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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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Unsure which data to use for ANOVA test

I have determined that a one-way ANOVA test of variances will work best for my data. However, the nature of my data makes me very concerned about making any claims based on significance or not. My ...
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80 views

Finding the UMP size $0.1$ test with $U\sim\text{Unif}(\theta, \theta+1)$

$U$ is a uniform $(\theta, \theta+1)$ random variable, where where $\theta\in(−0.5,0.5)$. Consider testing $$H_0:\theta\geq0$$ $$H_1: \theta \lt0$$ (a) Give the test function of a ...
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What are the problems if in a AB test the control group is not big enough?

I've been asked to analyze some data but I'm quite new in statistic. I want to compare the means of a continuous parameter in two independent population A and B: A can be seen as the treatment group ...
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42 views

What a tests do I use to show that two parts of observations come from a two-dimensional uniform distribution?

I have a two-dimensional uniform data. I have splitted the data on two parts with a ...
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ANOVA with dependent means?

I want to perform an ANOVA test on where hospital equipment is located within a hospital on different days of the week and months of the year. My dependent variable is the proportion of equipment in ...
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63 views

Appropriate hypothesis contrast between 4 different car brands (fuel consumption)

Is there any significant difference between the manufacturers regarding fuel consumption? I typically use t.test as: ...
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42 views

Type 1 and Type 2 errors trade-off

Reducing Type 1 error will always result in increasing the Type 2 error This statement is false. I understand the definitions of Type 1 and Type 2 errors. What I understand is that there is, in fact, ...
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Determine performance difference after software changes

Situation: For our software package, I want to check if there is performance degradation after software changes. Therefore we measure multiple operations and save the duration in milliseconds. There ...
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30 views

Model selection using p-values - tree inference

Suppose I have some i.i.d. normal observations from $\mathbb{R}^f$ with parameters $(\mu, \Sigma)$ and $\Sigma$ is known to be the identity matrix. I have the following hypotheses: $H_0^i$: $\mu_i = ...
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Hypothesis testing for difference in proportions when given only the 25th percentile (Q1), Median, and 75th percentile (Q3)

I have a question for an exam: A researcher hypothesizes that the proportion of students who spend more than $200 on books is greater for students in the social sciences than that for the students in ...
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1answer
74 views

Relation between t-value and correlation coefficient r

Page 6 of this article shows that following holds for an "independent samples t-test". I was wondering how the equation to the Right of equal sign would change if we consider a "paired samples t-...
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Is there a relationship between the response and predictors?

I have been reading Introduction to statistical learning and I was going through Multiple Linear Regression. This is the topic that Im reading As i was further reading I encountered an equation that ...
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Negative correlation with .000 p value [duplicate]

How do we interpret this result? Also, is a p value of .000 an error? The hypothesis should be tested with a .05 level of significance.
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How to compare agreement of two methods with gold standard?

Let's assume that there are two medical students who both guess the age of several patients. If the actual age of the patients is the gold standard, I can assess the agreement of each student with the ...
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Analysing the coefficients of a linear regression from multiple data sets

I have a constrained regression equation of the form $Y = a_iX_i$ from 10 data sets, where each $a_i \geq 0$ and each predictor $X_i$. Focusing on the coefficients of the predictors (5 terms), is it ...
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14 views

How to test for significance of bias in time series forecasts

Let's say I have some data $y(t)$ for a given series of $t$ values and also some forecasts from a black-box model $\hat y(t)$ over the same values of $t$. The mean of $y(t)$ is greater than the mean ...
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60 views

How can this boxplot be transformed suitably?

In R, I have produced a boxplot for two different groups, with discrete y-values between 1 and 20. My goal from this work is to investigate whether the average count differs between A and B: ...
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Repeated measures ANOVA vs ANCOVA

I’m trying to choose the appropriate statistical test for the reanalysis of a clinical trial. In the original trial, the investigators compared five outcome measures between two groups randomized to ...
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Test for occurrences of pairs from samples with different distributions?

I have two collections of data, A and B, each containing a large number of 10-digit binary strings. For instance, an element of A could be a=1011001111, and an element of B could be b=1001010000. I ...
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25 views

Best way to compare several cases to a null model

At the moment I am doing analysis in some data that is (currently) divided by number of individuals in a group. More or less like: Groups w/ two individuals: Value_1, Value_2, ..., Value_N Groups w/ ...
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160 views

Where is my mistake in this definition of Bayes Factor?

From "The Bayesian Choice" by Christian P. Robert. The definition of the Bayes factor is given to be the ratio of the posterior probabilities of the null and the alternative hypothesis over the ratio ...
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74 views

Multiple regression - Coefficients testing

I have a multiple regression model $Y=12.45+0.072X_1-0.15X_2+0.03X_3+0.17X_4$ with $R^2=0.972$ A second regression model is given as follows $Y=13.77+0.072X_1$ with $R^2=0.855$ The number of the ...
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How to test two or more than two incidence rate (new event/person-time) in r

The Definition of incidence rate is defined as : new event/person-time Now there's my data: ...
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1answer
27 views

Saving p.value of a test [closed]

i used jarque-bera test in a for cycle and i need to save the p-value of the test in a vector. the output of the test looks like this: ...
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2answers
28 views

Test if samples are paired

I have two samples without further information. In order to apply a t-test I want to know if they are paired. Is there a test in R that allows you to check if two samples are paired?
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Fairness of 6 sided die NOT using Chi Square Test

So I was reading a lot of online articles using the chi-square test to determine the fairness of a die. Correct me if I am wrong, but isn't the drawbacks of using a goodness of fit test is that you ...
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Bayesian hypotesis testing, can i use HPD?

I have a statistic question concerning the null hypotesis testing in bayesian inference. I red that i can use HPD for testing the null value in a linear bayesian regression: "We can then use the ...
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Sample size calculation for multiple hypotheses testing on two or more metrics

Let's say I want to run an experiment where there's a control and there's a feature group (say, 50-50 random split). The treatment can affect the feature group in 1, 2 or three ways (or any ...
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1answer
36 views

Can I use bootstrapping technique to get a 95% conf. interval of conversion rate

I have a sample data about user conversion at an ecommerce site. The data contains the following variables: User Id Site visits - count of the number of times the user visited the site during the ...
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1answer
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How do I evaluate the increase/decrease in a set of test scores between two groups?

I have two groups of students, one group who received tutoring, the other who did not. I have the test scores for both groups in the beginning of the year (Mark1). I also have their test scores at ...
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1answer
28 views

Test for significant differences in two groups of binomial data

In a study per-field disease incidences were collected by sampling 35 plants in each field and counting proportion of infected ones (# of infected/total sampled). In result, each sampling location ...
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Hypothesis Testing - Switch hypothesis and get same result?

Beginner to hypothesis testing. Have removed/replaced terminology, but these samples are from real-world populations doing a specific real world action where whichever option they picked splits them (...
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To find the Most Powerful Test (MP test) of the given hypothesis problem

A friend of mine asked me the question below on testing: Let $X$ be a single observation from one or other member of the family $\{f_0(x),f_1(x)\}$ where $$f_0(x)=\frac{1}{2^{x+1}}\mathbf1_{x\...
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What should my critical region look like in this LR test for shifted exponential distribution with pdf $e^{-(x-\theta)}\mathbf1_{x>\theta}$?

I have a small confusion over describing the cutoff point for the critical region in a likelihood ratio test when the null hypothesis is composite. Take this exercise in particular: Let $(X_1,X_2,\...
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1answer
126 views

Basic likelihood ratio test

I should perform a likelihood ratio test on the following null hypothesis : α = Aψ where α and A (p * m) are known vectors. ψ (m*r) is a matrix of free parameters. The likelihood ratio test is ...
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1answer
22 views

Formal interpretation of likelihood ratio tests?

The following is a hypothetical question and I don't have a specific model in mind... Consider two models $M_0, M_1$ such that $M_0$ is nested within $M_1$. I perform the likelihood ratio test with $...
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1answer
42 views

Choose between several confidence interval procedures for randomization test

I am trying to produce confidence intervals for a randomization test of no effect and I've found two different methods in the literature. I have a hard time comparing the two and selecting the best ...
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How to find false negative rate when there are multiple alternate Hypothesis?

I am testing for zero Pearson correlation and my null hypothesis is $\rho=0$. It is easy to find Type 1 error or rejection of Null hypothesis and hence the false positive rate. However, my ...
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How to validate if partitions of a training set have been generated by the same joint distribution?

Following Luxburg (2008) in a supervised learning problem: We do not make specific assumptions on the spaces $X$ or $Y$, but we do make an assumption on the mechanism which generates those training ...
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22 views

Is the R function wilcox.test only useful if samples have same variance?

I have two samples of observations drawn from distributions with different variances. To test whether they have the same mean, I plan to use the function wilcox.test...
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Statistical distribution of randomly-selected distances

As part of a complicated project relating to widgets being sent out to incorrect factories ("missorts"), I am examining a process which involves operators standing on a conveyor belt, removing widgets ...
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Testing that's there's no difference in conversion testing

I am looking at implementing a new website A/B testing tool. Before I turn everything over to it, I want to run a test where I divert traffic to two experiences that are exactly the same and show they ...
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3answers
206 views

How do I prove one company is actually doing better than another?

Suppose I have the return information for two reverse logistic companies--See example data. For certain groups companies A and B each receive 50% of the work from a client, but for another group ...
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1answer
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How to get posterior probability from Bayes factor

I ran into this question in my class and am not sure how to solve it: A positive test result gives you a Bayes factor of 71 in favor of being sick. If your prior probability of Being sick was 0.05, ...
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1answer
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Mismatch on T value obtained from t.test vs summary(lm(data)) on R

I'm doing an exercise on R about the hypothesis testing and I have the following data: ...
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1answer
39 views

Number of samples and Statistical Power

I know that as size of the sample $N$ increases, the $Z$ value increases. But as the $Z$ value increases, that means the $p$ value must decrease. So what happens to $\alpha$ If we had set it to $.05$...
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Recommended significance test for coefficients in regression mixture with bootstrap Standard errors?

I have fit a model that comprises of a mixture of regressions. Within each regression I have an estimate of the coefficient of each covariate within that component regression. The model was fit using ...
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Wilcoxon Signed Rank Test in Python (Reporting Siegel's T vs W?)

While using the Wilcoxon signed rank test in scypy over a subset of populations, I noticed that my test score was reported as zero for an array of differences whose distribution of medians is heavily ...
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2answers
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What's the right stats test?

Could anyone tell me what would be a suitable stats test to look at relationships between 4 continuous IVs and 1 continuous DV between 2 groups each of which has 2 levels i.e. male - female and ...
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Comparing groups? Wilcoxon, Paired test?

I am carrying out a simulation experiment where a fixed number of resources are, at the end of the simulation, divided between two groups of individuals, 'A' and 'B'. There may or may not be the same ...