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

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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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1answer
66 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
54 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
526 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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1answer
197 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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1answer
36 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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71 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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1answer
59 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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1answer
144 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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25 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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1answer
120 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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3answers
334 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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1answer
66 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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1answer
47 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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1answer
139 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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1answer
752 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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2answers
270 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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1answer
691 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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44 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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1answer
361 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
185 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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1answer
186 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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43 views

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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1answer
196 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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1answer
335 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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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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2answers
86 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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1answer
2k views

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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0answers
84 views

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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26 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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56 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
307 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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348 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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2answers
300 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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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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677 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 ...
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54 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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3answers
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 ...
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1answer
322 views

equivalence testing for a chi-squared test

I'm familiar with the concept of equivalence testing for testing whether two means are the same Is there an equivalent equivalence test as the counterpart to the chi-squared test for contingency ...
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2answers
264 views

What does statistical power mean when we are interested in the probability of correctly not rejecting the null hypothesis?

It seems that statisticians are usually only interested in statistical power. In other words, they are interested in the probability of correctly rejecting the null hypothesis. What if we are ...
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276 views

Restricted Boltzmann Machines and Markov Networks: relationship in inference?

I am wondering if there is some equivalence between retricted Boltzmann machines and pairwise Markov networks in terms of MAP inference. More specifically, let $y \in \{0,1\}^m$ be the ...
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39 views

How to test hypothesis of no group differences with repeated measures and determine the sample size?

I want to do a power analysis for a equivalence design but with repeated measures. Does anyone have a suggestion on how to proceed? Also, I want some suggestion on testing the difference of the means ...
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312 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 ...
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241 views

Confidence interval for the biggest difference between means

I have a number of samples $X_1,\ldots,X_n $ from Gaussian distributions centered at $\mu_1,\ldots,\mu_n $ respectively. I need to construct a confidence interval for the biggest difference between ...
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2answers
2k views

Test to prove two means do not have a difference

I have a population that I measure a value from once a day. I then made a change, and continued to measure that same value from the same population. What test could I use to prove that my change did ...
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7answers
6k views

Is it possible to prove a null hypothesis?

As the question states - Is it possible to prove the null hypothesis? From my (limited) understanding of hypothesis, the answer is no but I can't come up with a rigorous explanation for it. Does the ...
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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 ...
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1answer
119 views

Best method for comparing multiple ranging measures

I've been asked to give some advice for some clinicians who are comparing two different methods of blood pressure measurement. I suggested to them that we should proceed with a two-one-sided-test ...