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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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Understanding Uniformly Most Powerful vs Uniformly Most Powerful Unbiased tests

I am struggling a little to understand the difference between these two classes of tests. Suppose we were testing a simple null hypothesis and a composite two sided alternative hypothesis. I am ...
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Continuous between participant factors

for my doctorate thesis, I would like to test the effect of behavioural inhibition (continuous variable) on stress reactivity in two different groups that will be separated on their past stressful ...
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Use Pooled-Variance T-test or Paired Difference Test?

I am not asking for the answers! I am just confused why the solution is using the pooled-variance t-test, instead of the paired difference test. The samples are undoubtedly from the same population ...
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How to compare model performance across subpopulations?

I'm trying to determine if a model I'm working with performs differently across subpopulations of the general population I'm training on. Let's say that my population $P$ is made up of three ...
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Degrees of freedom of likelihood ratio test with equal dimension on the null and the parameter space?

Let $x_1,\dots,x_n$ be iid samples from a $N(\mu,\sigma^2)$ and consider the hypotesis $$H_0:\theta\in\Theta_0,\,\,\,\,\,\,vs\,\,\,\,\,\,H_1:\theta\in\Theta _{0}^c$$ where $\Theta _{0} = \{\mu>0,\...
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What are the null and alternative hypotheses in this phrase?

Suppose you work for a hotel chain and your boss makes the following claim: “I think that over 50 percent of hotels in large U.S. cities have a swimming pool.” Please test this claim using data from ...
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UMP Test of $H_0 : \theta \leq 0.1$ vs. $H_1 : \theta \gt 0.1$ for iid Geometric Random Variables

Consider $90$ iid geometric random variables having parameter $\theta$ (and thus mean $1/\theta$), and a UMP test of the null hypothesis that $\theta \leq 0.1$ against the alternative that $\theta ...
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Why reject Null Hypothesis when p value< alpha? [duplicate]

As per statistical literature, there seems to be this understanding that given a p value less than alpha, we are to reject the null hypothesis. The way I am interpreting this is that is the critical ...
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How do you test if three means significantly differ from each other using an F test?

I know the means, sample sizes, and standard deviations of three samples drawn independently from three populations. I need to test whether they differ significantly from each other using an $F$ ...
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1answer
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I have a p-value of nearly 1, but my t-statistic is in the rejection interval

I am given two sets of data: price0 and price1, both normally distributed. We denote the means of both sets $\mu_0$ and $\mu_1$ respectively. The question asked is: "For which values of $a$ can we ...
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Measure statistically significant relationship

I've a some data related to servers, there are mainly 2 tables I'm interested in analyzing. server_id | service_type | server_temp | cpu_utilization the other ...
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In R, how would you test for the joint significance of a set of parameters? [duplicate]

I have performed a simple linear regression which consists of an intercept and 20 variables in R. The variables can be seen as two groups, call the parameters for the first group the alpha group and ...
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Did I fill out this F1-Score Interpretation Matrix correctly?

My goal is to make a matrix in order to help me better understand the F1-Score and interpred it correctly in a classification problem. Following my research I came up with this Matrix, but had trouble ...
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What, if anything, is wrong with the SE welcome wagon blog post's statistical analysis?

It's been a while since I've done any major statistics, hence I have to base this question more on a gut feeling than a thorough analysis. It's about this stack overflow blog post https://...
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1answer
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Contradictory Ljung Box results

We want to apply extreme value theory to the maximum yearly temperatures. Before we choose the model we want to test whether or not we can assume independence. First we made a plot of the ...
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1answer
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How can I test whether two logistic regression coefficients are identical?

3 variables (1 continuous (X) and 2 categorical (A & B)) predict 1 dichotomous variable in logistic regression. Both variables A and B are dichotomous and are coded with 1 (reference category) ...
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MAP/MLE/Neyman Pearson Example Problem

I'm currently attempting a practice problem and wanted help checking my work: The random variable X is such that P(X=1) = 2/3 and P(X=0) = 1/3. When X = 1, the random variable Y is exponentially ...
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1answer
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Hypothesis Testing For Two Sample Mean Proportion

We've two samples of size n_1 and n_2 from two different normally distributed populations. We don't know their population means ...
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How can one verify distributional assumptions for testing procedures, if only one draw from each distribution is available

I am currently dealing with a situation in which the Wilcoxon signed rank test (WSRT) is a possible candidate to be applied to the data. So let`s say we have $n$ pairs of Random Variables $(X_i, Y_i)$ ...
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1answer
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Applying inferential statistics for customer data

This may be a dumb question, but I don't understand when to use which statistics. Please explain. So I have the customer data with columns like registration and tenure. Registration column values ...
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P-value for a biased estimator

I am asked the following: Let $X_1,X_2,X_3,X_4$ be $n$ observations, each of which is randomly drawn from normal distribution with mean $\mu$ and variance 25. Consider the null hypthesis $H_0: \mu \...
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Software upgrade before/after: independent or paired t-test?

Before software upgrade, we do a couple of tests for the software performance and after software upgrade, we do a couple of tests to see the results are signifcantly different or not. We assume the ...
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Compare Two Means Without Underlying Observations in R?

I have limited information with which to compare two means, is it still possible in R? We have a group of students (1,000 students) about whom we have mean and standard deviation information, and we ...
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Model comparison for predictors with differently shaped distributions

I want to use model comparison to evaluate the claim "Predictor A outperforms Predictor B in modeling Dependent X". The (potential) problem is that within my sample, Predictor A and Predictor B have ...
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1answer
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Two Means, Different Sample Size, How to Compare Using R?

There is a sample of a student population (1,000 individuals) and from these, some were selected for an experiment (230 individuals). Now I need to compare the average of the original population to ...
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test on fold change of the mean vs. mean of fold changes [duplicate]

Suppose we have 5 subjects. For each subject, biomarker is measured at t0, t1 and t2. Measured values are skewed. We want to compare the values at t1 and t2. When we have skewed data, usually we do ...
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1answer
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Statistical test for the difference in mean for two normal distributions

I have measured $x$ and $y$ and estimated their uncertainty. They are both distributed normally. I found $x = 5 \pm 0.25$ and $y = 7 \pm 0.5$. I want to know if these estimates are statistically ...
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Question about UMP tests collapsing back into a simple null?

So my question is pretty simple. If $\phi (X)$ is a test function that is UMP for testing $$H_0: \theta \leq \theta_0 \space \space \space vs \space \space \space H_1: \theta > \theta_0$$ Is $\...
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t test on original result, log2(result), fold change and log2(fold change)

I have some confusion about t test on original result, log2(result), fold change and log2(fold change). Hope to get some expert opinion on this. Our original results are, for example, some biomarker ...
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1answer
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Do we assume a t distribution for the estimate of the difference of normal distributions?

I am studying hypothesis testing. When performing a one sample t test, we assume a t distribution for the sample mean estimates of the true mean. When conducting a two independent sample test, it ...
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1answer
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Why is the deviance defined with a factor 2 (or likelihood ratio squared)?

Deviance is defined as I see the motivation in why we would define the deviance as a difference of logLikelihoods or just the log(Likelihood Ratio), but why the factor 2? Why square the ratio? Does ...
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Testing whether $X\sim\mathsf N(0,1)$ against the alternative that $f(x) =\frac{2}{\Gamma(1/4)}\text{exp}(−x^4)\text{ }I_{(-\infty,\infty)}(x)$

Consider the most powerful test of the null hypothesis that $X$ is a standard normal random variable against the alternative that $X$ is a random variable having pdf $$f(x) =\frac{2}{\Gamma(...
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Hypothesis testing with beta binomial. Dealing with overdispersion

To make the question more understandable I will use a reproducible example. I have count data, how many connections different groups share with a unique group. In my case I have an upper bound of <...
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What is Deborah Mayo's “severity”?

Can anyone give a detailed (and clear) explanation of what her "severity" means (isn't it just the power function assessed at different discrepancies taken as null hypothesis?) and how it fits in the ...
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Which test to use from a paired data that has only 4 cases of information from each group

I have a question from an exam: A Statistics Professor believes that adding videos of statisticians consulting on applied problems to her standard instructional material will help students solve ...
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Probability of Type II error for simple hypothesis

I'm working through Intro to Probability and Statistics... and I'm a little confused about how to calculate the probability of a type II error, particularly as it relates to a simple hypothesis test, ...
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One-sided hypothesis test (error rates)

Can someone please help me understand how the expressions after the equals (marked in red) are arrived at? I don't quite understand the very last one where the c.d.f. $\phi$ comes into the picture. My ...
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What type of test I shoud use between two samples to compare mean equal.? [closed]

I would do Wilcoxon rank sum test to compare mean equal. In R >wilcox.test(a, b) We can assume non-normality of the samples.
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Confused with What Kind of Test I Should be Using

I have a question from an exam: The chef rates the taste quality of 5 different brands of anchovies. The brands came packaged in both a jar and a can. The chef rates 10 combinations of brand/...
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1answer
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Most powerful test of simple vs. simple in $\mathrm{Unif}[0, \theta]$

Say $X \sim \mathrm{Unif}[0, \theta]$. Denote the observations as $x_i$ $(i=1, \cdots, n)$. Show that any test $\phi$ that satisfies the following two conditions is most powerful test of level $\...
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1answer
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How to realize binomial test in R using data? [closed]

I should do test these data using binomial test (2 first tasks). I have no idea how to do this! I will appreciate any help or mind-joggers!
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1answer
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Looking for a statistical test which will test whether the “spread” from a line is statistically significant

Below are two examples of two x-y data pairs: The top example clearly has more "spread" from any sort of linear trend between x and y. The data points are clustered together but there are some ...
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Binomial distribution, hypotheses testing

Suppose the following instance of the hypotheses testing: suppose that the true state of the coin is that it is either exactly fair, or that it shows heads with probability $0.51$, and there are no ...
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3answers
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Is there a constraint on the sum of the type-I & type II error probabilities?

Is it true that if $H_0$ and $H_a$ are complementary hypotheses of the Binomial trial, i.e., the negation of $H_0$ is $H_a$ then the type-I error $\alpha$ plus type-II error $\beta$ equals 1? Or is ...
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Can the Berry-Esseen theorem tell us whether acceptable inference may be achieved by parametric tests?

I refer in particular to such choices: 1) t-test (or its generalizations: ANOVA or Hotelling's $t^2$) vs its non-parametric alternatives (e.g., U Mann-Whitney test and its generalizations); 2) Pearson'...
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1answer
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which statistical test should I use: 5 schools

I have conducted a study in 5 schools to investigate whether use of a game could improve math performance. In each school there were two classes, one experimental (used the game) and one control (did ...
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Are differences in proportions meaningful in a sample's segmentation

I am setting up an A/B test of a webpage where users will be randomly distributed between either A or B. I'll be using the N-1 Proportion Test to determine which page converts better than the other. ...
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1answer
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randomization/permutation test for mean > 0

I'd like to know if the following procedure is a valid way to test if the mean of a population is greater than zero, based on a random sample of observations: 1) Calculate the sample mean 2) On each ...
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hypothesis testing - gamma distribution

Let W = Y/B0 be a Random variable that has a gamma(2n,1) distribution. [Y has a gamma(2n,B) distribution and W = Y/B]. i) Suppose you want to test H0 : B ≤ B0 against H1 : B > B0 for some B0 > 0. How ...