This app adds a user interface to the TOSTER package, demonstrating the usefulness of Two One-Sided Test (TOST) equivalence testing. In the current version only raw SESOI (smallest effect size of interest) input is implemented.
The TOSTER R package can be installed from CRAN using install.packages (TOSTER). Detailed example vignettes are available from: https://cran.rstudio.com/web/packages/TOSTER/vignettes/IntroductionToTOSTER.html
You can copy the app file app.R to your system and run it locally. Alternatively, you can launch it from GitHub without installation.
In both cases, the following packages need to be installed in order for the app to run:
shiny from https://cran.r-project.org/web/packages/shiny/index.html
TOSTER from https://cran.r-project.org/web/packages/TOSTER/index.html
MASS from https://cran.r-project.org/web/packages/MASS/index.html
tidyverse from https://cran.r-project.org/web/packages/tidyverse/index.html
You can launch the app by giving the name of its directory to the function runApp. If the app is in a folder of the working directory called "Shiny_TOSTER", run it with the following code:
library(shiny)
runApp("Shiny_TOSTER")
Alternatively, you can open the file app.R in the RStudio editor and click the "Run App" button at the top of the editor.
From the R console run the following commands to launch the App:
# Assuming 'shiny' package and all other prerequisites are already installed
library(shiny)
#name of the app dir and username
runGitHub("Shiny_TOSTER", "ontogenerator")
Your browser should launch the shiny app directly on your machine.
The interface allows the user to play around with the inputs and observe how the values change the output of the TOST tests. An additional feature is to let the inputs represent the hypothesized true parameters of interest, e.g. what the experimenter expects the results to look like and bootstrap from those values. A given Number of iterations is performed, resampling from the corresponding distributions.
This feature is activated by first selecting the radiobutton simulated, which changes the input and the output view. The simulations are only performed when the button Perform simulations is clicked, in order to avoid constant recalculation when the input is changed.
The output is displayed as a stack of all (e.g. 1000) iterations in a "dance of the confidence intervals" style. Both the 95% (for alpha = 0.05) and the 90% confidence intervals are plotted with the same width on top of each other, coded in different colors depending on statistical significance. Non-significant results are plotted in dark gray, significant results from NHST are plotted in orchid, and significant results from TOST are plotted in lime green. Additionally the plot displays the proportion of iterations that yielded all possible outcomes. These outcomes are labeled and color-coded as follows:
| Full name | Label & Color | Outcome of TOST | Outcome of NHST |
|---|---|---|---|
| inconclusive | inc  darkgray |
non-equivalent | non-significant |
| non-equivalent | nonequiv  orchid1 |
non-equivalent | significant |
| strictly equivalent | str_equiv  limegreen |
equivalent | non-significant |
| trivial | triv limegreen |
equivalent | significant |
| non-zero | nonzero orchid1 |
irrelevant | significant |
| equivalent | equiv limegreen |
significant | irrelevant |
The input options for the simulations (when the radiobutton simulated is selected) are in most cases identical to the ones for the standard input (when the radiobutton observed is selected), with the exception of the paired two-sample test and the correlations.
In the paired two-sample test only one standard deviation is given as an input, the standard deviation of a typical group. With repeated measures the observed total variance can be decomposed to the variance between individuals(or groups) and within individuals (or groups). The larger the variance between individuals (or groups), the higher the so-called repeatability is. For example, the repeatability of height in adult people is very high, because a group of people vary in height much more than every individual varies from day to day. The repeatability can be given values between 0 and 1 and corresponds to the proportion of the between-individual (or group) variance from the total variance.
The correlation test is simulated as follows: first a virtual population of a certain size (Total number of individuals in the virtual population) is chosen. Then two random vectors are generated, so that they have the chosen correlation (actually a value very close to it, because of the algorithm). Then the desired number of paired observations are sampled at random, and the correlations of these samples are calculated and taken as input for the statistical tests in each iteration.
Copyright (C) 2022 Vladislav Nachev
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.