# Questions tagged [tost]

TOST, an acronym for Two One-Sided Tests, is a straightforward way of constructing a test of the "negativist" null hypothesis that two population statistics differ by no more than a small researcher-selected equivalence threshold.

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### Is there a simple equivalence test version of the Kolmogorov–Smirnov test?

Has two one-sided tests for equivalence (TOST) been framed for the Kolmogorov–Smirnov test to test the negativist null hypothesis that two distributions differ by at least some researcher-specified ...
1answer
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### Equivalence test for non-normal distribution: how to determine equivalence bounds?

I am trying to conduct a Mann-Whitney equivalence test (as described in Wellek's book Testing Statistical Hypotheses of Equivalence and Noninferiority) with the following code in R: ...
0answers
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### Sample size determination for TOST

I am currently working on analyzing the behavior of two algorithms on the same input data and am trying to establish whether they are reasonably equivalent to each other within specified bounds to ...
1answer
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### Sample size for mean comparison

Suppose that I have a new machine so I want to compare it to the older one. I would like to conduct a mean comparison of a parameter, to verify if these 2 machines produce the same results or not. How ...
1answer
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### Equivalence testing and difference-in-difference measures

I have some data from a recent experiment that requires slightly more sophisticated testing than I'm used to. Any advice would be most appreciated! The setup: There are control (C) a treatment (T) ...
1answer
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### TOST and its two null hypotheses

Background I have a device which is used to size potatoes. I want to use statistics to assess how accurate this device is. To that end, I've collected two data sets, $X$ and $Y$, where $X$ is the set ...
0answers
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### Possible multiplicity issues in equivalence testing

I'm currently looking to compare 3 groups, trying to prove equivalence between them. For this, 5 specific parameters are measured for each group, and a pairwise comparison for each parameter among the ...
0answers
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### Combined equivalence and difference testing

I have some data with two conditions, and a pre- and post-measure for each condition. I would like to know 2 things: That there was a significant increase from pre to post in both conditions, That ...
3answers
882 views

### What is the best method of reporting multiple tests of equivalence?

I am doing a study which will involve multiple tests of equivalence. Is there a standard table for reporting such results? EDIT with more detail: It is a longitudinal study with 5 time points. Our ...
1answer
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### In the equivalence test (TOST procedure), why is the null hypothesis the presence of a real effect?

In the test for equivalence (or non-inferiority / non-superiority) we define a "minimal effect size" $d$, and test that the measured effect is not larger that $d$ $$X_1 \sim PDF1$$ $$X_2 \sim PDF2$$...
1answer
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### Intuitive explanation of differences between TOST and UMP tests for equivalence

Hypothesis tests for equivalence differ from the more common hypothesis tests for difference. In tests for difference, the null hypothesis is some form of "separate quantities are the same", and ...
1answer
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### equivalence test - why isn't it more common?

Often in frequentist hypothesis testing, the null hypothesis is of the form: $H_0: \theta = 0$ I've seen many posts about how the p-value when doing tests against this null hypothesis is just a ...
1answer
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### Equivalence test for binominal data

I want to apply an equivalence test on my sample to infer whether they are equivalent or not. Since my data are bionominal [0,1] I don’t know whether the TOST procedure (tost() in R) can handle my ...
0answers
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### TOST equivalence test in excel

I had a prof once refer to doing science in excel as doing watch repair with oven mitts. Nevertheless, I'm trying... I'm trying to do a TOST test using excel. I'm basing the equivalence of variances ...
0answers
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### What ANOVA non-superiority test corresponds to an omnibus set of TOST equivalence tests?

I am not sure if such a beast exists, but is there some non-superiority test for a oneway ANOVA of $k$ groups, probably based on a $\Delta^{2}$ equivalence threshold, for $m=\left[k(k-1)\right]/2$ ...
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### Understanding equivalence testing. Why there are two hypothesis?

I have to two groups and I would like to test that difference between means of these two groups is at least 0.02. I am using TOSTER R package. Here are details: ...
3answers
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### Equivalence tests for non-normal data?

I have some data that I can't necessarily assume to be drawn from normal distributions, and I would like to conduct tests of equivalence between groups. For normal data, there are techniques like TOST ...
0answers
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### How do I estimate sample size for a single-sample equivalence test?

From literature I have a theoretically proposed value for human performance in a particular task. I want to experimentally measure performance in this task across a sample of humans and test whether ...
0answers
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### Kolmogorov–Smirnov TOST based on confidence bands

I am trying to setup a two one-sided test (TOST) version of the Kolmogorov–Smirnov test (KS) based on confidence bands. I would like to know if there is anything wrong with my approach. Similar to ...
0answers
299 views

### Equivalence testing for repeated measures with two independent variables

I have a repeated measures experiment design with two independent variables ('condition' with 2 levels and 'repeat' with 10 levels) and one dependent variable ('performance'). I'd like to know whether ...
4answers
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### Why do statisticians say a non-significant result means “you can't reject the null” as opposed to accepting the null hypothesis?

Traditional statistical tests, like the two sample t-test, focus on trying to eliminate the hypothesis that there is no difference between a function of two independent samples. Then, we choose a ...
2answers
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### R - what is magnitude of region of similarity (epsilon) when using tost() from equivalence package

I have two vectors: ...
3answers
953 views

### Paired two one-sided t-tests (TOST) with unequal sample sizes

I have data from two populations (let's call them "before" and "after"), collected in a paired fashion. That is, I take a measurement under one set of conditions before, and then I can take multiple ...
1answer
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### TOST for equivalence test

Let's say that we are measuring the tracking position error of two controllers and we want to know if both controllers are similar (we already perform a "differences" test but we are requested to ...
2answers
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### Equivalence testing - tost method - why CI of 90%?

In testing for equivalence via the two one-sided test approach with confidence intervals, a (1–2α) × 100% confidence interval is calculated to check for equivalence. I assume this is because you ...
2answers
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### Can we accept the null in noninferiority tests?

In a usual t-test of means, using the usual hypothesis testing methods, we either reject the null or fail to reject the null but we never accept the null. One reason for this is that if we got more ...
8answers
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### How to test hypothesis of no group differences?

Imagine you have a study with two groups (e.g., males and females) looking at a numeric dependent variable (e.g., intelligence test scores) and you have the hypothesis that there are no group ...
0answers
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### Calculating epsilon for two one sided t-tests

I am using the equivalence::tost method in R. It takes a parameter epsilon, but I am unsure of how to calculate this when I require a test for non-zero Difference%. Currently, I do this by using the ...
1answer
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### Can you use the Kolmogorov-Smirnov test to directly test for equivalence of two distributions?

There has been talk on other questions of how one might use the Two One-Sided Tests (TOST) approach for the Kolmogorov-Smirnov (KS) test, but I was wondering whether it was possible to directly use ...
1answer
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### Point hypothesis and equivalence hypothesis at once

Sometimes researchers (especially in collaborations) have two opposite but sound theories: There is a difference between two groups or there is only negligible difference. Now they ask their ...
1answer
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### Use of Wilcoxon test for non-normal data akin to Two One Sided T-test

I'm analysing paired data for equivalency and it's not normally distributed, i.e., the difference of the paired result is not normally distributed due to, amongst other things, outliers. If it were ...
1answer
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### Null hypothesis of equivalence

Suppose $X_1, X_2, \, ... \, , X_n$ are a simple random sample from a Normal$(\mu,\sigma^2)$ distribution. I'm interested in doing the following hypothesis test:  H_0: | \mu| \le c \\ H_1: |\mu| &...