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 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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8 views

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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4 views

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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14 views

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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77 views

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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10 views

UMP test for 1-sided hypothesis: Why the focus on the monotonicity in the sufficient statistic, and not in the parameters?

Let's assume that we have $X_1,...,X_n\sim^{iid} Exp(\theta)$. The LRT is of the form $\Lambda(X,\theta_0,\theta_1)=e^{\left(\frac{1}{\theta_0}-\frac{1}{\theta_0}\right)\sum X_i}$. When $\theta_0<\...
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41 views

Calculating power of a sample (need a layman's/beginner's definition)?

We have a bi-annual survey and an intended sample size of 1,300. This sample size was determined using Krejcie's means formula for finite populations, and we drew the sample using 2-stage clustering. ...
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19 views

G*Power post hoc power analysis , unequal sample sizez

I am conducting post hoc power analysis using G*Power. The test conducted was Anova, fixed effects, one-way, with one control and two test groups. Control had 25K records, each of the test groups had ...
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1answer
16 views

2X2 ANOVA: low power, statistical significance for only 1 IV, medium-low effect size

BACKGROUND: I run a 2X2 Between-Subjects ANOVA. I obtained: a low power (< 0.30) for both Independent Variables a not statistically significant result for one of the Independent Variables. ...
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1answer
20 views

Power of statistical test(two densities)

I have the following problem: Consider two probability density functions on $[0,1]: f_0(x) = 1$, and $f_1(x) = 2x$. We want to test such hypotheses: $H_0: X \sim f_0(x)$ versus the alternative $X \...
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1answer
31 views

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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13 views

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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1answer
32 views

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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18 views

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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1answer
19 views

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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98 views

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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16 views

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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14 views

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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1answer
32 views

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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38 views

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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14 views

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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1answer
12 views

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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13 views

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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1answer
27 views

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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17 views

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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18 views

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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55 views

Power of Meta Regression

Why it is said that Meta Regression analyses have low power? & How to calculate the same?
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283 views

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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1answer
37 views

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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1answer
73 views

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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3answers
49 views

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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30 views

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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2answers
62 views

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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12 views

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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83 views

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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29 views

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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34 views

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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53 views

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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1answer
60 views

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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1answer
62 views

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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23 views

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 ...
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12 views

Clustering and power: increasing the n but not the number of clusters

I am designing an experimental study with N observations from M sampled clusters, where M << N. Half of the clusters will be assigned to treatment. I can spend more money to increase the number ...
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1answer
10 views

Optimally sampling a sequence of observations

Given a multivariate population, I'd like to define a sequence of observations to sample, such that coverage and representativeness is optimal at each step (cumulatively). For example, a sample of ...
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18 views

power of regression coefficient tests

does anyone know how I can calculate the power of a regression coefficient test in R? for example we have: H0:B0<=9 and H1: B0>9 if actually ...
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2answers
157 views

Post hoc power analysis for a non significant result?

I have submitted a paper to a journal reporting a non-significant finding. One of the reviewers has asked me to include a power analysis on my data to work out how big a sample size I would need to ...
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2answers
14 views

Prospective power using observed difference

In my line of research we often calculate prospective power of a proposed study as a way to determine what sample size we should aim for. However, I'm often studying phenomena, or interactions between ...
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11 views

Power calculation for assessing relatively success two different predictors on a continuous outcome, Fisher r-to-z?

I'm thinking about a study where I assess the relatively predictive power of two different measures. Let's say a patient comes to a clinic on 3 different days, and 3 different measures of a noisy ...
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1answer
206 views

What is the empirical size of a test?

Now I am doing research of a proposed test statistic. I want to calculate the empirical sizes for different sample size of the proposed test statistic under the nominal type I error,such as 0.05. ...
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25 views

Calculate power of a test - solution verification

Let $X_1,X_2,\cdots,X_n$ simple random sample from gaussian distribution $\mathcal{N}(m,4)$. Calculate power of a test ($1-\beta$) for $H_0:m=0$, $H_1:m=2$, when significance level of a test is $\...
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1answer
61 views

What does this mean “the standard deviation of a proportion is a function of the proportion itself”?

I was studying calculating power and sample sizes and i came across this paragraph: Calculating Power for comparing two proportions has the same idea as with comparing means, except that no ...