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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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Transitivity of statistical significance

Say I have three sets of observations, $A$, $B$, and $C$ (say, the heights of Australians, Americans and Brits). I assume that they are all normally distributed, independent etc. I perform two-sided ...
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How to calculate studentized bootstrap pvalue for test with H0 assuming lift (%)?

First of all I'd like to mention, that I've read at least 2 great discussions on the site, which helped me a lot. Very thorough explanations of H0 data generation are presented here and here. But ...
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Understanding equivalence testing. Why there are two hypothesis?

I have to two groups and I would like to test that difference between means of these two groups is at least 0.02. I am using TOSTER R package. Here are details: ...
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Sound unit testing of convergence of an implementation of a stochastic algorithm

(My statistics knowledge comes mainly from computer science, so I might be overthinking the following...) I have implementations of several stochastic optimization algorithms (evolutionary algorithms,...
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Break down a 2-by-3 within within ANOVA into two 2-by-2 within within ANOVA

I have data that may be arrayed as a 2 (Time: A1 vs. A2) by 3 (Difficulty: B1, B2, B3) within-within factorial. But I'm not interested in the comparison of difficulty B2 and B3 over Time. Is it ...
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1answer
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Wilcoxon signed-rank test or One Sample t-test?

I conducted a training session and for each of my users, I measured pre and post score (before and after training session). Each of my users (n=28) is measured twice, so my data is paired: Data: <...
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What statistical to use - variability between but not within

I have a data set where each line represents a participant's response to a series of questions (e.g., attitudes towards democracy, life satisfaction). Participants were recruited from different ...
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6 views

Confidence interval of one tailed Z-test

In an intelligence test of boys and girls, the question has asked to find if the boys and girls are equally intelligent against the alternative that girls are more intelligent than boys. While I have ...
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1answer
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Why replication studies use two-tailed tests?

I have been searching replication studies and I found that all of them use two-tailed tests. For example: Open Science Collaboration. (2015). Estimating the reproducibility of psychological science....
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Logical Hypothesis Modification

I performed an experiment with a treatment and a control group. It just so happened that my treatment could be modified to either increase or decrease my dependent variable. So, I decided to test two ...
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Why do we need alternative hypothesis?

When we do testing we end up with two outcomes. 1) We reject null hypothesis 2) We fail to reject null hypothesis. We do not talk about accepting alternative hypotheses. If we do not talk about ...
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One-sided variance test in r [duplicate]

I would like to compare variances of two independent samples (of different sizes) from two unknown distributions. It seems I should use a one-sided nonparametric test. Bartlett's and Fligner's tests ...
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test of relation when one variable is itself a mean?

What is an appropriate test to see if there is a relationship between two things, where one of them is itself obtained by averaging human rankings. As an example, there are good and bad bottles of ...
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How to test the homoskedacity using GQ test, Interpret R2 with VIF, Calculate Adjusted R-squared [on hold]

Can you please show me with some explanations how to test the homoskedacity using GQ test, calculate and interpret R2 with VIF for a model, Calculate Adjusted R-squared from the pictures from this ...
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1answer
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Setting up contrasts in lmer?

0 I have 139 subjects (ID), with measurements taken at two time points (Time1, Time2), at 148 brain regions, a dependent measure called volume, and a covariate called thickness. Each subject has 148 ...
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21 views

chi square testing visualization [on hold]

How can I plot something like the first plot, I do have only one sample called s_chi in order to get statistical chi and plot the hypothesis testing my code:
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Statistical Test of Model Mean and Std.Dev

I have thousands of real-world observations for the input/output of some stochastic system. I have made a mathematical model that I have strong reason to believe governs the underlying relation ...
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Solution verification for a hypothesis testing question

I am posting this question as a solution checking. Let $X_1,...,X_{30}$ be a random sample from the exponential distribution with unknown mean $\mu\in \{1,1/\delta\}$ (where $\delta>1)$. Consider ...
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Comparing main effects and interactions on the same significance scale

When we collect genomics/metabolomics/proteomics data (many variables) in a between-by-within 2-way experimental design, we are often interested in which variables change differently between groups (...
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Information gain or regression for measuring to what extent a continuous quantity detemines a discrete one?

I have a small population S and two quantities P and Q associated to its members. P is integer valued (say, age taking integer values between 1 and 20) and Q real valued (say, height in meters). I can ...
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1answer
21 views

Are there statistical tests for testing multiple sample proportion?

For categorical variable testing, we have chi-square test. For example, we want to test if a dice is fair (assuming sample has [6,5,7,7,6,5] and ...
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What test should one use when dealing with different treatments in plant clones?

In an experiment involving plant clones there are: 20+ treatments, 5 technical replicates for each treatment (plant clones in which the treatments were tested). Variable of interest is Biomass. Due ...
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1answer
19 views

Should I adjust for family-wise error when doing many logistic regressions and t tests

In my biomarker analysis, there are 100 biomarkers. Each biomarker is measured at 4 different time points. I'm looking for any biomarker that is associated with outcome variable at any timepoints. ...
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2answers
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Paired t-test with inequality in $H_0$

I have read that paired $t$-test works assuming a null hypothesis with equality, i.e: $$H_0 : \mu = \mu_0 $$ Is there any way to do the same test with an inequality, such as: $$H_0 : \mu \geq \mu_0 $$ ...
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1answer
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How to measure risk of a Type 2 error in A/B tests

I'm conducting A/B tests where outcomes are binary (success or failure in control and experiment populations). The assessment of the risk of a Type 1 error is relatively straightforward: given an ...
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1answer
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Why shift the mean of a bootstrap distribution when conducting a hypothesis test?

I'm wondering about why we do a particular thing (and not another) when conducting bootstrapped hypothesis tests. My understanding of bootstrapped hypothesis tests is this (based on this helpful ...
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1answer
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Analyse variation between distribution curves according to factors

I have a set of continuous distributions representing the leaf area density found at different heights through a forest canopy. e.g. like that found in Whitehurst et al. (2013): For each of these ...
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0answers
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Statistical test to compare the mean of two samples

There's a competition with 20 categories, and each category has 3 winners. I have an array of the winner's performance of the next year (60 values), and other array with the average of the competitors ...
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Pre- and post-intervention difference between standard deviation scores

My first research question is based on establishing whether mental toughness is a trait like construct or a skill that can be manipulated through training and experience. I am using descriptive ...
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1answer
27 views

Testing for randomness against Poisson distribution - what is the null hypothesis?

"This week, we examined the simplest theory of spatial criminology – that crimes are distributed at random. When spatial criminologists want to test observed data for randomness, they test that data’s ...
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2answers
34 views

different chi-square test results [duplicate]

I am doing chi-square tests using Scipy. Just realized the test statistics will change even though you simply rescale all data and the testing outcome could change. For example, using ...
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1answer
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Bootstrap Hypothesis Test: Comparing the Performance of two Models

I have two models $A$ and $B$ as well as a training set $X$. I want to test whether there is a significant difference in performance between model $A$ and $B$. I'm attempting to do this via ...
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P-value: Fisherian vs. contemporary frequentist definitions

I am trying to see if I understand the definition of $p$-value as used by Sir R. A. Fisher and the one used today by frequentist statisticians (not sure how to call it better). $p$-value according ...
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Test for average of independent, non-Identical binomial distributions

I have a box with $m$ coins, each with a probability $p_i$ for $1\leq i \leq m$ of flipping heads. As an experiment, I flip each coin $n_i$ times, recording the results. What is a statistical test I ...
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2answers
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Two sample t-test to show equality of the two means

Given two (numeric) samples I would like to show that there is not a significant difference between the two means $\mu_{1}$ and $\mu_{2}$. If my goal was to show a significant difference I would ...
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On a Bayesian hypothesis testing

Let $X_1,...,X_n$ be a random sample and $\lambda >0$ be a parameter, with $X_i |\lambda \sim Poisson (\lambda)$ and $\lambda \sim Gamma(\alpha, \beta) (\lambda)=\dfrac {1}{\Gamma(\alpha) \beta^\...
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How to choose confidence interval for clustered tests?

I'd like to test if requests to my system are succeeding at least 90% of the time. This system receives about 10 requests/minute. I'm ok getting a 1-in-20 false alarm. If my question ended here, I ...
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1answer
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'p-value' for clustering

I was just wondering if there is a way to check if the clustering found by a specific method (e.g., KMeans, DBSCAN, Mixture Models, ...) is significant. Something in line with, there is 5% chance that ...
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Calculating probability of voting results from small sample aize

2 million people voted in a poll for their favourite song. 35,000 votes have been counted so far, of which: 575 votes are for Song A 466 votes are for Song B 393 votes are for Song C (And the ...
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Replicating Dickey Fuller? How did they know something was wrong? [cross posted on QF] [on hold]

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here ...
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Using Multiple Comparisons for Kruskal Wallis Follow up analysis

I am performing the Kruskal Wallis test on ~100 samples and wish to group statistically ‘similar’ samples together. The method I am using is described in Andy Field’s ...
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1answer
60 views

Most powerful test for deciding probability mass function

Let $X$ be an integer valued random variable supported on $\{0.1.2...,12\}$ whose pmf is either $g(x)=1/13; x=0,1,...,12$ or $ f(x)=\dfrac x {36} 1_{\{0,1,...,6\}} + (\dfrac 13 - \dfrac x{36})1_{\{7,...
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Why don't we need to use a t-distribution for difference of proportions tests? [duplicate]

In difference of proportions tests we use a Z-distribution. And in Chi square tests which I understand are in practice the same test use the square of the Z-distribution, the Chi square distribution ...
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0answers
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Find supremum of Type II error in Neyman-Pearson framework

Let $X_1,\dots,X_n$ be an iid sample from an $N(\theta,1)$ distribution. We want to test $H_0:\:\theta=0$ against the alternative $H_1\:\theta \neq 0$ using the test statistic $$T_n(X_1,\dots,X_n) = \...
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1answer
32 views

How to Plot the density of Z if : “Z = Gaussian RV + Discrete RV ”?

I want to do a hypothesis testing excersise that comes after, but i'm a little bit confused about the plot of the density of Z, which i feel i need to understand first: More specifically, where do i ...
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0answers
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Significant difference help

I have a quick question regarding which statistical test to use to test for a significant difference. My set of data shows the monthly output of a product for the years between 2013-2017. A new ...
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0answers
9 views

Gradient signifiance test with tolerance and measurement uncertainties

I'm trying to test whether a likelihood has converged to walk around a single number or if it is increasing. In my (EM) algorithm, the noiseless likelihood cannot decrease, only ever increase. In my ...
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1answer
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One sided hypothesis testing with two-sided interval

So, I have a population which is believed to have $H_0:\mu = 4620$ and I should test for $H_1: \mu < 4620$. Given a sample of $n=81, \bar{X}=4450, S=900$, the p-value is: $pv=\Pr\left(\frac{\bar{X}-...
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Hypothesis statement for Factorial design

I have a factorial design with two independent variables A and B. The factor A has 2 levels and factor B has 5 levels. Now I want to see their main effect and interactive effects on X. I am not sure ...
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Given sample variance and sample size, test two variance which one holds

If I am given the sample size and the sample variances of a Normal population, how can I test the hypothesis: H0: $\sigma^2=\sigma_0^2$, H1: $\sigma^2=\sigma_1^2$