Quantify confidence on a difference between two groups

Question

I am looking to quantify certainty/confidence on a difference between two groups (see toy dataset):

# Create dataframe
df<-data.frame(
    Age=c(40,40,40,40,41,41,41,41),
    Strength=c(50,49,46,46,40,39,39,37)
    )

# Summarise 
mean40<-mean(subset(df,Age==40)$Strength)
sd40<-sd(subset(df,Age==40)$Strength)
sem40<-plotrix::std.error(subset(df,Age==40)$Strength)
CI40<-Rmisc::CI(subset(df,Age==40)$Strength)

mean41<-mean(subset(df,Age==41)$Strength)
sd41<-sd(subset(df,Age==41)$Strength)
sem41<-plotrix::std.error(subset(df,Age==41)$Strength)
CI41<-Rmisc::CI(subset(df,Age==41)$Strength)

# Calculate difference between 40 and 41 yrs
diff<-mean41-mean40

I know the mean, standard deviation, standard error of the mean, and 95% CI for 40 y/o and 41 y/o separately. I also know the difference between the two groups (in this case, 9). Can I calculate the error associated with the difference (e.g. a 95% CI, or something similar) for the difference. I want to quantify the certainty regarding the "difference".

Any help would be greatly appreciated. Thank you.

Answer 1

For a table of means, and then a test of their differences, I'd go with expss and then a linear model (the latter useful since age is really a continuous variable):

library(expss)
expss::expss_output_viewer() # send output to Viewer
df %>% tab_cells(Strength) %>% 
  tab_cols(Age) %>% 
  tab_stat_mean_sd_n() %>%
  tab_pivot()

summary(lm(Strength~Age,data=df))

Don't forget to consider the effect size, as well. Which is examined after establishing statistical significance.