# Questions tagged [equivalence]

An equivalence study is designed to test whether one treatment is nearly equal, or 'equivalent' to another.

105 questions
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### optimization based interpretation of Bayes' theorem

I read about one equivalent interpretation of bayes' theorem as follows: $P(\mathcal{M}|x) = \frac{P(x|\mathcal{M})\cdot\pi(\mathcal{M})}{\int P(x|\mathcal{M})\cdot\pi(\mathcal{M}) d\mathcal{M}}$ is ...
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### Comparison between series of two continuous monitor sampling the same parameter

Object: understand if the series collected by two dirrerent continuous samplers on the same sample are equivalent. General description: I have two different continuous monitors, determinating the ...
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### How to determine number of profile in a dataset derivated from repeated measures?

I'm currently working on datasets which have been derivated from repeated measures over time (blood concentrations). Actually the descriptors of these datasets are descripting the shape of the curves (...
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### Measuring equivalence/reliability (ICC and consorts)

For a reliability study I’m administering patient reported outcomes (questionnaires) with 2 modes of administration (on paper and via an electronic device). I’d like to measure equivalence/reliability ...
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### Test for equivalence after sampling into test groups

I want to test the effects of different versions of treatment across multiple test groups of a given population. In order to do that, I want to randomly sample my population into, let's say, 4 groups ...
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### two-sample $T^2$ testing with $n=1$

Assuming I have two populations $X\sim\mathcal{N}(\mu_X,\Sigma)$ and $Y\sim\mathcal{N}(\mu_Y,\Sigma)$ of sizes $n_X,n_Y$, the hypotheses for equivalence of means (each of length $p$, and assuming ...
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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: ...
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### Two sample t-test to show equality of the two means

Given two (numeric) samples I would like to show that there is not a significant difference between the two means $\mu_{1}$ and $\mu_{2}$. If my goal was to show a significant difference I would ...
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### Testing equivalence of two censored distributions

If we observe two censored distributions, where all observations above a cutoff are set at the value of the cutoff, how can we test whether the observable distributions suggest that the two censored ...
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### Equivalence test for binomial data?

I have two binomial (success=1 and failure=0) datasets and intend to apply a statistical test to show whether they are statistically equivalence or not. First dataset (x) includes around 164 data ...
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### Multivariate Test for Mean Equivalence

I am looking for an equivalence test for multivariate means (arbitrary or normally distributed). Any suggestions or hints in the right direction are appreciated.
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### Interpretation of EQUIVNONINF (gofind_t) test

Does anyone know how we can interpret the result of: EQUIVNONINF:gofind_t(alpha,r,s,eps,xv) I run the following code on this contingency table to find whether ...
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### Multinomial equivalence test?

I was wondering if there is any statistical equivalence test (in r or python) for multinomial data "a contingency table (4x4)" to know whether the observed and the expected values are equivalence?
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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 ...
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### Definition of stable distribution

In some places, I find the following definition of stable distribution: A distribution is said to be stable if a linear combination of two independent random variables with this distribution has ...
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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 ...
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### Mean Equivalence Test for different and arbitrary distributions

Is there any statistical hypothesis test with which I can test for the equivalence of the means of two arbitrary and different distributions?
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### A confirmation about elastic-net and lasso

I would like to confirm numerically that elastic-net and lasso are equivalent under a transformation on the data set using glmnet package in ...
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### Equivalence testing with p-values

I have two datasets and I want to determine whether they are statistically equivalent. Can I use a hypothesis test, obtain a p-value, and say that if p > 0.05, then the two datasets are ...
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### Direct MLE vs Estimating a parameter and then doing MLE

I'm attempting to solve a channel estimation problem for a wireless communications system with equiprobable discrete transmitter inputs $x \in \{+1,-1\}$ and receiver output $y \in \mathbb{R}$. The ...
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### 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 ...
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### Why doesn't the TOST equivalence testing procedure use non-central $t$ distribution to determine the $p$ value?

I'm looking at Lakens' (2017) primer and he tests the hypothesis that there is a difference between two groups $X_1$and $X_2$of magnitude $\Delta=E[X_1]-E[X_2] \neq0$ by subtracting $\Delta$ from the ...
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### A/B testing parity (A=B)

I can't find any information on how to run an A/B test that shows that the new implementation B is likely at least as good as A. My metric is visitor conversion so I could use a test of proportions ...
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### Is there a less arbitrary way define the margin in non-inferiority and/or equivalence trials?

In a typical equivalence trial, the researcher defines some threshold below which the difference between two means is not considered practically meaningful. In a non-inferiority trial, the same kind ...
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### When we compare groups on control variables should we be using tests of equivalence?

In many papers that consider treatments and outcomes, I see tables (usually "table 1") of what might be called nuisance variables (often demographics, sometimes medical conditions) with tests of ...
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### Regarding equivalence testing: what does this passage from the BEST method article mean?

The lab I work in uses equivalence. When we get a significant result from a two one-sided test, we conclude that true difference between mu1 and mu2 is likely inside the specified margin, which is ...
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### A test for similarity of 2 samples?

I have two samples - one is predicted values and one is actual values. Paired samples t-test suggested that there are no differences between these two samples. Because I remember from stats courses ...
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### Alternative to Chi-squared test to check if categorical distribution in two sets are the same

I have expected frequencies in each category as shown below: So my initial data: category - and number of observation of it. There are too many observations, this why: As the sample size grows ...
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### Question about group equivalence between treatment and control groups

I was wondering if there are there situations in research wherein equivalence between the treatment and control groups is dependent on time... for instance could there be situations wherein the ...
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### Comparing Non-Converged Results of Monte-Carlo Integration

I would like to know which would be the "best" way to compare the results of two different Monte Carlo integration schemes at a non-converged state, and check if they actually compute (converge to) ...
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### Is there such thing as a reverse T-Test?

My understanding of the T-Test is that it is a test for checking if two samples are different enough to be considered from different distributions. In the test the default position is that they are ...
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### Kruskal-Wallis Test for H0: ranks differ between groups and H1: ranks do not differ

The traditional Kruskal-Wallis Test tests null hypothesis $H_A$: ranks do not differ between groups against the alternative hypothesis $H_B$ in which the ranks differ between groups. However, what if ...
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### measurementInvarianceCat() - procedure and interpretation - lavaan

I have identified that sequentially constraining my models I have obtained significant p-value for each. ...
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### lavaan - measurement Invariance - partial metric model

I have used the measurementInvarianceCat() function to conduct Measurement Invariance Multigroup Confirmatory Factor Analyses (MGCFA). The output is the following: ...
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### Significant difference one sample T-test fits with my hypotheses?

My hypotheses are as following: Energy intake H0= the mean energy intake is between 90-110% of the calculated requirement. H1= the mean energy intake is not between 90-110% of the calculated ...
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### Baseline Equivalency & Validity of Exploratory Analysis

In a non-random control group study of teachers, I find that treatment and control groups have rather unequal baseline scores (of their self-efficacy). Despite this, there are interesting interactions ...
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### Method for proving no difference in a set of paired samples

I'm trying to analyze a set of 15 paired samples. The elements of each pair are results of a measurement that produces a scalar value. The first measurement of the pair was done in presence of some ...
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### Exact meaning of equivalence in distribution

Consider the real-valued random variables $X,Y,Z,W$ all defined on the same probability space. Let $Y\equiv f(Z,W)$ for some measurable function $f$. Suppose I am told that "$X$ is equivalent in ...
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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 ...
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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) ...
I know: Let be $X$ a random variable and $c\in\mathbb{R}$. Then is $$Var(cX)=c^2Var(X).$$ But is it true that $$Var(cX)=\underbrace{Var[Var[\ldots Var}_{c \text{ times}}[X]\ldots]]?$$