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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What are the k-means algorithm assumptions?

I'm trying to understand what are the assumptions/hypothesis underlying the k-means clustering algorythm; specifically, I'm looking for a research/academic paper listing such hypothesis and explaining ...
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What would be a likelihood ratio test based on nested multinomial logistic regression models for one-sample testing of categorical distributions?

(Let’s assume a multinomial distribution with a size of just one, so a categorical distribution: either dog, cat, or alligator.) I have done multinomial two-sample tests a few times lately, and I’ve ...
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Statistical Test for multinomial distribution

Suppose there is a multinomial distribution $X \sim Mul(p_1, ..., p_k)$ and I have $n$ samples, where $n_i$ samples gives the first category, .... Then, the sample mean are $\hat p_1 = \frac {n_1}n, \...
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Hypothesis testing Cohen's D -> actual difference in means (proportions)?

I'm trying to execute power analysis regarding proportions (successes of trials.) Using Python's stats models package I can specify a number of trials, an alpha and a beta and the MDE returned will be ...
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How to generate confidence interval for population proportion for a multi class variable

I need to find the appropriate test for the following scenario: I have a population (let's say of an unknown size, for now) which I sampled from it and found the following distribution for some ...
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Interpreting error bars when conducting a one-sided test

I have learned that when interpreting error bars on a bar chart, given that the sample sizes are equal (or nearly equal), that we can trust the error bars if they overlap (or not) in terms of ...
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Statistical comparison of hierarchical data with pair-wise comparison

I am a bit confused how to use hypothesis testing here and please let me know if this question was already asked. Imagine the following hierarchical setup: There are 8 schools in a city. Within each ...
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Compare Wald test statistics and Score test statistics in a Bernoulli Problem

For testing $$H_0: p=p_0, H_1:p \neq p_0$$ in Ber(p). The Wald test statistics is $$Z_1=\frac{\hat{p}-p_0}{\sqrt{\hat{p}(1-\hat{p})/n}}$$ We reject the null if $|Z_1| \geq 1.96$ And the Score test ...
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Testing multiple landing pages simultaneously

Let's say we are wanting to test the conversion rate for multiple landing pages. To be safe, we must allocate 50% of our traffic to our current "champion" page. We then have 8 "...
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Independence Testing for Discrete Random Variable

Suppose $X$ and $Y$ are two discrete random variable take values on $\mathcal{X}$ and $\mathcal{Y}$ with their iid observation $\{ X_i\}_{i = 1}^n$ and $\{ Y_i\}_{i = 1}^n$. If both $\mathcal{X}$ and $...
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Comparing classification models with multiple runs over multiple datasets

I've got 2 classification models and 8 datasets. Each model runs (train/test) 5 times over each dataset. This gives me 40 scores per model, or 8 average scores (if I do the average per dataset). I ...
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Why n-1 instead of n in pooled sample variance

I am currently self-learning hypothesis testing and am looking at the independent samples t-test whose test statistic involves the pooled sample variance (https://libguides.library.kent.edu/spss/...
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Asymptotic distribution of t-test with two coefficients

I have the following CEF: $$ y_{i}=\beta_{1} d_{i}+\beta_{2}\left(1-d_{i}\right)+e_{i} $$ And the following assumptions: $$ d_{i} \perp\left(y_{i}(0), y_{i}(1)\right) $$ $$ \mathrm{E}\left[e_{i} \mid ...
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How can the power of a clinical trial be estimated mid-recruitment?

For my PhD I started a three-arm, clinical trial which due to the pandemic I have to stop after having recruited 69 participants instead of 150 originally calculated to give a power of 80%. The trial ...
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Selecting a test to prove that the observed changes in the performance of two machine learning models are statistically significant

I have developed two machine learning models which I evaluated with two different datasets. My initial hypothesis was that their performance would be higher in dataset 2 as compared to dataset 1. ...
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Finding confidence interval given z-score and null hypothesis

I am working on a homework question and got stumped on this question. Suppose researchers perform a large-sample test of a population proportion where the null hypothesis is that the population ...
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Why use normality tests if we have goodness-of-fit tests?

What are the reason/s to use a nonparametric normality test (e.gr., Shapiro-Wilk, Jarque-Bera) instead of generic, parametric goodness-of-fit tests (good for any distribution including but not limited ...
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Chi-Square Difference Test for Nested Models with a Continuous Outcome

Apologies if this is a very basic question - I'm still definitely a beginner when it comes to statistical tests. I understand that chi-square tests are conducted to determine the relationship between ...
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Testing for a common intersection of p linear regression lines [closed]

I'm trying to derive a test for testing if p regression lines have a common point of intersection. Let the p regression lines intersect at a point $(x_0,y_0)$. We are to test: $H_0: a_1+b_1*x_0 = a_2+...
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Double dipping/p-hacking and interim sample size reestimation

When one applies interim sample size reestimation based on nuisance parameter estimates (observe fraction of initial sample size, estimate nuisance parameter(s) based on the obtained data, reestimate ...
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Is it possible to combine two u-tests to get strictly greater than alternative?

When applying the u-test we can have the null hypotheses $a<b$, $a=b$, and $a>b$ which leads to the alternative hypotheses $a\geq b$, $a\neq b$, and $a \leq b$, respectively (at least using ...
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Analysing Likert scale responses

I have a dataset consisting of Learner's response for Likert scale questions. The data consists of questions from different courses, therefore not all questions belonging to any particular group. ...
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Showing that the given critical value (?) gives a test with significance level 0.05

So I have a maths problem that I'm struggling to understand... The original language isn't English, but I have done my best to translate the necessary background information into English. Assume that ...
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Do asymptotic statistics "solve" the Behrens-Fisher problem?

The Behrens-Fisher problem concerns comparing two means from independent (maybe multivariate) samples in a way robust to heteroskedasticity in the populations being compared. It seems that if one ...
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Appropriate test for categorical independent variables with sub-level

I am stuck on how to analyse my data. I have one dependent variable and a number of indepen dent variables which are divided into further sub-categories. Some of the options for the value of an ...
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How do you test if the average of a population is the same as the variance of the same population?

What can be a statistical test to find out if a population has the mean equal to its own variance? I.e. Mean(X)=Var(X)? I am interested in it because Poisson regression makes the assumption that the ...
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Dealing with a warning message from prop.test in R

I did a prop.test for my data and I got this warning message : ...
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Jackknife estimation and testing

I'm using jacknife method to get the uncertainty of my estimation. My estimation restricted to (0,1) and some can be very small. For example, the jackknife estimate for variable A is 0.0000503 and ...
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power and sample size estimation

For a one-sided test: $$H_0: \mu_1 \leq \mu_2 \ H_1: \mu_1 >\mu2$$ $$\alpha=0.025,\beta=0.1$$ How to calculate the sample size needed? Is this information enough to calculate the sample size?
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Proper way to report on Confidence Intervals for 2 Proportions means

Disclaimer: Stat noob Context: I'm trying to figure out the best way to report CI to a non-data/stat/math savy audience. I'm performing a two proportion z test for an experiment. Control: 0.3097 ...
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Two Sample Independent Test for Proportions (z test or t test)

Context: I have two independent samples that I want to compare for equality through an AB test. The metric being evaluated is binary: user clicks or not (proportions). Question: I keep reading that z ...
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Seasonality test for poissonian counts

I have a count $N_i$ of rare evevents for each season, where $i$ identifies the season. The counts' rates are not high enough to justify a normal distribution aproximation of the poissonian. I want to ...
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What test to use for comparison of multiple groups based on multiple dependent variables?

If I have 3 groups X, Y, Z and two dependent variables of interest a, b, what is the appropriate test to compare whether group Y is more similar to X or Z based on both a, b simultaneous?
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Asymptotic Distribution of Likelihood Ratio under Nonlinear Hypothesis

Suppose we are testing $\mathbf h(\boldsymbol\theta) = \mathbf 0$ versus $\mathbf h(\boldsymbol\theta) \neq \mathbf 0$ for a vector of parameters $\boldsymbol\theta \in \boldsymbol\Theta\subset \...
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What is the appropriate test for this type of dataset?

I was wondering which is the best test for a dataset like this (just showing first 3 variables): ...
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Which Hypothesis Test for AB test with 4 variants

Disclosure: Stat noob trying to understand the basics of ab testing Context: I'm running an AB test with 3 treatment test to see which one yields the highest click thru rate. Q: What is the recommend ...
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How to validate the effect of the type of Task on participants' performance using count data

We conducted a user testing with two groups of participants (Group_A, Group_B). Group_A performed Task_A (a writing) under Condition_A. Group_B performed Task_B (a writing) under Condition_B. Group_A ...
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Does the "type" of standard error affect the relationship between the standard errors of standardized vs. unstandardized estimates?

While previous answers explain how to convert between standardized and unstandardized coefficients and their standard errors, it is not clear if this formula applies across different types of standard ...
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Find the confidence level used based on multiple intervals

I am given the following table of confidence levels for a $\mu$ of a $X\cap N(0,1)$. and I'm asked to find the level of confidence used. Initially I thought when I chose, for exemple, a 90% ...
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Objective criteria for assumption violations that do not utilize p-values?

Suppose we have a standard regression model and want to identify whether we have violated the assumptions of the model. Traditionally, we might utilize a significance test to determine whether (for ...
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Appropriate test for proportions data

I want to compare how my computation model performs to the experimental data. For the experimental data I have proportions of different type of cells like the below table - Cell Type Proportion Type ...
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how can I do this hypothesis test without assuming normal distribution [closed]

the question is attached, I am thinking of using t-distribution to test it...
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how to determine the appropriate form of test-statistic when central limit theorem is used [closed]

I have a research and a report about the stated topic above. Can you kindly help me and provide me more information about it? Thank you very much.
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What is the p-value of tables of variables comparing treatment and control group under presence of missing entries?

I have seen a lot of papers in medical research comparing two groups of population's baseline characteristics. It is inevitable to see that there are variables with missing entries for two groups. ...
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Interpretation of p-value near alpha level

If the alpha is set to 0.05 I have encountered many scientific publications saying that a "tendency for an effect" is present based on a p-value of 0.05 < p-value < 0.1. On the other ...
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N-Way ANOVA for Participation Rate Data

I am trying to conduct a test of statistical significance in a dataset with multiple categorical variables (which in reality have >2 levels each), each of which combine into different population ...
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Permutation testing: Which variable should be shuffled?

When conducting a permutation test, which variable should be shuffled? Let's say I have two variables X and Y, and my test statistic is the correlation coefficient between the two variables. To test ...
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Statistical test to check if data come from two different lines or just one

I have a very basic problem, can you give me some insights on how to solve it, or just some keywords to search online? I have two sets of points in $\mathbb{R}^2$, let say $S_1 = \{(x_i, y_i)\}_{i=1}^{...
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calculate critical value and Compute the test value using R given below data [closed]

An athletic director suggests the median number for the paid attendance at 20 local football games is 3000. The data for a random sample are shown. At α = 0.05, is there enough evidence to reject the ...
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Would the Mantel-Haenszel test for linear trend be appropriate for this data/hypothesis?

I am testing whether or not there is an association between the parents education level and the pupils grades in the oral exam in social studies in the last year of danish primary school from the ...
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