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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Regression F and t statistic

My understanding was that, to make a hypothesis test of a linear combination of regression parameters (e.g. of the type $\beta_1+2\beta_2=0$), you should use a decision rule of the form $|T| = \left| ...
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Basic hypothesis testing homework question

Suppose that random variable $X$ has the probability density function $$f_X(x)=\sqrt{\frac{\theta}{\pi x}}\exp(-x\theta), \quad x>0,$$ where $\theta$ is a positive parameter. It can be shown that $...
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Bayesian Homework: Uniform Prior

Suppose posterior density of parameter $\theta$ is $$\pi(\theta|\mathbf x)=\frac{\Gamma(5)}{\Gamma(3)\Gamma(2)}\theta^{3-1}(1-\theta)^{2-1}.$$ Now I have to find which of the two hypotheses $H_1:\...
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Bayes factor homework question

Suppose my $H_0:\theta=\frac{1}{2}$ Vs $H_1:\theta>\frac{1}{2}$. I got Bayes factor $$B_{01}(x)=\frac{f(\mathbf x|\theta_0)}{\int_{\Theta_1}f(\mathbf x|\theta)\pi_1(\theta)d\theta}=0.35.$$ From ...
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What's the rationale behind a normality test followed by a $t$-test?

Correct me if I'm wrong, but from my understanding, the standard procedure of testing whether data from an unknown source have a specific mean is to (a) perform a normality test to see if the data are ...
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Permutation Tests: How to Interpret a Non-zero-centered Null Distribution

In a "textbook" experiment (e.g., a single treatment is randomly given to a subset of independent units, the SUTVA holds, etc.), my understanding is that a permutation test of the experiment should ...
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ANOVA-like analysis for geometric distribution

I have a dataset (>10,000 samples total) that strongly appears to be geometrically distributed. For this dataset I have a way of partitioning that makes sense theoretically and I would like to know if ...
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If Maximum Likelihood estimation finds the best set of parameters for a regression model, then are likelihood ratio tests unnecessary? [closed]

My logic is this. Models are sufficiently defined by their parameters. Since MLE picks the n parameters that maximize the log-likelihood, then MLE picks the best model given n degrees of freedom of ...
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Which statistical test : Anova or T-Test for between subject experiment (repeated measures ) with one IV with two levels( control and treatment)

It's a between-subject design with a control group and a treatment group with 50 people each. Each participant undergoes 100 trails. (repeated measures). So the only within-subject factor is the ...
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Tests for significant difference between prediction errors of machine learning regression models

Are there any recommended statistical tests for significant differences between cross-validation (CV) estimates of prediction error of machine learning regression models? I have 5 different random ...
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Sample size for stores AB testing with profit as the measurable metric

I have a group of test and control stores and I want to run AB testing on these stores to check if the proposed change in the Test store increase the profit by more than 1% from the control store. I ...
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Does it make sense to run chi-square for independence if I have the whole population?

The context is a large (over 10K employees) company where we want to determine if a number of categorical characteristics are independent or not: gender and pay cycle, business unit and gender, roles ...
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Hypothesis testing of logistic regression coefficient [duplicate]

We define there is a deterministic model between X and Y(which takes the value of either 0 or 1). However, due to some unobservable variables were left out, our equation becomes Y=βX+ ϵ. Furthur, P(Y=...
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Statistical testing on discrete time series data?

I am trying to analyse some data which has 40 different subjects, 1 categorical factor with two levels (20 male and 20 female). The rate of tree cutting was recorded at 4 different time points for ...
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What statistical test can I use to analyse my data? [closed]

I have a simple data set to analyse and have gotten myself confused. There are 6 students which have taken three different measurements each of the same animal. They all took the measurements in a ...
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Null Hypothesis testing fail to reject [closed]

I am confused with the way we reject the null hypothesis. I am not sure whether to continue running the same experiment until we find an edge case to reject the hypothesis or to stop after n ...
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Should I use Mann-Whitney U test, T-test, or something else?

I have a problem where I experimentally want to see if a fall-time for a given a triangular pyramid differ compared to a square pyramid with the same cross-sectional area. Here is the data I have. P3:...
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Power function on a calculator (=normalcdf)

I am preparing myself for a statistics exam and got stuck on a question. Namely, when asked to calculate the power 1-beta of a statistical test I see that in solutions to some exercises they use 1-...
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Is there an alternative to Box's M test for data that is not multivariate normally distributed?

My research question is to test whether two groups have a difference in variance-covariance across multiple measures. However, the data do not follow the multivariate normality assumption required for ...
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What I can know about my probability distribution from the below hypotesis test table?

I have computed the distribution fit test of my probability distribution i got it 0 , then I have tried to creat the hypothesis data for that distribution I have got the below table , Now am not ...
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Proper way to test proportions of data points output by a model

I have a dataset with a series $1000$ categoric observations. There are around 250 distinct categories, with $20$ distinct categories comprising around $55 \%$ of the dataset, thus most of them repeat ...
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Classical tests of hypothesis vs. regressions in small studies

I'm wondering if a study size is relatively small and for whatever reason you insist on doing inferential statistics, would classical tests of hypothesis be more appropriate than regression analyses? ...
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What is the difference between white noise and “strict” white noise?

The normwhn.test package in R has a function to test if data is white noise. The documentation of the function states the following : Performs an Univariate Test ...
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Test statistic of event study

Following the event study paper USING DAILY STOCK RETURNS The Case of Event Studies (1985) by Brown and Warner, let us suppose that I have daily stock returns for 50 companies from the date 2012-01-01 ...
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Show estimator is unbiased [duplicate]

Consider the estimator of the variance given by the formula: $(S')^2 = \frac{1}{n} \sum_{i=1}^{n}(Y_i − µ)^2$ Is this a biased or unbiased estimator? I'm not sure if it is possible to prove ...
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Testing First-Order Stochastic Dominance of Two Samples from Discrete Distributions

Suppose that $X$ and $Y$ are two independent random variables with common finite support on $\mathcal S =\{0,1,...,K\}$ and let $F_X$ and $F_Y$ be their CDFs. Let $\{X_i\}_{i=1}^n$ and $\{Y_j\}_{j=1}^...
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Statistically significant means with small mean difference

I ran an ANOVA on 3 sample sets with means 7.8, 8, and 7.9. The sample with a mean of 8 was statistically different than the other two. The sample size for each mean=200 and 95 confidence level. Why ...
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Which way does an alpha significance level move when a test becomes more conservative?

From NIST 800-90b §5, there is a two sided IID test, with a threshold at $\alpha = 0.001$ as:- And the full test uses 10,000 samples. That seems to be worked out as $ 0.001 \times 10,000 = 10$ which ...
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Is this just a consequence of Publication bias or has a name of its own? [duplicate]

Scenario: In our world, only statistically significant ($p<0.05$) results are published, everything else is rejected or not even handed in. Let's now assume an experiment is $100$ times conducted ...
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Gender (Male&Female) and wage help in R [closed]

I'm having trouble doing a hypothesis test in R. I have a very large dataset with the column "gender" (1=male, 2= female). In another column I have "Wage". I simply wonder how do I calculate the ...
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Binomial distibution with mean 0

I give the following context. Test hypothesis $H_0:p=p_o$ for Bernoulli distributed random variable $X$, with parameter $p$ and samples $X_i$. For estimate $\hat{p}=\frac{1}{n}\sum_{k=1}^n X_i$, $n\...
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Suggesting the Most Powerful test based on NP lemma- Bernoullie distribution

A country that gives the UK points in the Eurovision Song Contest with a probability of $p=0.5$ would be called "a UK supporter", whereas a country that gives the UK points with a low probability of $...
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Application of Yates's correction in chi-square tests

There are a couple of points related to 'Yates's correction' I cannot figure out. Should I always do this correction when calculating the 'chi-square' criterion for 2x2 'contingency tables' (to ...
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Notation and meaning of a general probability distribution

I had two questions regarding the meaning and notation of a probability distribution when it is not specifically specified. For example, some papers jump right into their approach with notation like (...
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Can the null hypothesis of a t-test of “no significant difference” be used as a result?

I am not so familiar with statistics, since I am a computer science student. I hope it is alright to ask this question here. I am currently working towards the end of a thesis. I compared the User ...
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Can I use t test for a large sample? [closed]

I used a Kolmogorov-Smirnov normality test and the sample isn't normally distributed. The number of observations is 397, can I use a variation test (to see if the two variations are equal or not) and ...
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Potential problems when doing hypothesis testing on large number of variables

I encounter this question in an interview. We were discussing AB testing on one categorical variable and this was the follow up question: what if now instead of one variable we want to test 100 ...
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why there different standard error form in Hypothesis testing

In Hypothesis testing,Comparison of a sample mean with an assigned population mean: $$Z=\frac{\overline x-\mu_0}{\frac{\sigma}{\sqrt n}}\text{ Or }Z=\frac{\overline x-\mu_0}{\frac{s}{\sqrt n}}$$ But ...
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How to test for statistical significance with multiple visits and technical replicates?

I have a data set with 100 columns that's divided between 40 normal columns and 60 MI columns. Samples from each patient were taken at two separate visits, and each sample has two technical ...
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Correction for multiple testing required for combined metrics

Let's say I compare two diagnostic procedures (A and B) and want to check if one outperforms the other one using the metric diagnostic accuracy where diagnostic accuracy is commonly described using ...
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Wald test for Overdispersion in Poisson Regression model

could you kindly help me with the test statistics for performing an overdispersion test in R for Poisson and negative binomial regression models?
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Hypothesis testing for apriori market basket analysis

I'm wondering if there is a possibility to perform hypothesis tests to show that the resulting rules from an apriori market basket analysis are statistically significant? Maybe I'm missing the forest ...
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Comparisons within the control and experimental groups. Pottentialy multiple comparisions problem

I have a question: Does something will be wrong, if me, in addition to comparing the control and experimental groups, I will make an analysis inside these groups? Someone pointed this out to me, ...
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Performing t-test in binary classification problem?

I have a binary data (0 and 1) and I created an XGboost model to predict it. The data are related to insurance contracts, it is a lapse model. The predicted lapse rates are grouped by contractors age ...
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Why the joint hypothesis (F-test) cannot be substituted by multiple individual hypothesis (T-test)

In the book Basic Econometrics (Page254), the author writes: In testing the significance of β2_hat under the null hypothesis, it was assumed tacitly that the testing was based on a different sample ...
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A bit confused on p values on ttest in Stata output

In Stata the output of a ttest shows p values as: Pr(T<t), Pr(|T|>|t|) and Pr(T>t) I understand the two sides to be the tails of the test and the middle ...
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A question about hypothesis testing on non normal distributions

I have a set of 20 distributions (4 sets of 5) none of them are normally distributed but all are qualitatively similar and all have ~700k data points. The images below are a typical example. First ...
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Constructing a Neyman-Pearson Test

I want to construct an NP-Test for simple Null- and Alternative-hypothesis. In particular the likelihood for the Nullhypothesis and Alternativehypothesis is given by $$h_0(x)=\chi_{(-2,2)}(x)\\h_1(x)=\...
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Most powerful test for simple hypothesis for $N(0,\sigma^2)$

Let $X_1,X_2,...,X_n$ denote a random sample from density, $N(0,\sigma^2)$, Find the most powerful test for testing the simple hypothesis $H_0:\sigma= \sigma_0^2$ vs $H_1:\sigma=\sigma_1^2$ where $\...
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Checking Statistical Hypothesis Testing

Let my dataset with $n=100$ samples have the sample mean $\bar{x} = 2.012$ and a standard deviation of $\sigma = 1.057$. Suppose that the data follows a normal distribution with variance $\sigma^2=1$....