A two sample t test fucntion to output p-value from inputs of means and standard error

T Test via summary stats

t.test_SEM <- function(mean1, mean2, SE1, SE2, n1, n2) {
  # Calculate t-statistic
  t_statistic <- (mean1 - mean2) / sqrt(SE1^2 + SE2^2)

  # Calculate degrees of freedom
  df <- ((SE1^2 + SE2^2)^2) / (((SE1^2)^2 / (n1 - 1)) + ((SE2^2)^2 / (n2 - 1)))

  # Calculate p-value
  p_value <- 2 * pt(abs(t_statistic), df = df, lower.tail = FALSE)

  return(p_value)
}

# Example usage:
mean1 <- 5 #means
mean2 <- 7
SE1 <- 0.1 # standard errors
SE2 <- 0.15
n1 <- 10 # number of samples 
n2 <- 12

p_value <- t.test_SEM(mean1, mean2, SE1, SE2, n1, n2)
print(p_value)