This is a link to a graphical user interface (gui) that lets you do a sensitivity analysis in an observational study about smoking and periodontal disease without running statistical software.  It runs R in the background, but you will see the R code only if you ask to see it by clicking a button.  At the bottom of the page, there is text, labeled "Results of the sensitivity analysis at the specified Gamma," that interprets the sensitivity analysis in English.  As you change the sensitivity parameter, Gamma, this text interpretation will change.  

You can vary several items to see how they affect the interpretation of the sensitivity analysis.  There are two outcomes, upper teeth and lower teeth, and they turn out to be different.  You can use the mean or design various versions of Huber's M-statistics to learn which ones are best in an observational study (Rosenbaum 2014).  You can split Gamma into two parameters to reinterpret the sensitivity analysis -- this is a so-called amplification (Rosenbaum and Silber 2019).  You can ask to see the R code and how it changes as you click the buttons; then, you can go to R or rstudio and the same R code applied to your own data.

Copy and paste the web link into a browser.  Read the text on the web page, and then click buttons and see what happens.  This gui is a so-called "Shiny" app; see Chapter 19 Shiny Documents in the book by Xie, Allaire and Grolemund (2019) in the references.   

Or copy and paste the link:    https://rosenbap.shinyapps.io/learnsenShiny/

Here is a sample of the R code and interpretation that you might see if you request it.

# Here is the R code:

library(sensitivitymult)

data(teeth)

attach(teeth)

senm(either4up,smoker,mset,gamma=2,trim=4,inner=0.5)

senmCI(either4up,smoker,mset,gamma=2,trim=4,inner=0.5,twosided=FALSE)

amplify(2,3)

Test of the null hypothesis of no treatment effect:

Using the M-statistic with trim = 4 and inner = 0.5 at Gamma=2, the upper bound on the one-sided P-value is 0.0156023.

One-sided 95 percent confidence interval for a constant effect, tau:

Using the M-statistic with trim = 4 and inner = 0.5 at Gamma=2, the one-sided 95% confidence interval is tau>= 0.46.

Amplification: In a matched pair, Gamma=2 is equivalent to an unobserved covariate that increases the odds of treatment by a factor of Lambda=3 and increases the odds of a positive pair difference in outcomes by a factor of Delta=5.