Hypothesis testing assesses whether data support a given hypothesis rather than being an effect of random fluctuations or some other process described by an alternative hypothesis.

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A contrast suggested by the data

One approach to testing hypotheses suggested by the data is Scheffé's method. According to the Wikipedia article, the contrast $C = \sum_{i=1}^r c_i \mu_i$ (where $\sum_{i=1}^r c_i=0$) is estimated ...
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Is the likelihood ratio test for the global null considered to be an omnibus test

Continue from my last question about an omnibus test. When the (global) null is the intersection of several individual nulls, I was wondering if the likelihood ratio test for the global null is ...
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21 views

Questions about large-scale multiple testing

From Wikipedia Traditional methods for multiple comparisons adjustments focus on correcting for modest numbers of comparisons, often in an analysis of variance. A different set of techniques ...
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46 views

Relation between omnibus test and multiple comparison?

Wikipedia says Methods which rely on an omnibus test before proceeding to multiple comparisons. Typically these methods require a significant ANOVA/Tukey's range test before proceeding to ...
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45 views

Understanding the definition of omnibus tests

From Wikipedia Omnibus tests ... test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall. ... Omnibus test as a ...
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11 views

The definitions of Simultaneous inference and selective inference?

What are the definitions of Simultaneous inference and selective inference? I think they are two different ways of doing multiple comparison. I encountered them from Wikipedia, which I think only ...
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14 views

Power Calculation for Disease Modeling in iPS cells

I apologize in advance if the question is rather simple, but I have been having a difficult time figuring it out. I am an experimental scientist interested in modeling human disease with induced ...
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26 views

Meaning of significance test [duplicate]

I was wondering what relation and differences are between a significance test and a hypothesis test? Are they the same concept, or is the former a special case of the latter, or ...? What does a ...
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60 views

Given samples from multiple normal RVs, how do we recover the histogram of their means?

Let $X_1,...,X_N$ be independent normal random variables. $X_i$ is normal with mean $\mu_i$ and standard deviation $\sigma_i$. Let $x_i$ be a single random sample from $X_i$. Input: We get all ...
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27 views

Test on the properties of two betas?

I have a set of observation. When I do an OLS I get a beta. After I remove some values I also get a beta. Now I want to test if the properties of two betas are the same? Pls give me a hint how to do ...
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53 views

Test whether variables follow the same distribution

If you want to test whether two variables follow the same distribution, would it be a good test to simply sort both variables, and then check their correlation? If it is high (at least 0.9?), then the ...
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Interpretation of a Durbin-Watson test?

I have calculated a Durbin-Watson test and got as far as $$\eqalign{ d&=2.207551844, \\ dL&= 1.6164, \\ dU&= 1.7896. }$$ I want to test $$H_0 \gt 0,\ H_1 \le 0.$$ However, I do not ...
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Testing Spearman's rho between-groups

I am analysing ordinal, non-normally distributed dependent measures using Spearman's rho. Specifically, we have an independent groups design, and I have found a significant relationship between the ...
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Is FWER the FP rate of the global test?

In multiple comparisons, FWER is defined as $$FWER = \Pr(V \ge 1),$$ where $V$ is the number of false positives made on the individual null hypotheses. So here $V$is a random variable, because it is ...
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11 views

Why is controlling FDR less stringent than controlling FWER?

I have read that controlling FDR is less stringent than controlling FWER, such as in Wikipedia: FDR controlling procedures exert a less stringent control over false discovery compared to ...
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19 views

Which variable vary previously to the other one

Here are two variable (a and b) and their value through time (time.a, time.b) ...
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34 views

Mallows distance hypothesis test: p-value =?

I am using Mallow's Distance (normalized Earth Mover's Distance) to characterize the similarity between two histograms. This is working very well, but I would like to identify a specific cut-off where ...
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2answers
59 views

How to choose the test statistic for permutation test?

Is the purpose of permutation test to test the null that several groups of samples come from the same distribution? I found its steps are The steps in a permutation-based computation of the ...
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1answer
44 views

Confusion about P-values

Okay, this might seem like a stupid question and it sure feels that way. And I have probably just lost myself by overthinking it or something, but here goes: In Cohrans C-test you take the ratio ...
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74 views

When does replication reveal fraud?

Found this question here, and I couldn't answser it and thought it would be a wonderful question for this site. Here's a little thought experiment for your weekend pleasure. Consider the ...
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33 views

How do I analyse a two-alternative forced choice test?

I have recently as part of my bachelor project at my university conducted a two-alternative forced choice test. I have looked at ways to say something with significance about which images (the test ...
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85 views

Is there a general definition of the effect size?

The effect-size tag has no wiki. The wikipedia page about the effect size does not provide a precise general definition. And I have never seen a general definition ...
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68 views

F test for equality of variances

I know that the test statistic is $$F=S_1^2/S_2^2 $$ But I am looking at some example questions from my lecturer and some have confused me. For example: For a certain game, individual game scores ...
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33 views

Likelihood ratio test for a random variable following the Gamma Distribution

Assuming we have a random variable $X\sim \operatorname{Gamma}\left(\alpha,\beta \right )$:$\frac{1}{\Gamma (\alpha )\beta ^{\alpha}}x^{\alpha-1}e^{\frac{-x}{\beta }}$ I'd like to test the ...
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Ways of choosing test statistics: likelihood-based or not?

I just learned that there are three ways of constructing test statistics based on likelihood: likelihood ratio test, Wald test, and score test. I think it nicely categorizes various tests, and I liked ...
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Can Neyman-Pearson lemma apply to the case when simple null and alternative don't belong to the same family of distributions?

Can the Neyman-Pearson lemma apply to the case when a simple null and a simple alternative don't belong to the same family of distributions? From its proof, I don't see why it can't. For example, ...
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Idea of the Nyblom test?

The nyblom-hansen test gives informations about the stability of the estimated parameters in a model. As far as I understand this test, it looks at the score of the ML at evaluates, how near to zero ...
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79 views

Relation between observed power and p-value?

I am trying to understand the relation between observed power and p-value in Stephane's reply, which I think is based on J. M. Hoenig and D. M. Heisey (2001) "The Abuse of Power: The Abuse of Power ...
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Implications of lower-bounded total variation distance on hypothesis testing

Let $\{X_i\}_n$ be a sequence of $n$ random variables independently and identically drawn from either $P$ or $Q$. Thus the sequence $\{X_i\}_n$ has a product distribution, which is either $P^n$ or ...
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28 views

Significance level, effect size, power and sample size: why do any three determine the other?

In Statistical Power Analysis for the Behavioral Sciencies by Jack Cohen (from the limited preview on Google books), he said in a hypothesis testing, any three of significance level, effect size, ...
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How to test whether mean and variance is the same in two small samples?

I would like to test two relatively small samples against the null hypothesis that both their means and variances are the same. The alternative would be that they in fact differ. I saw a post on this ...
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How to extend multiple regression hypothesis tests to multivariate?

I have a basic multivariate regression model $\mathbf{Y}$ = $\mathbf{XB}$ + error $\begin{bmatrix}y_{1i} \\ y_{2i} \\ \vdots \\ y_{ki} \end{bmatrix}$ = $\begin{bmatrix} X_{11} & ... & X_{1p} ...
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27 views

Statistical Significance test for difference in FScore

For a classification task, I have developed two methods and FScore(harmonic mean of precision and recall) of both the classes serves as the performance criteria. How can I check whether the difference ...
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Why will a statistic be significant with sufficiently large samples unless the population effect is exactly zero?

From Wikipedia Given a sufficiently large sample size, a statistical comparison will always show a significant difference unless the population effect size is exactly zero. For example, a ...
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What is the proper way of converting ordinal values to numbers?

I have two painkillers and I have given them to two groups and recorded how the pain level changed in three categories: "Helped a lot", "Slightly better", "Did not help" Now I want to do a t-test ...
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27 views

Rejection regions nested or not?

When varying the significance level, the rejection regions can be chosen to be nested or not nested. I was wondering what some theoretical and practical considerations are in using either nested or ...
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Econometrics : White Test with R [migrated]

Good morning, I am trying to realize the white test on my linear model with R. I don't know how to write the R codes to realize the White Test. Price : house price, in millions dollars Bdrms : ...
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27 views

Cointegration of a VAR(1) process

I am using a Johansen procedure to test for cointegration a vectorial 4-dim vector (timeserie). First I tested for differential stationarity of each individual vector, all of those have a unit root ...
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About 2 unit root tests and null hypothesis

I have been looking at unit root testing. Specifically 2 tests: The ADF test. The ADF (augmented Dickey Fuller) test has the null hypothesis that "the time series has a unit root" (meaning that the ...
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Significance testing for a group of samples

For instance, I have a bar chart - in which I have 4 samples/bars. for these 4 bars, I want to check statistical significance for all combinations. How can I do it? Can unpaired t-test be used - to ...
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85 views

How to test for simultaneous equality of choosen coefficients in logit or probit model?

How to test for simultaneous equality of choosen coefficients in logit or probit model ? What is the standard approach and what is the state of art approach ?
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Measuring the performance of Logistic Regression

Being quite new to the field, it occurs to me that there are multiple and fundamentally different ways of assessing the quality of a logistic regression: One can evaluate it by looking at the ...
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Is the p-value still uniformly distributed when the null hypothesis is composite?

When the null hypothesis is simple (i.e., has only distribution of the sample) and the only distribution of the sample is continuous, the p-value can be shown to be uniformly distributed over (0,1). ...
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27 views

How to test a yes/no outcome with different inputs?

I have what I think is a very simple beginner question, but I do not have any formal training or knowledge of statistics or design of experiments. Let's say I have a yes,no (0,1) outcome of an ...
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33 views

Working out probability with alpha and beta

Working out probability with alpha and beta? Let's say in an experiment, the Null hypothesis is patients having Condition A. Alpha (type I error) is 0.05 and beta (type II error) is 0.15. If i have ...
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55 views

How can statistical tests be categorized?

There are many tests in statistics. I noted that some of them may be grouped together, since they are used for similar purposes. For example tests of independence tests that compare distributions ...
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33 views

How to compare two matrices?

I am working on Markov transition matrices. I would like to find a statistical test to compare them. The first matrix is considered the population transition matrix and the second one is obtained by ...
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3answers
48 views

Testing whether two groups formed from a continuous variable differ on a binary outcome

18 people, who have been divided into 2 groups based on the semiquantitative expression of a protein (low vs high). Group 1 (low protein levels) has 6 people, Group 2 (high protein levels) has 12 ...
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Exponential family in testing and estimation

In the Annals of Statistics paper "Defining the curvature of a statistical problem(with applications to second order efficiency)" by Bradley Efron, he claims the following two statements in the first ...
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How to test if two samples are distributed from the same Gaussian process

Given a sequence $\mathbf{x} = (x_1,x_2,\dots,x_n)$ which is sampled from some Gaussian process $GP(\mu_1,\Sigma_1)$ and a "target" sequence $\mathbf{y} = (y_1,y_2,\dots,y_n)$ sampled from another ...

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