = 46.27, sd = 4.09, n = 26), # nin
           rep(0, 25)                              # m
  )
)

# Check means
my_df %>% 
  group_by(., group) %>% 
  summarize(., wm_mean = mean(wm), 
               wm_sd = sd(wm), 
               dele_mean = mean(dele), 
               dele_sd = sd(dele), 
               n = n())


# Bartlet test of homogeneity of variance
bartlett.test(wm ~ group, data = my_df)
# Bartlett's K-squared = 4.778, df = 2, p-value = 0.09172



# wm toast m vs nin
TOSTtwo(m1 = 9.16, sd1 = 1.93, n1 = 25, # m
        m2 = 9.04, sd2 = 2.11, n2 = 25, # nin
        low_eqbound_d = -0.4, 
        high_eqbound_d = 0.4, 
        alpha = 0.05)

# wm toast m vs in
TOSTtwo(m1 = 9.16, sd1 = 1.93, n1 = 25, # m
        m2 = 8.67, sd2 = 1.15, n2 = 12, # n
        low_eqbound_d = -0.3, 
        high_eqbound_d = 0.3, 
        alpha = 0.05)

# wm toast in vs nin
TOSTtwo(m1 = 8.67, sd1 = 1.15, n1 = 12, # n
        m2 = 9.04, sd2 = 2.11, n2 = 25, # nin
        low_eqbound_d = -0.3, 
        high_eqbound_d = 0.3, 
        alpha = 0.05)


# dele toast in vs nin
TOSTtwo(m1 = 49.17, sd1 = 4.43, n1 = 12, # n
        m2 = 46.27, sd2 = 4.09, n2 = 26, # nin
        low_eqbound_d = -0.3, 
        high_eqbound_d = 0.3, 
        alpha = 0.05)


# Furthermore, the TOST procedure suggested that the observed effects were 
# statistically not different from zero for all pairwise comparisons for 
# working memory 
# (M vs. N: t(47.62) = -1.204, p = 0.117; 
# M vs. NIN: t(33.11) = 0.0263, p = 0.510; 
# N vs. NIN: t(34.26) = 0.260, p = 0.398) 
# and for L2 proficiency 
# (N vs. NIN: t(20) = 1.074, p = 0.852)






# TOST for lexical frequency
lex_df <- structure(list(target = c("corta", "firma", "grita", "lleva", 
"llena", "manda", "graba", "gasta", "bebe", "come", "busca", 
"llama", "besa", "mira", "vive", "compra", "vende", "lava", "fuma", 
"pinta", "toca", "limpia", "cambia", "corto", "firmo", "grito", 
"llevo", "lleno", "mando", "grabo", "gasto", "bebio", "comio", 
"busco", "llamo", "beso", "miro", "vivio", "compro", "vendio", 
"lavo", "fumo", "pinto", "toco", "limpio", "cambio"), freq = c(203, 
174, 77, 765, 371, 110, 10, 41, 50, 87, 468, 631, 28, 547, 417, 
197, 72, 45, 38, 87, 125, 92, 128, 62, 47, 182, 402, 61, 89, 
9, 14, 53, 23, 90, 240, 62, 486, 105, 72, 23, 10, 12, 17, 105, 
26, 109)), class = c("spec_tbl_df", "tbl_df", "tbl", "data.frame"
), row.names = c(NA, -46L), spec = structure(list(cols = list(
    target = structure(list(), class = c("collector_character", 
    "collector")), freq = structure(list(), class = c("collector_double", 
    "collector"))), default = structure(list(), class = c("collector_guess", 
"collector")), skip = 1), class = "col_spec"))

coda_words <- c("corta", "firma", "manda", "gasta", "busca", "compra", 
                "vende", "pinta", "limpia", "cambia", "corto", "firmo", 
                "mando", "gasto", "busco", "compro", "vendio", "pinto", 
                "limpio", "cambio")

lex_df <- lex_df %>% 
  mutate(., coda = if_else(target %in% coda_words, 1, 0))



bartlett.test(freq ~ coda, data = lex_df)



lex_df %>% 
  group_by(., coda) %>% 
  summarize(., freq_mean = mean(freq), 
               freq_sd = sd(freq), 
               n = n())

# dele toast in vs nin
TOSTtwo(m1 = 190, sd1 = 220, n1 = 26, # n
        m2 = 106, sd2 = 102, n2 = 20, # nin
        low_eqbound_d = -0.3, 
        high_eqbound_d = 0.3, 
        alpha = 0.05)

Nicely explained :-) I think the first TOStwo has a small mistake in regards to the Cohen's D,

TOSTtwo(m1 = 9.16, sd1 = 1.93, n1 = 25, # m
        m2 = 9.04, sd2 = 2.11, n2 = 25, # nin
        low_eqbound_d = -0.4, 
        high_eqbound_d = 0.4, 
        alpha = 0.05)

should be

TOSTtwo(m1 = 9.16, sd1 = 1.93, n1 = 25, # m
        m2 = 9.04, sd2 = 2.11, n2 = 25, # nin
        low_eqbound_d = -0.3, 
        high_eqbound_d = 0.3, 
        alpha = 0.05)

right?