t-test_each-_row_by_mean_sd.R

df <- data.frame(
  ctrl1 = c(5.2, 6.1, 4.8, 5.5, 6.3),
  ctrl2 = c(4.9, 6.5, 5.0, 5.3, 6.1),
  ctrl3 = c(5.0, 6.0, 5.2, 5.7, 6.4),
  trt1  = c(5.5, 6.2, 5.3, 5.9, 6.7),
  trt2  = c(5.4, 6.3, 5.4, 6.0, 6.5),
  trt3  = c(5.6, 6.4, 5.5, 6.1, 6.6)
)
rownames(df) <- paste0("Row", 1:5)
print(df)

##      ctrl1 ctrl2 ctrl3 trt1 trt2 trt3
## Row1   5.2   4.9   5.0  5.5  5.4  5.6
## Row2   6.1   6.5   6.0  6.2  6.3  6.4
## Row3   4.8   5.0   5.2  5.3  5.4  5.5
## Row4   5.5   5.3   5.7  5.9  6.0  6.1
## Row5   6.3   6.1   6.4  6.7  6.5  6.6

df$ctrl_mean <- apply(df[,1:3], 1, mean)
df$ctrl_sd   <- apply(df[,1:3], 1, sd)

df$trt_mean  <- apply(df[,4:6], 1, mean)
df$trt_sd    <- apply(df[,4:6], 1, sd)
#######################
n1 <- n2 <- 3
t_test_from_summary <- function(mean1, sd1, n1, mean2, sd2, n2) {
  se_diff <- sqrt((sd1^2)/n1 + (sd2^2)/n2)
  t_stat <- (mean1 - mean2) / se_diff
  dfree <- ((sd1^2 / n1 + sd2^2 / n2)^2) /
    (((sd1^2 / n1)^2) / (n1 - 1) + ((sd2^2 / n2)^2) / (n2 - 1))
  p_value <- 2 * (1 - pt(abs(t_stat), df = dfree))
  return(p_value)
}

p_values <- mapply(
  function(mean1, sd1, mean2, sd2) {
    t_test_from_summary(mean1, sd1, n1, mean2, sd2, n2)
  },
  mean1 = df$ctrl_mean,
  sd1   = df$ctrl_sd,
  mean2 = df$trt_mean,
  sd2   = df$trt_sd
)

p_values 

## [1] 0.01590216 0.59033182 0.05478677 0.03156223 0.04191452

p_values2 <- apply(df, 1, function(x) {
  t.test(x[1:3], x[4:6])$p.value
})
p_values2

##       Row1       Row2       Row3       Row4       Row5 
## 0.01590216 0.59033182 0.05478677 0.03156223 0.04191452

df$p_values <- p_values2
df

##      ctrl1 ctrl2 ctrl3 trt1 trt2 trt3 ctrl_mean   ctrl_sd trt_mean trt_sd
## Row1   5.2   4.9   5.0  5.5  5.4  5.6  5.033333 0.1527525      5.5    0.1
## Row2   6.1   6.5   6.0  6.2  6.3  6.4  6.200000 0.2645751      6.3    0.1
## Row3   4.8   5.0   5.2  5.3  5.4  5.5  5.000000 0.2000000      5.4    0.1
## Row4   5.5   5.3   5.7  5.9  6.0  6.1  5.500000 0.2000000      6.0    0.1
## Row5   6.3   6.1   6.4  6.7  6.5  6.6  6.266667 0.1527525      6.6    0.1
##        p_values
## Row1 0.01590216
## Row2 0.59033182
## Row3 0.05478677
## Row4 0.03156223
## Row5 0.04191452