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

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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) ...
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14 views

Equivalency test for non parametric data?

I would like to perform a TOST test in order to test for equivalency between two independent sets of data. However, the data in both sets is not necessarily normally distributed. Is it ok to ...
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242 views

Is the following statement for variance true?

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 $$Var(cX)=\underbrace{Var[Var[\ldots Var}_{c \text{ times}}[X]\ldots]]?$$
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16 views

How can I test for multivariate equivalence?

I have two sets of data and I want to test to see if they were drawn from the same population/distribution. The data sets have around 200 variables, and I want to be able to take into account the ...
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45 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 ...
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31 views

Can I merge independent samples collected by the same survey?

I have 3 independent data sets collected from the same population using an identical survey design. They are about consumer attitudes toward foreign products, so, 3 countries of origin were used but ...
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110 views

How to formally prove two formulas are asymptotically equivalent?

I have two formulas about variance estimation of linear combination of order statistics given order statistics $X_{1}\leqslant X_{2} \leqslant ...\leqslant X_{n} $ from a random sample of arbitrary ...
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3answers
52 views

How can I test if the frequencies of alleles and genotypes in two populationes are similar?

I want to test if the frequencies of alleles and genotypes in two different populations can be considered similar. I've read a little, and it seems to be that I should use an equivalence test, but I'm ...
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40 views

When using Kolmogorov-Smirnov equivalence test approach, does a large number of samples invalidate the test?

I've been using the Kolmogorov--Smirnov test to test for equivalence between two sets of data. I have around 150 samples in each dataset. Following the process for Two One-Sided Tests in this ...
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14 views

Can Cronbach’s alpha be used to assess the equivalence of two different questionnaires?

I have a very simple quality-of-life (QOL) questionnaire that is much easier to implement than two currently used in practice and a longitudinal data set in which patients were administered all three ...
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212 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 ...
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75 views

What is the R code for a 2 one-sided equivalence log-rank test? [closed]

I am trying to perform an equivalence test (alpha = 0.1, beta = 0.8, equivalence interval = 0.85-1.25) for two samples of survival data. Is there a code in R in the Survival package or any other ...
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213 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 ...
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1answer
78 views

Equivalence testing exam results

For reasons of economy, a college has moved from live lectures to videotaped. They have exam results from the year/years before the change, and the year/years after. They want to be reassured that ...
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3answers
679 views

“Reversed” Shapiro–Wilk

The Sharipo-Wilk test, according to wikipedia, tests the null-hypothesis ($H_0$) "The population is normally distributed". I am looking for a similar normality test with $H_0$ "The population is not ...
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796 views

MANOVA multiple comparisons with equivalence testing

For a MANOVA with $n$ variables, I would like to do pairwise comparisons between $k$ levels for one of the variables. What is the suitable method to adopt for ...
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84 views

How to Correlate Parameter Distributions Across Conditions Over A Subject Population?

I'd like some help trying to understand if the conceptual question I'm asking makes sense, and if so, how I would go about implementing the statistics for it. I designed an experiment with two ...
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90 views

How to compare three groups to one control group without assuming equal variances?

I need to determine if one dependent variable (tensile strength) for each of three new groups is equivalent to that from my original ("control") group. I am not concerned with how the three new groups ...
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78 views

Difficulty with power analysis

I need to estimate sample size for an experiment but I am not very knowledgeable about power analysis. In my experiment, I am asking if a user can notice the two possible states of a system. I ...
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380 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 ...
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27 views

Paired data with independent groups of treatment, how to plan and analyze?

I need your assistance, I am trying to design an experiment, and in order to do so I need to know how the data will be analyzed. The experiment in on rats. Each rat gets some treatment, and a measure ...
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133 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 ...
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546 views

Comparing the mean difference between data measured by different equipment, t-test suitable?

My problem is as follows: I have 2 measuring devices, both using different measuring techniques, each trying to quantify properties of objects passing their measurement area. The devices measure the ...
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103 views

Inverse Differencing and ARIMA Model Equivalence

I've developed a ARIMA model with exogenous variable. Before fitting the model, I made every time series stationary by differencing (each variable had a different order of integration). For ...
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61 views

How can I determine if two features, given a set of data, are the same feature or not?

Thanks in advance for the help. Suppose I have a set of data of the form [feature, rating]. For the sake of argument lets assume feature can be movie A or movie B and rating is a ranked, continuous ...
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223 views

Equivalence testing vs ANOVA post hoc tests

How is statistical equivalence testing different from post hoc tests done after ANOVA?
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1k views

Does statistically insignificant difference of means imply equality of means?

Suppose I have sets A and B of normally distributed data so that: A: mean=250, SD=200, N=25 B: mean=248, SD=200, N=20 Clearly, there is no statistically ...
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437 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 ...
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1k views

Comparing two distributions

I have more than five hundred thousands samples of a continuous variable measured in two groups: a treatment and a control one. I would like to decide whether the measurements follow the same ...
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57 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 $m=\left[k(k-1)\right]/2$ ...
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547 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 ...
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2answers
220 views

Obtaining $p$-values for UMP $t$ tests for equivalence

I am trying to understand the uniformly most powerful (UMP) equivalence tests presented by Welleck (2010) with respect to $p$-values for the tests. In the case of the paired $t$ test example ...
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270 views

Quantile regression estimator formula

I have seen two different representations of the quantile regression estimator which are $$Q(\beta_{q}) = \sum^{n}_{i:y_{i}\geq x'_{i}\beta} q\mid y_i - x'_i \beta_q \mid + \sum^{n}_{i:y_{i}< ...
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Assumption with alternative hypothesis?

I am testing the reproducibility of two drug concentrations between two sites of the same individual. I am assuming response between sites should be similar. To test the significance I created a ...
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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 ...
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306 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 ...
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498 views

How can I compare variables with uneven data sets?

I'm doing a stationary sport in which I use different colored equipment for different weather. I am recording my scores along with the color of the equipment and the weather in which I am using it. I ...
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30 views

Test when and how often 2 time series have similar values

I am monitoring two moving cars and collecting data on their instantaneous speeds three times per second for approximately two hours. I would like to create some kind of hypothesis that will tell me ...
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94 views

How to test (and accept) that a coefficient in a linear regression model equals zero

I understand that in a linear regression model like: $y_i = b_0 + b_1 x_i + \epsilon_i$ I can have a null and an alternative hypothesis: $H_0: b_1 = 0$ and $H_1: b_1 \neq 0$. And then I can ...
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Hypothesis testing for equality of proportions with 3 samples

I have a data set of cell phone customer information data with twocolumns. The first column contains the certain category that an account falls in (either A, B or C) and second column contains is ...
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One-way independent ANOVA where I expect two levels to be very similar and the other to be different. What's the right test?

I'm expecting Groups 1 & 2 to be very similar and Group 3 to be different. I'm using a very large data set and feel that power won't be an issue. Initially I felt that I'd then be expecting a ...
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30 views

Testing for equivalent variation within twins

I am interested in determining if, for a certain type of trait, there is just as much variation between twins as there are between non-related individuals. However, I am having difficulties in ...
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64 views

Making two equal groups from exponentially distributed data

I'm running an experiment where we are taking 1500 of a certain type of product and changing the price of half of them to see if this influences sales. There are 5 categories on which I will be ...
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3answers
475 views

Test if two samples are equal

I have two samples, say sample A and B, and a negative control. I expect that the sample A to be different than the negative control, so I use a t-test to check for that. Then, I expect sample B ...
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385 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| ...
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441 views

Equivalence test for two multivariate normal distributions?

I'm trying to compare two samples from multivariate normal distributions to see if their distributions are equivalent (within a factor of epsilon). The standard version of this test is the energy ...
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32 views

Equivalence tests for STP3 - location of maximum power

Lehmann and Romano show in their Th 3.7.1 (Lehmann and Romano 2005, p81) when a UMP equivalence test $\phi_1$ exists and that it has a power that is maximised at some point $\theta^\star$ inside the ...
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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 ...
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67 views

How to use a meta-analysis to assess the equivalence of two different procedures?

I'm making a comparison of two surgical procedures, and I want to know how I can analyze the data I have for a meta-analysis. The overall surgical procedure is the same, but some authors choose to ...
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2k views

non-parametric two-sample equivalence tests with unequal sample sizes

I would like to compare means/medians of two samples that may be very skewed in size, e.g. 25 points and 1 or 2 points and test them for similarity, rather than difference. I realize that the power ...