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Questions tagged [hypothesis-testing]

Hypothesis testing assesses whether data are inconsistent with a given hypothesis rather than being an effect of random fluctuations.

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which stat test?

I am doing a health interventional study in the community. I calculate the "pre-intervention" proportion of behavior of the community before applying the interventions. And after 1 years of various ...
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3answers
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How can I test whether two logistic regression coefficients are identical in mixed models?

Similar to question here. 3 variables (1 continuous (X) and 2 categorical (A & B)) predict 1 dichotomous variable in generalized linear mixed models. Both variables A and B are dichotomous and ...
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How to calculate multiple correlation coefficients and test hypothesis?

I found the estimation of S and $\overline{x}$ of a data set to be approximately $\overline{x} = \begin{pmatrix} 185 & 151 & 183 & 149 \\ \end{pmatrix}'.$ and $S = \begin{pmatrix} 95 &...
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Appropriate method to assess scatter or variation in groups with dramatically different means

I am working on a product fabrication process, and I want to demonstrate the consistency of my product. To do this, I am trying to measure the variation in the extent to which a biological material is ...
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1answer
35 views

p-value adjustment for correlation matrix

Suppose I have a large number of features, and I want to figure out which of them (if any) are "significantly" correlated. In short, how I can estimate significance in a way that appropriately ...
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Finding a critical region for a simple test, with PDF $f(x) = (\frac{x}{\theta} + \frac{1}{2}) \space \mathbb{1}_{(-1,1)} (x)$

I'm dealing with a simple inference problem which involve a PDF I've never dealt with before. We have $X_1, ..., X_n$ iid variables where $X_i$ has a PDF $$f(x) = (\frac{x}{\theta} + \frac{1}{2}) \...
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Should we trust statistics? [closed]

My mathematical statistics theory professor, an expert in the field, said today he doesn't trust statistics enough to use it in practice. He just likes the beauty of the math. He said he would never ...
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How to assess the effect of an intervention when having a control sample is unethical?

I'd like to assess the effect of a medication X on some scalar, nominal and ordinal parameters of disease Y. Problem is, this medication X has proven to greatly reduce mortality in patients with ...
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Comparing two difference-in-difference models when making the treatment group larger

I have a question regarding some potentially existing empirical tests in the difference-in-difference context. Assume that I have the usual setting of observing some hypothetical outcome for a ...
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1answer
22 views

Train classifiers on a subset and validate on a full dataset

Let's say I want to train a classifier and use it on 20% of "known" data; the rest of the "known" data is reserved for training (60%) and testing (20%). In the end I also want to apply it on "unknown" ...
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A question about selection of appropriate test procedure in Testing of Hypothesis

Q. Let (X, Y) be a paired response measured in continuous scale and obtained by administering a a certain drug on a patient. Let 'm1' and 'm2' denote the expected responses. Under suitable assumptions,...
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determine cutoff for independant variable based on outcome

I have very limited understanding of statistics so have failed to find the correct question to ask, let alone the answer. I have put multiple samples through a series of experiments where for each ...
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Derive the Likelihood Ratio Test for multivariate normal and specific covariance matrix

Let $X_1,\ldots, X_n$ be i.i.d. $N(µ, C)$ random $p$-vectors. Derive the Likelihood Ratio Test for $H_0: C = σ^2(1 − ρ)I_p + ρ1_p1_p^T$, where $1_p = \begin{pmatrix} 1 \\ 1 \\ \vdots \\ 1 \end{...
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1answer
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A question about Testing of Hypothesis

Q. Suppose for an experiment, the test for normality of an underlying population is accepted on the basis of a data set. To cross check the result, the experimener repeated the test with another ...
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Cross-Sectional Dependence Test in Panel-Data Models

I did cross section Dependence test in Eviews for panel data (EGLS Model) and Breusch-Pagan LM test, Pesaran scaled LM test, Bias-corrected scaled LM test confirmed the cross-section dependece but ...
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2answers
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Which test are useful for testing significant changes in mean values over three years?

for my term paper, I want to compare broadband internet price data in the US. There are three datasets, each represent retail prices from 2016, 2017 and 2018. All data is clustered into 6 download ...
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How to do an equidistribution test? [duplicate]

Suppose I have a sample of $N$ numbers $a_1,\dots,a_N$ from $1,\dots,k$. How can I test whether they are equidistributed? I'm not interested in a full randomness test as the order does not matter to ...
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Type I error question

I have this question from a previous exam, since it didn't worth much points I suspect it should be something tricky. How to achieve a statistical test where the Type I error risk is $0$? Is it ...
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Is there a statistical test for this experiment?

We have developed a Benders decomposition algorithm for an inventory-routing problem. We have considered that optimality and feasibility gaps could get different values. Therefore, choosing an ...
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1answer
29 views

Which test statistics is better in the hypothesis test for variance?

Most of the time, to do hypothesis tests is to follow the tedious processes given on statistics textbooks. But recently I find that there are, in general, more than several test statistics that can be ...
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1answer
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Correct usage/understanding of Bayes Factor when comparing two proportions

I'm just starting to learn R and explore Bayesian statistics, but I keep getting tripped on using Bayes Factor and (honestly), I'd love a little confirmation if my process is correct in interpreting ...
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Simulating optional stopping in data collection with respect to p values

In null-hypothesis significance testing, if we were to optionally stop data collection every so often and check the p value on the data, the null hypothesis may be eventually be rejected even when it ...
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1answer
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Sample size needed when combining multiple t-tests

I am designing an experiment that tests a difference in means between two groups in which data points take very long to generate (1 month each). Accordingly, I'd like to run several tests of the same ...
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1answer
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Breusch–Pagan test: what exactly is the z-variable

I want to perform a Breusch-Pagan-Test. I did calculate some very small examples following the procedure described below, just to understand what the test does: found here: (https://ipfs.io/ipfs/...
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Constructing an appropriate null hypothesis?

I have a collection of 20 2D surfaces embedded in 3D. The mean curvature of each surface has been sampled. The number of samples per surface varies from ~700,000 to ~20,000,000. The choice of ...
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1answer
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Using CLT for hypothesis testing

I have two not normal distributions (~1k samples in each), looks like exponential: So, I need to check its means, that's why I have following questions: The easiest way to do it - is to use Mann-...
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1answer
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Adjust ROC analysis for multiple testing?

we did an exploratory prospective study in medicine in order to find parameters which are able to predict a specific post-surgical event (0/1) before the actual surgery. We have about 10 parameters ...
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Are confidence intervals useful?

In frequentist statistics, a 95% confidence interval is an interval-producing procedure that, if repeated an infinite number of times, would contain the true parameter 95% of the time. Why is this ...
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2answers
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Profile likelihood confidence interval proof

I have read that for null hypothesis $H_0 : \beta = \beta_0$, the likelihood ratio statistic from profile-likelihood is $$LR = 2 (\log L_p(\hat{\beta_p}) - \log L_p(\beta_0))$$ where $\hat{\beta_p}$ ...
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how to set up my one sample test

The more I read the more I get confused. I have 1 control sample and 1 treated sample. I want to know which one of my genes are expressed higher or lower than others. This is RNA seq data Since the ...
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1answer
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Explanatory multiple linear regression

I have a data set consisting of 104 responses from an online survey (data have been cleaned) and I want to test the relation between 14 independent variables (12 variables about which hypothesis have ...
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1answer
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The MLR increasing property (for Karlin-Rubin) with indicator functions

Let $\theta_0<\theta_1$, and let the ratio of likelihood functions for the random variables $X_1,...,X_n$ be $$\frac{L(x ; \theta_1)}{L(x; \theta_0)}=\frac{I(x_{(n)}<\theta_1}{I(x_{(n)}<\...
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1answer
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Which Statistic Test should I apply in the following scenarios

I have a survey data with Yes/No response variable and a categorical variable assigning survey takers to one of the 4 groups: 16-24 years old 25-34 years old 35-54 years old 55+ years old I want to ...
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1answer
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Null hypothesis for individual coefficient's p-value in multivariate logistic regression

When calculating $p$-values for individual coefficient $a_i$ (for variable $X_i$) in a multivariate logistic regression, is the null hypothesis that all $a$'s are zero? that $a_i$ is zero and others ...
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LDA for statistical test

I was searching for which statistical test to use when: The dependent (target) variable is discrete. The independent variable is continuous. I stumbled onto this table: https://www.analyticsvidhya....
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Standard deviation in a non normal distribution

I have two datasets, dataset A with 5-10 values and dataset B with around 20 values. Both are non normally distributed and right skewed. Can I use standard deviation to compare the elements ...
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How to compare 2 regression models?

Suppose I have 2 regerssion models A and B, and dataset for evaluation containing N samples, ...
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type 1 error for mean

I was trying to do an exercise that says to calculate the Type 1 error for the test function $\delta$ given by $$\delta(X_1,...,X_n) = 1 ~~~~~~~if~~~~~ |\overline{X}|\geq Q,~~~~~~~~\delta(X_1,...,X_n) ...
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1answer
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Test hypothesis against true population distribution

I have drawn a sample from a population. For an hour I have asked all the visitors to a website their age. population = people in Germany sample = 32 German visitors to the website (international ...
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1answer
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How can I use the distribution of run lengths to test if a sequence is generated from flips of a fair coin?

I have a very long sequence (in the tens of thousands) of binary outcomes from some data-generating process. I believe that these outcomes are iid Bernoulli trials with p = 0.5, equivalent to flipping ...
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Best test for 2xK contingency table with low cell counts and small overall sample size?

I am looking for the optimal test to use on a contingency table with 2 categorical variables (first variable has 2 levels, second has 4 variables). The cell counts can be as low as 1 or 2 and the ...
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1answer
24 views

How to decide which is the numerator in F test?

Suppose we have two samples of size 20, the first, we have sample standard deviation of 50 the second , we have sample standard deviation of 100 If we want to test $H_{0}: \sigma^{2}_{1}=\sigma^{...
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1answer
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How to run Friedman test correctly across three sets of questionnaire data divided into sub-groups?

I am trying to evaluate the usability of three prototypes of an application and want to see if there is a significant difference in terms of usability. For this I have collected responses from users ...
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1answer
49 views

How do you reconcile a statistically insignificant logistic regression with a significant AUC?

Suppose I run logistic regression with one continuous predictor. The Wald tests of significance show a p-value that is not significant at the 5% level. Looking at the receiver operating ...
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2answers
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Is a $\chi^2$ test appropriate where data points are themselves totals?

My is a series of individuals have attempted a test. They can fail this test for multiple reasons. Furthermore, on an test, a fail can be awarded multiple times for one reason, i.e.: Steve: 1,0,2,1 ...
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Faulty hypothesos or bad preformed Chi-Square Test

I'm trying to test data from my survey with the hypothesis; when most of Gen Y is brought up with mobile devices, and an opportunity to always be online and accessible, more accessibility is to be ...
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Event study - Standardized Cumulative Abnormal Return Testing

I am conducting an event study and have difficulties testing CAR values. My estimation window length (L1) = 252, event window (L2) = 11. I followed the market model when calculating abnormal returns ...
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2answers
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Which tests can be used for variables that are non-normal, but have homogenous variances?

I am trying to compare the effect of two treatments (planting distance) on the growth of plants (multiple species), using the variable growth rate in diameter for multiple years. I have 4 sets of ...
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1answer
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Why there's never a good reason to use the Jarque-Bera test

This question was inspired by a comment made by @whuber in response to this question regarding the use of distributional tests. The comment stated there is never any reason to use [the Jarque-Bera ...
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1answer
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Is there an inductive version of a traditional hypothesis test?

Here's my specific question: Is there a statistical procedure that compares a hypothesized value to the empirical distribution, rather comparing an empirical value to a null distribution? Put ...