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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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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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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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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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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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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
49 views

'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] [closed]

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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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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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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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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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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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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Compute posterior expected loss for choosing B over A

The bayesAB package in r computes the posterior expected loss for choosing B over A when running the following commands: ...
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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: $\sigma^2=\sigma_1^2$
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Is this a valid method to adjust for multiple testing?

Assuming I have 100 variables and I do a t-test for each of them without adjusting the p-values, and get 8 significant p-values out of the 100 tests. If my alpha is 5% can I just say that since I ...
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Bayes inference: hypothesis testing on the average parameter

Bayesian inference field: given a dataset, if I assume a normal a priori distribution on the average parameter with zero mean and a given variance, those hypothesis tests can be carried out on the ...
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Comparing gas pipe failure rates by soil type

I'm trying to establish whether certain soil types are associated with (statistically significant) higher rates of gas pipe failure. I have a set of polygons representing different soil ...
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Simplification using Cauchy Schwartz Inequality

Can someone please help me understand how the last step in the highlighted part in the equation is arrived at? I did not get how the Cauchy Schwartz Inequality comes into play here. The full paper is ...
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Sampling theory of correlation; sign of population correlation coefficient & hypothesis design

I'm currently studying 'Estimation of population correlation coefficient from sample correlation coefficient. Source: https://newonlinecourses.science.psu.edu/stat501/node/259/ Test statistic is like ...
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1answer
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One sided test $H_0:\mu=0$ or $H_0:\mu\leq 0$? [duplicate]

I want to test $$H_0: \mu \leq 0 \,\,\,\,\,\, vs \,\,\,\,\,\, H_1: \mu > 0.$$ I am using a t test, so the statistic $T$ has $\nu$ degrees of freedom which depend on the sample size. What is ...
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1answer
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Choosing the fastest code between two equivalent codes

I want to learn how to use statistics to help me choose between two equivalent code. I want to choose the "fastest", the one that would take the less time to execute. How should I collect data? And ...
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Testing equality of two coefficients of two separate regressions in R [duplicate]

I run the following regressions: Y_1 ~ c_1 + b_1*X Y_2 ~ c_2 + b_2*X and I get two estimates for b_1 and b_2. What is the appropiate statistic to test if ...
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A/B test : Is there a way interpreting factor “A” group is greater than factor “B” group?

Plz.. understand my lack of English skills.. T.T I have a problem dealing with statistical hypothesis testing. To be specific, we have two special delivery method like (new) : method "A", (old) : ...
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1answer
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How to handle and test categorical dummy variables when interested only in certain levels?

I want to build a multiple linear regression model. I want to test the effect of a nominal variable with 10+ levels, but I am interested in testing only the effect of 2 of them. 1st Question: How ...
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1answer
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testing whether two correlation coefficients are different from a non zero value

Hello I have 2 bivariate normal populations with correlation coefficients p1 and p2 respectively. I could easily obtain samples from both. I am interested in testing whether the difference in these ...
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1answer
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testing whether categorical distributions differ

i have data on how a large population (N ~ 1e8) is distributed into (many) categories (i.e. i have count of instances in each category). some categories have low ...
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Determine if attributes of sample users are similar to attributes of the full population

I'm a product owner responsible for running a lot of A/B tests comparing an experiment vs a control group. Usually, both groups are a subset of a larger overall population (million plus users). I'm ...
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Is it necessary to keep the regression model linear for checking the Granger-Causality relationships between the variables of a data-set?

For checking the Granger's Causality between two variables of a data-set, lets say to check X granger-causes Y, we create two regression models, a restricted model(containing the lagged values of ...
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1answer
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How to compare my machine learning system results with another state of art systems

I'm writing a report of a machine learning system I built. The best F-score measures are similar or greater than another ML approaches in the state of art. However, my advisor outlines that I can't ...
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Z-score and Hypothesis Testing [closed]

I have a large dataset of vehicles's speeds. My goal is to infer an upper bound on the (average) speed of the population of all vehicles $U$ The way this is to be done is like this: Given a potential ...
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1answer
40 views

Hypothesis Testing: Is a Tool Better Than Random?

I am testing a tool that tries to select the correct outcome. I am trying to do significance testing to see if the tool is better then choosing the outcome at random. It picks from 4 categories, and ...
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1answer
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Using a simulation to show sceptics that t-test gives the right answer, and how to do the same for a bayesian inference case

I want to demonstrate to sceptical colleagues and friends that statistical analysis works. And there’s a follow-on question regarding doing the same with bayesian inference. Suppose that I want to ...
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38 views

Calculate Power of Bootstrap Test for Equality of Means

I am new to statistical resampling techniques. Here is a problem I am having difficulty with: I am given two independent Gaussian samples of size $30$ with equal underlying parameters ($mean = 15$ and ...
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Statistical Test: 2 Nominal Independent Variables; 1 Nominal and 1 Numerical Dependent Variable

I have a data like this, I want to do statistical test to determine whether "App Opens" and "Click on Cards" differ by "Group" (Control/Treatment). What should I do? Can I separate this dependent ...
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Why is the Neyman-Pearson lemma a lemma and not a theorem?

This is more of a history question than a technical question. Why is the ``Neyman-Pearson lemma'' a Lemma and not a Theorem? link to wiki: https://en.wikipedia.org/wiki/Neyman%E2%80%93Pearson_lemma ...
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Cross section dependence in a fixed effects model

I have a fixed effects model and I tested for cross sectional dependence using a Pasaran CD test. My understanding is that, even in the presence of cross sectional dependence, if the model is ...
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Simple arithmetic approximations to categorical analyses

Suppose I have a two by two table: $$ \begin{array}{c|ccc} & Y & \neg Y & \\ \hline X & a & b& &\\ \neg X & c & d& &\\ \end{array} $$ and I am interested ...
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1answer
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Wilcoxon Test - non normality, non equal variances, sample size not the same

I know there are already a lot of posts out there, but I couldn't find this exact combination in any of them. Comparing two samples (Prices associated with men and with women), but I have neither the ...
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1answer
17 views

Chi-squared test for homogeneity to compare subsets of a population?

Everything I have read states that one of the conditions for inference of chi-squared is that random sampling is carried out (e.g. https://stattrek.com/chi-square-test/homogeneity.aspx). Can I still ...
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Equality of Means (Student, Bootstrap Permutation) Using R

I am getting acquainted with resampling methods. Here is a problem I tried to tackle: I have two normal independent samples of size $60$ of equal variance but possibly different means. The two ...
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Check if data set is drawn from a distribution/Check if sample is representative

I have a data set $X$ and there is another sample $Y$. I suspect that $Y$ is a subsample of $X$ and I want to check that hypothesis. Obviously, both contain the same number of variables (data types ...