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Hypothesis testing assesses whether data are inconsistent with a given hypothesis rather than being an effect of random fluctuations.

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How to determine whether a classifier is significantly better than random guessing?

I have a classifier Y that selects between three categories: A, B and C. I need to be able to quantitatively prove that my model is better (and by how much?), than a random classifier R that randomly ...
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26 views

Statistic of Wilcoxon-Mann-Whitney test with two-sided alternative hypothesis

I am learning about some non-parametric tests. In my textbook (the one that my teachers drafted), it is said that "The Wilcoxon,Mann-Whitney test does not allow testing the two-sided alternative ...
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1answer
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Which statistical test is appropriate if we can not measure normality

Say I have two devices that purifies milk, device A and device B. I assume Device B is better and it produces milk that is 5% better than A. If I want to test this assumption, I take 8 sample from the ...
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statistical check if minimum spec values are exceeded

Detailed fatigue data are available for our materials. These describe the failure probability at defined stress levels with a known log-normal distribution. So I know mean and standard deviation. Now ...
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25 views

T-Test in Excel - two samples, with different number of observations [on hold]

Let us assume that we have two random samples, $X$ and $Y$, where $Y=X+Z$, so $X$ and $Y$ are dependent and have different number of observations. What is more, suppose that $X$ and $Y$ do not have ...
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21 views

Difference between independence and stationarity tests in time series

This is meant to be a general question, aiming to clarify the topic for a beginner in TSA, as I haven't found any clear introductory explaination yet. Suppose I am working with some data which ...
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16 views

What are the implications of asymmetry in the Wilcoxon signed-rank test?

I have samples $a$ and $b$ from pre and post treatment conditions on same participants. The empirical distributions of both these samples are skewed positively. The paired differences $a_i-b_i$ do not ...
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17 views

Inferring incidence from prevalence

I have a data set of patients with a risk factor for disease "A", which can be of grade 1, 2 or 3. The grade is determined by a lab value, i.e. Healthy <20, <...
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13 views

which non parametric test should i use [on hold]

use an appropriate non-parametric test to test hypothesis that the average sleep hours per week is equal between males and females in given population of males 156 and females 115.Use RCommander for ...
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23 views

Where am I wrong? ( Completely solved normal sum)

A sample of 40 observations from a normal distribution X gave $Σx = 24$ and $Σx^2 = 596$. Performing a two-tailed test at the 5% level, test whether the mean of the distribution is zero. What I did: ...
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7 views

TEST: relationship of minority students academic performance to CRT

Which test should I run if I am looking at the relationship of academic performance (outcome) by minority students (nominal variable) to their cultural responsive experience/perception (ordinal ...
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How to choose the correct sample and hypothesis test for spatiotemporal observations?

Consider the following scenario: There exist $N=10$ participants in a study. Each participant $i$ is monitored under baseline conditions and later under experiment conditions. That is, the baseline ...
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Difference between using a confidence interval and using the z-score for a two-sided test?

From what I have read so far, it seems that in a two-sided hypothesis test of the form: $H_0: \mu = 10$ $H_A: \mu \ne 10$ where you choose a significance level of let's say $\alpha = 0.05$, there ...
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8 views

How two calculate the combined likelihood of two independent cues?

I am working on the following setup. A person goes through a maze made of 32 T-intersections. At each intersection they can decide to turn either left or right; each time, on one side there will be ...
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1answer
12 views

MVT/ABn pricing test comparison

I have results for a a 5 variant pricing test: A 0% (control group) B +5% C -5% D +10% E -10% Below are my results (all normalised to give if exactly 20% of traffic goes through the variant, ...
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22 views

How to interpret results of “betareg” function in R?

I have a response variable which is CONTINUOUS and in the form of FREQUENCIES (ranging between 0 and 1 - converted from percentages). I only have a single predictor and it is water level measurement (...
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13 views

What is the accurate null hypothesis for the Hosmer-Lemeshow test?

I've read some works on the Hosmer-Lemeshow test (HLT) but still I'm uncertain what is the exact null hypothesis for the HLT. I'd like to formulate a nullhypothesis as precisely as possible. I think ...
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2answers
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Should I use null models when I do GLM?

I'm using generalized linear models (with negative bin. most of the time) to examine relations between waterbird abundance (response variable) and some environmental variables such as water level (...
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1answer
27 views

proof that p-value is uniformly distributed when the null hypothesis is true

this is a follow up to the following response: https://stats.stackexchange.com/a/11288/221142 the response makes sense if $P=F(T)$ but what if the hypothesis you're testing requires $P$ to be ...
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1answer
23 views

t test of individual coefficient and wald test of euqality of two coefficients

I've run a regression $Y = a + \beta_1X_1 + \beta_2X_2 + \epsilon$, and I have an interest in testing which coefficient of $X_1$ and $X_2$ has a stronger impact on $Y$. Here are the parameter ...
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Estimation of the mean and the the variance in Shapiro-Wilk test

I have started to learn about the non-parametric tests recently. And in my textbook, the introduction to the Shapiro-Wilk test ( a test of normality) is as below: " ... Let $X_1,...,X_n$ be i.i.d. We ...
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Hypothesis testing using spectra

How does hypothesis testing work when a measurement is not a single number, but an entire spectrum? For instance, suppose we want to distinguish a species of plant based on its absorption spectrum. ...
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31 views

Different p-value between KS test and Wilcoxon test

I would like to know if the values in vector A are greater than the values in vector B. Here are my two vectors: ...
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22 views

Using Neyman-Parson Lemma

Let $X$ be a random variable with density $f(x)=(\theta+1)(\theta+2)x^{\theta}(1-x)$, $0 \leq x \leq 1$. Use the Neyman-Pearson lemma to show that the most powerful test of the hypothesis $H_{0}: \...
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Reproducing this chi-square probability from published work

So i'm working on a Greenhouse-Geisser correction and i found this "John, Nagao & Sugiura’s test for sphericity" in this publication (https://www.utdallas.edu/~herve/abdi-GreenhouseGeisser2010-...
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Which statistical test to compare between and within differences?

I have two groups of patients with two different treatments applied, Treatment A vs Treatment B. In addition, I have measurements on 4 different time points for an ordinal variable (scale 1 to 4, ...
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20 views

How do I formally test outliers from a linear regression?

I have a set of data that looks at the area of remaining retina against age. I have three points of data per patient. We know that over time, the area of remaining retina decreases exponentially. I ...
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8 views

Multi-arm bandit Time Lag in the Update

Normally the multi-arm bandit problem relies on an instantaneous update on the success criteria (i.e. CTR either happens or it doesn't instantaneously). What does one do if there is a time lag in the ...
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11 views

Multivariate Test for Mean Equivalence

I am looking for an equivalence test for multivariate means (arbitrary or normally distributed). Any suggestions or hints in the right direction are appreciated.
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16 views

Updating probabilities based on unreliable data

This is a big data problem, matching entities in incomplete data sets, but I'll couch it in other terms to protect the innocent. Let's say I have a town with population 10,000, where a murder has ...
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39 views

$\chi^2$-test for smoothing splines: degrees of freedom

Suppose we are given raw data, e.g. raw mortality rates $\widetilde{q_x}$, which are graduated by a smoothing (cubic natural) spline $S$. That is, we obtain smoothed rates by setting $q_x:=S(x).$ Let ...
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Finding the value of KL divergence to determine whether one distribution is distrinct from another?

Given the KL divergence value between 2 distributions, how should someone use this to determine whether the value is significant for the distributions $P$ and $Q$ to be different? One method I can ...
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What kind of significance test should I use when the dependent variable is being measured over time?

In my experimental design, mice are given 2 small wounds on either side of their bodies. The first wound is treated with an experimental drug A, and the second with a control drug B. Over the course ...
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Testing for difference in means for utility of wealth

Assume you have 2 different investment strategies, A and B. You simulate how A and B perform on the same $N$ time series of returns and compute the resulting utility of wealth. $N$ is large, say ...
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17 views

Appropriate statistical test binary variables

Basic questions, I know.. any help is appreciated! I conducted a survey on people with an impairment. This survey was either filled online, or by phone: the respondent could choose. I want to know ...
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How to test if an event produces behaviour changes?

im learning and im curious about to know if an event generate behaviour changes in messagery application usage. In this case, the hours in which an users gets online for chatting, and the hours this ...
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31 views

P values all equal to 1 after using bonferroni or hommel

Several topics are talking about this but in my case my p values are generated differently. My p values will be calculated simulating $N$ (in this case 5000) random gene groups of size $g$ of the ...
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1answer
21 views

How to test equality of asymptotically gaussian estimators across 3 or more independent samples

Let $n \in \mathbb{N}$ and suppose we are given $K\geq 3$ independent samples $(\mathcal{X}_n^i)_{1\leq i \leq K}$ where $\mathcal{X}_n^i = (X_1^i,\dots,X_n^i)$ is a $n$-sample of i.i.d. real valued ...
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Which statistical test would you suggest I use?

I'll try to keep my question as short as I can: For my study I will include 30-40 patients. For each patient, I will already have retrospective data for creatinine, a substance found in urine and ...
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Test Hypothesis using Binomial Test

I conducted a survey with 116 participants and asked several single choice questions with different numbers of possible answers. I would like to test the hypothesis whether a majority identified the ...
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7answers
468 views

How do frequentists address this paradox of hypothesis testing?

Suppose we sample a person from the population. They are a member of US Congress. We define the null hypothesis $H_0$ as "the person is American". We calculate the $p$-value: $P[member\ of\ Congress | ...
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1answer
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Which of these scenarios are multiple or repeated comparisons?

I believed I knew what multiple comparison or repeated testing meant but upon reading more on the subject and listening to others I have become more confused. My confusion started with A/B testing ...
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Is the Dickey-Fuller tests is a seasonality test as it tests the existence of the unit root?

Knowing that the "Dickey-Fuller tests" tests if the times series is stationary or not by testing the existence of the unit root, after fitting the time series to AR(1) process. Does "Dickey-Fuller ...
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13 views

How to generate train / test data for a classifier with only simulated feature data?

We are working on a binary classification problem for which real world data is extremely rare. We are using an HMM model for performing classification, and the feature data is derived from simulating ...
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8 views

How to demonstrate that a generation process outperforms some others, given a parameter?

Dear statistical stackexchanger, I would like to evaluate whether an algorithm outperforms others for a task of increasing and increasing complexity. I am measuring the impact of the selected ...
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1answer
37 views

test to use while comparing two frequencies

I have a column A with the following frequency distribution for all the values in that column A ...
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1answer
32 views

finding p value for pre/post and treatment/control groups (using r)

I need to find p value for a set of variables in a 2 groups (treatment and control) 2-times scenario (same subjects, pre and post). groups have the same n, with different subjects that have been ...
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What statistical test should I use for my data set?

I have a data set on 20 patients. These patients were administered a cognitive test over the duration of their stay in an inpatient clinic. The cognitive test measured 5 different outcomes (like ...
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Find sample size given mean, stdv, probability [closed]

Management wishes to estimate the average time taken by its workers to assemble an electronic component to within 2 minutes with a probability of 0.95. If the standard deviation of assembly time is ...
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rank-sum statistic Storey and Tibshirani

This seems to be a pretty basic question, but I can't seem to completely follow this definition of the rank-sum statistic. The below can be found in the article Statistical Methods For Identifying ...