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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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44
votes
4answers
13k views

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 ...
39
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8answers
19k views

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 ...
13
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2answers
998 views

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 ...
11
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1answer
475 views

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| &...
9
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2answers
409 views

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 ...
9
votes
3answers
3k views

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 ...
8
votes
1answer
917 views

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 ...
7
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2answers
2k views

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 ...
6
votes
3answers
753 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 ...
6
votes
1answer
912 views

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 ...
6
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1answer
1k views

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 ...
6
votes
1answer
200 views

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 ...
5
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1answer
179 views

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 ...
4
votes
1answer
724 views

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 ...
3
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0answers
246 views

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 ...
3
votes
0answers
626 views

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 ...
2
votes
1answer
668 views

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) ...
2
votes
0answers
124 views

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 ...
2
votes
0answers
285 views

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 ...
2
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0answers
140 views

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 $m=\left[k(k-1)\right]/2$ ...
1
vote
1answer
823 views

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 ...
1
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0answers
322 views

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: ...
0
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3answers
772 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 ...
0
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0answers
167 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 ...
-2
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2answers
686 views