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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How sampling distribution affects the result of hypothesis t-test

I am aware that t-test can be used for sample that is not strictly normally distributed according central limit theorem. My confusion is that, since the formula of t-test is fix, we can just ...
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96 views

Why use the partial F test instead of testing variables in an isolated model?

Assume that I have $p$ independent variables: $$X_{1}, X_{2}, \ldots, X_{p}$$ I wish to test the hypothesis $$H_{0}\!: b_{1}=b_{2}=0$$ According to the partial $F$-test (Wald test), I need to run ...
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How does one evaluate a null hypothesis of an absolute value of a parameter?

Say I am evaluating a null hypothesis such that H0: |p| = 1 Ha: |p| < 1 And want to understand how this differs in implementation and evaluation from the test: H0: p = 1 Ha: p < 1 Is this ...
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What statistical property is absent in 2-sample hypothesis tests of 5 measurements?

Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $\mu_1$ and unknown variance $\sigma_1^2$. A second random sample from another ...
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33 views

Question regarding Taleb's meta-probability of p-values

There has been one question here regarding Taleb's article The Meta-Distribution of Standard P-Values. I have a somewhat different question, at the very end of the article Taleb claims that: • One ...
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52 views

Two sample t-test vs one sample t-test (use mean of another dataset)

If I compare two dataset for difference using t-test. I am aware that I should use two sample t-test. However, what if I take the mean of one dataset and use one sample t-test instead? From what I ...
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20 views

Equating two different sample sizes [closed]

I have two scores, Score 1 and score 2. Score 1 has 150 samples and Score 2 has 85 samples. Is it possible to equate scores, especially using R packages?
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33 views

Is the t-interval and student's t-distribution the same?

I'm taking this course on statistical inference through datacamp. The instructor went over the idea of a confidence interval. The instructor said that we take a large number of bootstrapped samples ...
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38 views

What's the right way to make a null distribution?

I want to run an a/b test. I'd like to check if my results in the experimental variant are extreme, under the null hypothesis. I haven't created my sample, yet, and I'd like to do a power analysis to ...
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1answer
70 views

Appropriateness of nonparametric bootstrap methods to assess difference between two groups [closed]

This question is motivated by the discussion of this earlier question. I have two samples $X$ and $Y$, where both samples have $n$ elements. Both samples represent optimal solutions returned from two ...
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573 views

2 sample t test for sample sizes - 30,000 and 150,000

I have 2 samples, one with sample size of 30,000 customers and the other with 150,000. I have to perform a 2 sample t test(on conversion rates of the 2 groups). My question is, will t test in this ...
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Does heteroskedasticity matter when estimating a regression using the entire population?

The F-statistic, t-statistics, p-values and standard errors of the estimated coefficients will all be incorrect in the presence of heteroskedasticity. However, does this even matter if I am working ...
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How to interpret the results of a t test?

I'm currently in an undergraduate statistics course and we are investigating a dataset with R. The dataset is traffic data for roads in the state of Kentucky. We formulated hypothesis about the mean ...
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12 views

Strings coming from distinct distributions

I have a binary classification problem. Two distinct classes of strings are available. The strings are of fixed size and made of three different characters only. I have around $10000$ instances of ...
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59 views

Approximate the critical region such that the size of the test tends to $\alpha$

Consider this question, Suppose $X_1, X_2, . . . , X_n$ is a random sample from an exponential distribution with mean $\lambda$. Assume that the observed data is available on $[X_1], . . . , [X_n]$,...
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p-value definition and inadequacy of tail events [duplicate]

Wikipedia defines p-values as (The probability of obtaining a test statistic) equal to or more extreme than what was actually observed For starters, usage of extreme there is subjective. To make ...
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30 views

Meaning of “was produced by the null hypothesis”

There was a question about p value interpretation and one of the comments made me wonder whether there is some basic misunderstanding I have about p values. I wrote "you can discard the null ...
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24 views

Score test for multiple parameter model

Suppose I have a multivariate linear model: $y = Z\bar{\alpha} + x\beta + \epsilon$ Where $Z$ is a matrix of covariates and $\bar{\alpha}$ are their effects. I refer to them as covariates as I am ...
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374 views

Understanding p-values using an example

Definition of p-values: A p-value is a probability that provides a measure of the evidence against the null hypothesis provided by the sample. Smaller p-values indicate more evidence against null ...
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19 views

Comparing the First Names in two population samples

I'm not great at stats and hope for a bit of help ... I have two sets of peoples first and last names the first group has about 5000 unique first and last names and the second about 300. When I ...
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1answer
13 views

What statistical method should I resort to to analyze the generational difference?

So I would like to analyze the value attitude differences between two generations (Young people's generation and their parents' generation). I understand that normally independent t test or Anova can ...
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2answers
102 views

How to report t statistic from R

I'm wondering how to report the result of a t-test from R given that the degrees of freedom change when the lengths of the vectors are the same. For example ...
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Durbin-Watson test and coefficient significance yield different conclusions?

I'm not sure where my confusion is stemming from, but it seems that equivalent tests (Durbin Watson, and a simple significance test) for serial correlation in the errors (of lag 1) sometimes yield ...
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1answer
140 views

Interpretation of R output from Cohen's Kappa

I have the following result from carrying out Cohen's kappa in R ...
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12 views

2 way ANOVA one repeated measures factor and percentages

We're investigating the effect of two different types of feedback on motor learning. We have two groups that performed 4 different tests and we'd like to see whether an interaction between these ...
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23 views

How to know which statistical test to use?

I'm working on a project and was wondering how I could perform statistical tests between two correlations to prove significance. The background of my project is that I was trying to see if Twitter ...
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24 views

Confusion regarding multiple testing correction

Here is what I am confused about: Say we have conducted multiple hypothesis tests on the same experiment. One test gives insignificant p-value only after correction is applied. If I happen to ...
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25 views

SPSS Paired Samples T-Test outcome interpretation

Hypothesis: -Blood pressure will decrease after intervention Results (blood pressure): Systolic bp before mean: 102.00 Systolic bp after mean: 97.10 Diastolic bp before mean: 70.80 ...
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27 views

Is there a test for omitted variable bias?

I study finance and economics and every time i study an econometric study with OLS regression i wonder how the author can be sure of the non existance of omitted variable bias. I guess that in almost ...
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2answers
33 views

Testing a null hypothesis using positive and negative z-score; accept or reject

Theorem:: To test null hypothesis $H_0$: $p_0$=$p_{1}$ versus alternate hypothesis $H_1$: $p_0 \ne p_{1}$ at the $\alpha$ level of significance, $H_0$ should be rejected if $z$ is either $(1)\le -z_{\...
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30 views

Questions about Uniformly Powerful Test

I'm using likelihood ratio test and I got to the point where I need to find the distribution of the sum of X1^m, X2^m...Xn^m. My work so far:
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2answers
46 views

How to find out if there is any real pattern in the data set?

Let's assume that we have a regression problem (in the machine learning sense). Our data set consists of pairs of features vectors and numeric targets. It might be the case that there is absolutely ...
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23 views

Null and alternative distribution of test statistic

This question is based on this paper. I am trying to find out whether two samples ($S_p$~$P^n$ and $S_Q$~$Q^m$ ) are drawn from the same distribution. So my $H_0: P=Q$ and $H_1: P \neq Q$. I have also ...
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Hypothesis testing on two disproportionate samples

I want to conduct hypothesis testing on conversion rate of two disproportionate samples. One contains 20k Data points and other contains 180k datapoints. How can I do a hypothesis testing on such ...
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Compute an approximate power when lambda = 10

I wanna reconfirm, is this the right way to answer this question? I'm pretty confused. And if not, how?: Answer: Thank you so much.
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24 views

Indicator function expression for two sample test

I am trying to understand the theory of this paper. Basically, the paper tries to lay down a framework for using two sample tests using binary classifiers. Let there be two samples $S_p$~$P^n$ and $...
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35 views

Calculating empirical p-value for Anderson-Darling test

I have the data $x_1,\ldots,x_n$. First, I fit the stable distribution to this data and obtain a vector of estimated parameters $\hat{\theta}$. Now, I want to use Anderson-Darling test for stable ...
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Providing Statistical evidence that credit portfolios have different risk behaviour

I work in the risk department of a credit company and I was asked to analyse and bring some statistical evidence that two portfolios have different risk behaviour. So, my goal is to find if, for ...
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24 views

What statistical signifcance test should I use?

I would like to compare the averages of two list of numbers, and see whether one average (from one "system" output) is higher than the average of another in a statistically significant way. I already ...
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1answer
31 views

How to check if a data is poisson sampled?

I was reading one article which develops a theory for the Poisson sampled data. That is the data is collected over time-points $\{T_k, k>1\}$, which are jump-moments of a homogeneous Poisson ...
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23 views

Forward Model Selection Using p-value

I know that it is not advised to use the p-value as the criterion in practice, but I am not asking about that. I am wondering how this p-value would actually be calculated. In other words: Forward ...
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1answer
19 views

comparing incidence rate

I have a data set of individual level data for the outcome in question. I also have aggregated data (at a national level) from which I'm obtaining the denominator. Using this information, I've ...
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2answers
40 views

checking of correctness of excel program for F test

i would like to express my doubt about F test performed by Analysis toolpak , let us consider following link F Test in excel everything seems ok until calculation of one tail critical value, ...
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1answer
105 views

Does the UMP exist?

Suppose $X_1, X_2, X_3,\ldots, X_n$ are i.i.d. random variables with a common Poisson$(\lambda)$ distribution. $$X=(X_1, X_2, X_3,\ldots, X_n)$$ and $g(λ)=\lambda(1 - e^{-λ})$ Is there a UMP (...
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3answers
218 views

How to test the equality of two Pearson correlation coefficients computed from the same sample?

Is there a reliable way to say if two Pearson correlations from the same sample (do not) differ significantly? More concrete, I calculated the correlation between a total score on a questionnaire and ...
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2answers
141 views

How to test whether $\mu_1 < \mu_2 <\mu_3$?

Suppose I have three independent groups, with mean $\mu_1,~ \mu_2,~\mu_3$ respectively. How can I test whether $\mu_1 < \mu_2 <\mu_3$ or not using $n_1,~n_2,~n_3$ samples from each group? I ...
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1answer
16 views

Spikes impact on time series stationarity

I have a demand time series that are highly impacted by promotion (spikes). Do spikes violate the assumptions of stationarity? Can we apply the KPSS test or ADF to test whether the series is ...
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1answer
90 views

Comparing ways to create a composite score

Objective: I have biomarkers $X_1,\ldots,X_p$ (all in continuous scale) and a binary dependent variable $Y$. Because $p$ is large (there are many biomarkers), I want to make a composite score ...
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Find the most powerful test

This question appeared in ISI 2004 MStat sample paper. On a particular day let X1,X2 & X3 be the no. of boys born before the first girl is born in hospital 1, 2, 3 respectively. If the ...
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1answer
97 views

Likelihood ratio test of log normal distribution

$X_{1},X_{2}, … , X_{n}$ be a random sample from a $𝑁(\theta, 1)$ distribution. Instead of observing $X_{1},X_{2}, … , X_{n}$, $Y_{1},Y_{2}, … , Y_{n}$ was observed where $Y_{𝑖}= 𝑒^{X_{i}}$. Find ...