# Tagged Questions

Is a property of a hypothesis testing method: the probability of rejecting the null hypothesis given that it is false, i.e. the probability of not making a type II error. The power of a test depends on sample size, effect size, and the significance ($\alpha$) level of the test.

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### How do I calculate sample size and What is the is the meaning of power in a cross-sectional study?

Here is an example: Previous research reported that the prevalence of HIV testing among gays is 19.2% . Sample size required to detect this percentage with 95% confidence and .05 precision is 273 (...
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### Kruskal-wallis v ANOVA v robust methods

I have data from 3 groups which don't follow a normal distribution, my sample sizes are ~600 for the control group and ~300 for the test ones. I made a density plot of the data which looks like: ...
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### Calculating “sample size”/power when I already have a group

I am doing a project on carpal tunnel syndrome. I am looking at electrophysiological and symptomatic data before surgical intervention and again afterwards to assess whether symptomatic relief ...
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### Calculating Power Z*score

I am trying to present sample size determination based on determining a certain difference between two proportions and the power of the test. As I understand it, my calculation requires both z-alpha ...
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### Power Model & linear regression model

What does it mean if linear regression coefficients and power model coefficients (using Log transformed value of explanatory variable) are same and only difference in intercept value? Thanks, Meera
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### Power analysis in structural equation models

I’m getting different estimates when estimating sample size for a structural equation model when I use different utilities online. How would you calculate the sample size a priori for such a model?
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### How to calculate the power of my quantile regression model?

I have a quantile regression model that I fit with the rq() function in the quantreg package ...
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### How does imputation affect significance test power?

There are many different imputation methods that make different assumptions about the missingness of the data (MCAR, MNAR, MAR). Since this assumption may not be met, I'm interested in knowing how the ...
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### Power Analysis for 1-sample Longitudinal Observational Study

I need to calculate the minimum detectable effect given a known N and desired power. I have a CONTINUOUS EXPOSURE and continuous outcome, each measured twice (baseline + 1 follow-up). If possible, I ...
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### sample size for longitudinal quasi-experimental evaluation

I am working on the evaluation of a proyect designed to help crime victims to overcome their experiences. My main hypothesis is that the program prevent these victims being crime victims again. Since ...
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### How do you stop difference in power from biasing comparison of statistical tests?

I have two sets of values A and B, and I am conducting a Mann-Whitney U test (the distributions cannot be assumed to be normal) on these sets. However, I have an a priori hypothesis that some values ...
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### Does the use of EFA factor scores (vs. sum/average scores) impact statistical power of subsequent analyses?

Imagine a hypothetical scenario: You have data a short survey of 9 questions that participants respond to on a continuous rating scale. You suspect that Questions 1-3 assess one particular factor (...
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### Power Calculations using “Percent Change” vs. “Absolute Values”

Percent change can be extremely misleading for a number of reasons (e.g. regression to the mean), even though in the medical literature percent change is used quite frequently to "normalize" clinical ...
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### Sequential testing and power

Consider an ARMA(p,q). Why when we run an iterated F-test in order to find p and q the statistics used are correlated and the power is likely to decrease?
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### Why does R power.prop.test & R prop.test show inconsistent results?

I am a bit confused by the differences I am seeing between R's power.prop.test & prop.test functions. To estimate the sample size needed for an A/B test I am conducting I am using the following ...
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### Best way to calculate power, precision & sample size using complex pilot data set?

I have a large and complex pilot data set of electromyographic (EMG) data collected from human subjects performing several different exercises. A single subject was used for all data collection in ...
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### What is the proper way to increase power when randomizing at the village level?

Let's say that we have a hypothetical RCT with the following information: --We are interested in seeing whether a particular belief held among some individuals in a developing country can be ...
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### Power of lady tasting tea experiment

In the famous Fisher's experiment the observable is the number of corrected guessed cup $k$ having two kind of cup $A$ and $B$. Usually it is interesting to compute the critical region to reject the ...
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### Power Function Manipulation

Assume that $X_1, \ldots, X_n$ are i.i.d. with the normal distribution that has mean $μ$ and variance $1$. Suppose that we wish to test the hypotheses $$H0: μ ≤ μ_0, \\ H1: μ > μ_0.$$ Consider ...
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### The effect of prognostic factors on the power in survival analysis

I was curious to know if there exists closed form equations for calculating the power in survival analysis, using either Cox-regression or the log-rank test, when their is an important prognostic ...
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### How to compare predictive power of sports odds

For my MSc Thesis I would like to compare the predictive power of classic bookmakers on the one hand and a betting exchange on the other. I have a lot of data on both types of betting, mostly on ...
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### How to compare groups when the control group is 100 times larger than the group in question?

I am working with NIS data which are basically a 20% sample of all in-hospital admissions in the US every year. I have small group of cases that carry diagnosis "X" in their record and overall the ...
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### Power calculation for panel regression

How do you perform a power calculation in a panel regression setting? In particular what do you use as your sample size. The number of individuals or the number of observations (individuals x time ...
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### If we were given differences in variances, and power, find n?

If we have a given difference in the variances x and 80% power, how would you find the sample size needed to detect the difference in variances equal to x? I know that power = 1-P(type II error) but I ...
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### Inference and generalization from a small data set (for publication)

My question is about how to present my findings properly (for publication). I work on the classification problem of a small medical data set. There are 10 and 21 subjects in groups labeled by "0" ...
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### Measures of minimal detectable effect size

Statistical power is defined as the probability of wrongly accepting the null hypothesis for a given sample size, p-value cutoff and effect size. I am after accepted measures of the converse: the ...
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### How is the risk function related to the power function?

I have been going through Chapters 7 and 8 of Caselle&Berger and stumbled upon one issue I do not understand even theoretically: how is the risk function related to the power function? Also, I was ...
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### Power analysis for polynomial regression

There are two variables, $X$ and $Y$. I am interested in the shape of the relationship between $X$ and $Y$, specifically whether it is linear, curved, or some higher order polynomial function, because ...
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### Power of Meta Regression

Why it is said that Meta Regression analyses have low power? & How to calculate the same?
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### Why does using a non-parametric test decrease power?

I am thinking about using the Mann Whitney U test over Student's classic t-test. But I was warned that I'd lose power and would require a higher sample size to compensate. I don't understand: Why ...
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### Power calculation (a posteriori) of a cohort study - R software

Does anyone know if there's any R library to calculate the power of a cohort study with n=9511 Reference: 50 year trends in atrial fibrillation prevalence, incidence, risk factors, and mortality in ...
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### Is the concept of “Regression toward the mean” closely related to Power Analysis?

Regression toward the mean says that if a measurement is extreme at first, it will gradually tend towards the average value in subsequent measurements. Isn't this what Power analysis all about? Why ...
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### What is a good effect size in power analysis?

Power is the probability of rejecting the null hypothesis when the null is truly False. It depends on effect size, sample size and the signifance level. If I want to estimate the sample size I need ...
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### Power of permutation test for testing whether X,Y are independent- Homework question

I'm trying to solve my homework question in the attached Image:I'm stuck on 1.(c). Two directions I had in mind were: the central limit theorem, and the Poisson estimation for a large number of ...
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### Why do they call the power law distribution a 'law'

Power law distribution is a distribution not a law. Very simple question: why is it called a law?
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### Experimental Power Calculation with Uneven Split and Correlated Observations

I want to run an experiment. I have prior knowledge that the treatment is better, so I will run the experiment with my $N$ units with 80% of the response in treatment and 20% of the response in ...
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### Power Analysis By Simulation

Background: We have a developed an alternative website which we believe will increase sales by a small percentage (1-4%). Although small this is very valuable. Our Site: Visitors are tracked by a ...
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### Does Imposing a Constraint Make a Method More Powerful?

Suppose we have 100 patients in a randomized trial. Fifty of them are in the treatment group and the rest are in the placebo group. This is a longitudinal study so that we measure the response from ...
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### Barnard's Exact Test (Boschloo's variant) when distribution is hypergeometric

Let's say, we have a standard $2 \times 2$ contingency table and because of low sample size we're about to use some type of Exact Test, e.g. Fisher's Exact Test (FET) or Barnard's Exact Test. It's ...
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### Estimating sample size for Mann Whitney U test

I'm trying to estimate the required sample size for 80% power in an A/B testing, comparing user ratings with the Mann Whitney U test, and I'm having a problem with the power estimation. I'm using ...
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### Making simple simulation to confirm power of statistical test?

Might seem odd by I'm trying to make a simple simulation to verify some power calculations that I'm finding with the package pwr in R (https://cran.r-project.org/web/packages/pwr/pwr.pdf). What I did ...
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### Probability of significant result in a second sample given first was significant

It's an example mentioned in Amos Tversky and Daniel Kahneman's Belief in the Law of Small Numbers: Suppose you have run an experiment on 20 subjects, and have obtained a significant result which ...
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### Power Analysis for Within Subject ANOVA

I am going to be collecting survey data that asks for participants' attitudes towards four groups of people. For the sake of this example, let's say that it's black women, black men, white women, and ...