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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7 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
17 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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53 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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13 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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9 views

Diffrence in required sample size for estimating a trend with GEE in longitudinal Data

I am currently working on GEE's for longitudinal data and the model I am using to simulate and evaluate the data is: $y_{ijk}=\beta_1+\beta_2\cdot j+\beta_3\cdot k+\beta_4 \cdot j \cdot ...
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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
13 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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27 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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8 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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11 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
23 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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14 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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14 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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42 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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2answers
257 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
27 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
72 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
44 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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0answers
25 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
54 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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0answers
65 views

Power Analysis By Simulation

Problem : A simulation of power gives a far more conservative sample size to just using power.prop.test in R (say). Question : Is the simulation we are using a reasonable way to estimate power. Are ...
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28 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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32 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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41 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
43 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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48 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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17 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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17 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 ...
2
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2answers
116 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
13 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
121 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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23 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
54 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 ...
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59 views

Sample size needed to detect a three-way interaction?

I am hoping to propose a study for which the predicted outcome would be a three-way interaction. I am wondering if this is going to be possible at all with the resources at my disposal, or if the ...
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0answers
119 views

chi-squared goodness-of-fit: effect size and power

How can effect size and power of the chi-square goodness-of-fit test be calculated such that: Effect size is linear and standardized (given effect size $E_{x^2}$, $0 \le E_{x^2} \le 1$) so that ...
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1answer
24 views

Why is the noncentral chi-squared approximate of the deviance bad?

The statistical model under consideration is given by the independent realizations of two independent binomial distributions: $$ x_1 \sim \mathrm{Bin}(n_1, p_1), \quad x_2 \sim \mathrm{Bin}(n_2,p_2), ...
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1answer
53 views

Why is mixed factorial ANOVA more powerful than between-groups ANOVA

Why is a two-way mixed factorial ANOVA involving six conditions more powerful than a between-groups ANOVA with involving three conditions? I understand that between-groups analyses are less powerful ...
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75 views

Calculating the required sample size for a 2x2 repeated measures ANOVA?

I have conducted an experiment with two independent variables, each with two levels. I had one group of participants who were tested under four conditions. I have performed the ANOVA using SPSS, and ...
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1answer
15 views

Can interactions save power in a regression (vs. stratification)?

I have data with about 700 observations total. There are 9 subgroups in my sample with sizes ranging from 54-96. I want to use linear regression to explore how 8 independent variables might predict ...
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47 views

R code for multiple treatments power analysis

I tried the following code mentioned on this site- http://egap.org/content/power-analysis-simulations-r for multiple treatment power analysis in R. However, R mentions "could not find function ...
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38 views

Finding the uniformly most powerful test

Let $X_1,X_2,...,X_n$ denote a random sample from density, $f(x;\theta)={1\over 2\theta}$, $0<x<2\theta.$ Find the uniformly most powerful test for testing $H_0:\theta<=\theta_0$ vs ...
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28 views

finding the critical region of most powerful test

Let $X_1,X_2,...,X_n$ be from a density function $f(x;\theta)=3\theta x^2e^{-\theta x^3} ;x>0,\theta>0$. From the Neyman-Pearson Lemma the most powerful test to test $H_0:\theta=\theta_0$ vs ...
2
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1answer
68 views

Uniformly most powerful test in poisson

This is example in Hogg and Craig's book page 254 I have shown that the best critical region is $\sum X_i>=3$. I don't understand why, after finding $\sum X_i>=3$ is the best ...
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24 views

Power of t test with pwr package

I am not sure I understand what power.t.test(n,d) calculates, e.g. ...
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1answer
24 views

Is a single longitudinal model better than two independent analyses?

I'm planning to study a variable from a group of patients before and after a particular operation. I do not want to, or plan to, compare measurements across the "before" and "after" data (that is, I ...