Hypothesis testing assesses whether data support a given hypothesis rather than being an effect of random fluctuations or some other process described by an alternative hypothesis.

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Statistical comparison between binomial distributions, two groups and many trials

I have a data set with two groups. I have multiple trials with different Ns in each trial, and different numbers of trials for each group. In each trial, for each ...
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10 views

How should I compare these three groups?

My situation: I am assessing outcomes of a university course redesign. One of the goals of the redesign project was to increase successful course completion, as measured by a decrease in the course ...
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9 views

Is data poisson distributed when comparing mean sample occurrences per area?

A question similar to this came up in a colleague's analysis and I cannot seem to decide the right way to think about this. The question is a moot point for her work, but I'm interested in the ...
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3answers
113 views

Statistical test for increasing incidence of a rare event

I have following simulated data of 2500 persons regarding the incidence of a rare disease over 20 years ...
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47 views

What statistical test should I use for variable which has all values identical and zero?

I'm a neuroscientist and I count protein aggregates in the brain. I use tissue from MND patients with and without a certain mutation, and from healthy controls (3 groups in total). When I use healthy ...
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1answer
12 views

Correlation or dependence between NDVI and pollution data sets

Is there any statistical test or measure to evaluation the degree of correlation or dependence between two sets of data-points ? First set is represented by NDVI values in each pixel and second set is ...
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1answer
19 views

How to check if the correlation between two continous variables is influenced by a categorical factor?

I have a data frame (df) where I see correlation between two continuous variables (c1 and c2). I need to know whether the observed correlation between the two variables differs between groups, which ...
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21 views

Post-hoc analyses with a synthetic control?

When running a traditional hypothesis test, it's common to "break out" the result by sub-groups using various post-hoc methods that control for multiple comparisons, such as the False Discovery Rate. ...
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16 views

Cutoff point detection question

Suppose I have two methods $A$ and $B$ that can be used to measure the value $y$ for an outcome variable given the value of an explanatory value $x$. The following figure shows the scatter-plot of ...
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1answer
27 views

Testing for differences between populations of individuals with binomial data

So I am trying to compare between populuations and determine whether there is a difference in count based data. My data look like this: ...
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1answer
61 views

Significance of regression coefficients and their equality

Suppose, we want to regress $y$ on $x_1$ and $x_2$, i.e. $$ y = \alpha + \beta_1 x_1 + \beta_2 x_2 + \varepsilon \hspace{1cm} (1)$$ Is it, in principle, possible that simultaneously: $\beta_1$ is ...
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16 views

Maximum lag selection for panel unit root tests

I am interested in conducting panel unit root tests on a panel of subregional annual data where N>100 and T<10 (more specifically, depending on the independent variables included in each ...
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2answers
20 views

Test Control. A longitudinal study

I have two samples of the same size, one being the 'treated' group, and the other used as a 'control' group. Each group have a different univariate variable (stress level), repeatedly observed over ...
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13 views

Regarding Bootstrap Hypothesis Test for difference of means, why not absolute differences?

Looking at the Algorithm 16.2 from "Introduction to the Bootstrap, Efron and Tibshirani" I was wondering why isn't the t(.) being tested the absolute difference of the means, instead of the ...
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25 views

Figuring out which test to use

It's been a while since I've taken a stat's class and I came across a problem I need to solve. I was hoping someone could point me in the right direction. I know a question similar to this has ...
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1answer
29 views

What is a good test for comparing frequency counts between two groups?

I am looking for statistical methods used to compare frequency of observations between two groups. I have two geographical locations with data on different soil types present. for example, my data ...
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2answers
89 views

Why reject, not accept $H_0$ when $p$ value less than $\alpha$? [duplicate]

Let's say ABC drug company claims their medicine cures 90% of patients. Now a doctor conducts a trial by taking a random sample of 15 patients. Result shows 11 of them are cured but 4 are not. In ...
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24 views

Sampling Distribution of Sample Correlation Coefficient

For a linear process $X_t=\mu+\sum_j\varphi_jW_{t-j}$ where $W_t$ is white noise and $\mathbb E(W_t^4)<\infty$ , $$ \begin{pmatrix} \hat\rho(1) \\ \hat\rho(2) \\ \vdots \\ ...
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763 views

If all 1000 test patients are not cured by the drug, can't we say that we accept the null hypothesis?

In many places I have read that we can never say that we "accept" the null hypothesis. Instead we must say that we "fail to reject" the null hypothesis. But I don't see how that squares with this ...
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72 views

Karlin-Rubin theorem and exponential family

Let $X_1,...X_n$ a random sample of $X$ with density $$f(x;\alpha,\beta)=\frac{\alpha}{x^{\alpha+1}}\beta^\alpha I_{[\beta,\infty]}(x)\space\alpha>0,\beta>0$$ with $\beta$ known. Find ...
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1answer
24 views

Joint inclusion probability for Horvitz–Thompson estimator

There is a Wikipedia page for the Horvitz–Thompson estimator. It is an estimator for the population total. Unfortunately the page has failed to state the standard error. From here, the standard ...
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1answer
21 views

Which is the best way to check (with some certainty) if the mean of a time series is a constant?

I am testing the time series output by a light sensor, and trying to know when dawn and dusk end. I used a cusum test to check when light level starts changing, and now I need to know when it ...
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1answer
20 views

How to quantify whether the difference between two groups is relevant?

I'm sorry that I am not at all an expert in statistics, so my question may sound vague, or very easy. I have a group of people that I divide into two categories, $A$ and $B$, depending on some ...
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1answer
14 views

Comparison of time series models

I'm trying to create a model for a series $X = \{X_1, X_2, ...\}$. I don't assume that the $X_i$ are identical distributed nor that they are independent but at least that they have something in common ...
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1answer
21 views

Joint Hypothesis Testing in Multivariate Regression

I am fitting the following model to my data $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$ and the claim I want to be able to make is that $\beta_1 = 0$ and $\beta_2 \neq 0$. I am going to use ...
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2answers
27 views

Test for statistical significance in performance variability

I'm analysing data collected from a call centre activity in which agents are calling prospective leads. For each call made, if the lead coverts the call is a success and if the lead does not convert ...
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1answer
72 views

Ways to find a UMP test

I'm studying for my final exams and the subject of proof will basically test hypotheses, I will try to summarize here my doubts. For found the UMP test the ways are 1) Use Neyman–Pearson lemma ...
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1answer
26 views

Possibility to run multiple chi-square tests on 2x5 table

I'm analyzing data in which I have a dependent variable with two possible outcomes (yes or no) and an independent variable with five emotion conditions, neutral, angry, sad, ashamed, and afraid. The ...
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1answer
86 views

What tool should I use to find improper relationship between doctor and patient?

I have a data table in R where I summarized the dollar value of prescribed medicines for each doctor-patient combination. In all, I have about half a million observations, with about 3000 doctors and ...
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1answer
25 views

Test of proportions or chi-squared? [duplicate]

These data are from an A/B test of free trials to conversion. Someone can sign up for a 30 day free trial of the product. If they like it they stay on and become paying customers. By default (A), ...
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42 views

Easy Stats analysis?

Would be grateful if anyone can help. I have answers to a questionnaire and I want to compare between group A and B, possible say there is no difference in their response between these two groups. ...
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0answers
47 views

Embarrassingly easy stats question

I have a large set of values (1000) that are each a measure of accuracy for a large set of corresponding models that were generated using random data. I want to compare a single measure of accuracy, ...
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1answer
46 views

How to handle multiple measurements per participant, with categorical data?

I've done an experiment where I've collected measurements from a number of participants. Each relevant data point has two variables, both categorical: in fact, each variable has two possible values ...
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Test analysis - repeated measures

I lack the experience and can't find an answer anywhere at the moment. The situation is as follows: I would like to test a new device measuring the heart rate of a patient. For this, I have observed ...
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63 views

How to test the difference in two proportions when the outcomes aren't binary?

An e-commerce website is testing two different designs for a checkout page. Customers who visit the checkout page are randomly presented with one of the two designs. The first metric of interest, ...
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2answers
32 views

Relationship between distributions and hypothesis testing

Here on chi-squared distribution wikipedia page is mentioned that many statistical tests use chi-squared distribution. I would like to ask why? What is so special about chi-squared that predetermines ...
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1answer
26 views

Studying the distribution of the p-value?

I have two data vectors $X=(X_1, X_2, \dots, X_n)$ and $Y=(Y_1, Y_2, \dots, Y_m)$ where $X_i \overset{iid}{\sim} P$ and $Y_i \overset{iid}{\sim} Q$, and I am performing a two-sample test (i.e KS test ...
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31 views

Inference of user activity on binary condition variable

I recently ran a test on our application that models a fairly contrived example: Users are expected to add things to a bucket. We count the things in this bucket. A binary condition variable exists ...
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In-Class Hypothesis Test Activity

I am teaching introductory statistics to a group of gifted middle-school kids. We are covering hypothesis testing tomorrow (starting out with the z-test, then 1-sample t-test, etc.). Do any of you all ...
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1answer
28 views

Pairwise non-parametric test for small sample sizes

I was asked to check a small dataset (3 replicates for 5 treatments, each) for significant outcome differences. I give an example: The variance within replicates in the data cannot be assumed ...
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35 views

Correlation between two samples of different size

I have all price quotes from a stock (to be more precisely CSAN3 from Ibovespa Exchange - Brazil) from 2010 to 2015. I was asked to get the correlation from the log returns year-by-year. This is ...
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2answers
35 views

Statistical significance / hypothesis testing for web experiment

I'm running a test where two groups of people are shown two different sets of search results or suggestions. We track what percentage of results each person is happy with. I've shown histograms for ...
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1answer
34 views

Plotting power curve for a two-sided binomial test in R

n = 30 p = 0.35 p_hat_seq = seq(0, 1, 0.01) sd = sqrt((p * (1 - p)/n)) z = (p_hat_seq - p)/sd plot(pnorm(z), type = "l", ylab = "Power") Here the sample size n ...
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60 views

Ranking based on binomial data (example: website conversions)

Let's say I have a database of all websites and their corresponding viewers and buyers. I want to rank the websites based on the conversion rate or where we see more conversion. So example: ...
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20 views

Incorporating uncertainty in hypergeometric probability test

Wikipedia's page on determining the hypergeometric probability describes the variables in the following way: N is the population size, K is the number of success states in the population, n ...
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1answer
26 views

Testing for three means in order

Say I have data as follows: type|value where type takes values $A$, $B$ and $C$ and value is ...
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1answer
18 views

T-test equal variances, unequal sample sizes

I have two groups with equal variances and unequal sample size (28 and 8) and I want to run a Student t-test. Can I use Mann-Whitney considering that the variances are equal? Do you think if there is ...
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3answers
68 views

Is power always associated with hypothesis testing?

Suppose I know that the true population proportion of a mutation is p = 0.3493119. I want to know that given power = 0.8, what's the proportion of of mutation in my sample of n = 30? Here's what I ...
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1answer
38 views

Neyman-Pearson Lemma and hypothesis-testing

Consider testing $H_0:\theta=\theta_0$ vs $H_1:\theta=\theta_1$, where the pdf or pmf corresponding to $\theta_i$ is $f(x|\theta_i)$, $i=0,1$ using a test with rejection region R that satisfies ...