# 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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### Chi Square Goodness of Fit vs. Igloo

I am very new to Chi square goodness of fit tests but have done a fair bit of research. Basically, I have the following 12 data points: 7392, 7656, 7241, 6164, 4984, 4664, 15262, 17053, ...
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### Unit testing sampling methods

I'm writing a bit of code that makes pretty heavy use of sampling (eg, MCMC, Particle Filters, etc), and I would really like to test it to make sure that it's doing what I think it is before claiming ...
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### Test on a parameter in which $H_1$ is not complementary to $H_0$. Is this possible?

I have the following problem and I don't know how to solve it. We have a population of $N=20$ enterprises. Each enterprise has a probability $p$ to reduce his customers independently from the others. ...
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### Measuring “uniqueness of fit” or “unique goodness of fit” of a model to some data

Given some parametric model, we can determine the best-fit parameters to some data set. Once we have quantified goodness of fit for each parameter set, we can easily generalize from this to measure ...
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### Failing to obtain $\chi^2(1)$ asymptotic distribution under $H_0$ in a likelihood ratio test: example 1

I have a large sample (a vector) $\mathbf{x}$ from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test the null ...
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### Why do some formulas for statistical power not take into account variance?

I just read this article on power analysis. I want to figure out the size of a sample needed to detect a 1% change in proportions for independent samples with a dichotomous outcome (see "Sample Sizes ...
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### Normality test for circular data

I have some angles and I am wondering how can I test whether the distribution of my data is normal or not. In fact, I want something similar to KS test. Howver, I want to use it for circular data to ...
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### Verbiage on rejecting null hypothesis, Sample Size, testing

I'm new to using statistics in psychology, and I'd like to seek some guidance from this forum. Context: I'm running an experiment involving 5,000 participants. Half of them (2500) will receive a ...
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### Mutant analysis - should the t-test be paired or unpaired?

I have two bacterial strains - one is wild type and the other has one gene deleted. In my experiment, I calculate some observable characteristic (which is continuous) for both of these strains. I ...
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### Tobit for corner solution models: normality and homoskedasticity tests

I would like to regress several explanatory variables (called X) on a dependent variable called Y where Y is strictly positive and continuous. It is left-censored at 0. Y represents how much a ...
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### Hypothesis testing on subsamples and cross validation

When working on very large datasets, identifying effects rests more on quantification than significance and many questions/answers give insight on what to do regarding large samples like this (very ...
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### Are there examples where errors in numerical analysis has caused wrong decisions in statistics?

I read from statistics books that numerical analysis is not in important role in statistics. Are there any examples in history where numerical approximation has been caused wrong decisions in ...
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### Is an ANOVA appropriate?

I am trying to describe a data set measuring toxicity by group with and without a treatment. The data was collected in pairs, such that the researcher would take the difference in toxicity between a ...
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### How to test/validate if a 1% week-on-week drop in a KPI(say Daily Active Users) is significant or due to random chance?

If seen that DAUs of a company are dropping for some time in the past 6 weeks by some small factor, nothing concerning to raise a red flag, just around 1% week-on-week. How can i know if this is ...
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### Testing hypothesis for a fraction

Let's say I have a sample of $70$ people rating a book from $1$ to $5$: $n_1 = 5$ $n_2 = 8$ $n_3 = 20$ $n_4 = 31$ $n_5 = 6$ Where $n_i$ is a number of people who gave a rating $i$. I have to obtain a ...
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### Carrying out a hypothesis test to check whether the marginal effect of education (on wage) is positively related with the level of experience

I used STATA to estimate regression of log of wage (monthly earnings) on education (in years), experience (in years), interaction between education and experience, tenure (years with current employer),...
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### Hypothesis testing, type I and II error

A sample $X_1, X_2, X_3, X_4$ comes from a normal distribution $N(m, 2^2)$. To verify $H_0: m=4$ against $H_1: m = 1$ one uses a test with a critical region: $K = \{4X_1 − 2X_2 − 2X_3 + X_4 < −2\}$....
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### What is a noise-resistant method for testing correlations of proportions

I have a friend who is trying to analyse a large Sanskrit corpus with many verbs in. Verbs can occur in the active or the passive, and they can occur in the past tense or the present tense. She wants ...
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### What is a test function?

From what I understand, when we do hypothesis testing, we compare a test statistic, which represents some data, to a critical value that allows us to accept/reject our null hypothesis. However, I have ...
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### Study association between continuous and categorical variables

I have independent continuous variables like Age, Price and outcome variable like purchased ...
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### What follows after a Mann-Whitney U Test?

I have a statistically significant result for the Mann-Whitney U Test. The groups used are slightly overlapping so what i am interested in now is finding out the best splitting point between two ...