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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White's Reality Check Hypothesis Testing question

I am running a hypothesis test based on White's reality check p-value. I am getting a weird result for my univariate time series of returns. In essence, I am following a code on MATlab to run the test ...
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Hypothesis testing question (two Bernoulli sequences)

Consider two sequences of random variables: and . X_i's are drawn iid from a Bernoulli distribution D_1 and Y_i's are drawn iid from a Bernoulli distribution D_2. If it makes things easier assume ...
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Relationship between observations [on hold]

My question is how can test the hypothesis H0 H0 : Relationship between observations. How to get this? Thanks.
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How to quantify and test Cricket statistics, the model is number theory based? [on hold]

For forecasting cricket scores, last year I developed an highly simple 'congruence' based formula. In a live match, we note down the data of wicket one, wicket two batsman. We add the balls faced to ...
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10 views

How to test statistical significance to prove that a particular technique estimates a variable better than another technique?

Suppose the following is the scenario: I am estimating the measure of a construct. I have Subject Matter Experts (SME) who have manually (through observation) estimated the measures. Suppose I have ...
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Appropriate test for comparison of 50+ groups

I am currently working with a data set containing several hundreds of thousands of instances for which I am trying to find the most appropriate analysis. The goal is to determine whether there are ...
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19 views

How to Collapse Correlated Data for Wilcoxon Signed Rank Test and Sign Test Such that the Power Loss is Minimum?

Data Description: I am trying to evaluate my algorithm against 1 benchmark and 3 other algorithms (so, 5 total algorithms). I collected some data using the following procedure: I feed 10 iid ...
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2answers
36 views

Parametric vs Non parametric test difference

I'm reading PDQ Statistics[1], I have a small base of statistics and I can't figure out this statement from the book. They assure in the book that It seems that most people who have taken a stats ...
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How do I compare the size and power of the tests?

Let $X_{1},\dots,X_{9}$ be a random sample from $N(\theta,1)$, where $-\infty<\theta<\infty$. Consider the following two tests for testing $H_{0}:\theta=2.5$ against $H_{1}:\theta=4$. Test1: ...
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1answer
50 views

Likelihood Ratio Test statistic for the exponential distribution

I need to test null hypothesis $\lambda = \frac12$ against the alternative hypothesis $\lambda \neq \frac12$ based on data $x_1, x_2, ..., x_n$ that follow the exponential distribution with parameter ...
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Determining minimum required sample size for control (for purposes of measuring lift)

SO in a sales setting where people can either buy or not buy (i.e. binary response), say I have a treatment that I know (or believe strongly) to be effective. I want to give it to as many people as ...
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22 views

Interim analyses without any stopping rules

I've got some questions about interim analysis rules. Do I need to make alpha/beta corrections in the following situation: One interim analysis is planned in the study The interim analysis is ...
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13 views

power of regression coefficient tests

does anyone know how I can calculate the power of a regression coefficient test in R? for example we have: H0:B0<=9 and H1: B0>9 if actually ...
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3answers
67 views

Why do we do hypothesis testing on estimates of linear regression?

I was reading about linear regression and what I understood is that once we minimize OLS equation we get the beta parameters. Its just like solving a normal equation to get the unknowns. Then why do ...
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21 views

Measuring change in performance over time

I have two performance scores for multiple companies over a ten year period (10 sets of scores, one set for each year). Which would be the best method to test the hypothesis that one score has dropped ...
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16 views

Do the number of choices in a A/B test affect sample size needed for statistical significance?

I apologize if I sound too stupid, but my statistics knowledge is very basic. I'm a software engineer and I'm conducting an experiment over web page conversions in which I'm trying to determine the ...
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1answer
64 views

Null-hypothesis testing and likelihood-ratio testing

In this book Wickens, T. D. (2002). Elementary signal detection theory. Oxford: Oxford University Press. You can read: and this confuses me as I thought that likelihood-ratio testing was a ...
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14 views

What test used when DV is Ordinal and IVs are ratio?

I have a problem in doing my research. I want to predict the rank of a variable (that is, dependent variable) based on some factors (independent variable) that influence the dependent variable. The ...
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20 views

testing nonlinear hypothesis glm R

I estimate probit model: \begin{align*} P(y=1|x_1, x_2, x_3) = \Phi(\alpha_0 + \alpha_1 x_1 + \alpha_2 x_2+ \alpha_3 x_3) \end{align*} using: ...
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26 views

How to use Taguchi method when doing online multivariate A/B testing?

I want to run a multivariate test on my website landing page. I have a click on subscribe KPI, and I want to test many different color / calls to action / positions on that button. I heard of ...
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47 views

Statistical analysis flowchart implementation in R

I have seen lots of flowcharts describing the different questions you should ask yourself when doing statistical analysis and the corresponding tests you should run based on your answer. For instance, ...
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1answer
24 views

$p$-value for non-standard asymptotics

Suppose I have an asymptotic result like $$\sqrt{n}(T_n - \theta) \overset{D}{\to} \sum_{i=1}^k \lambda_i X_i$$ where $X_i$ are independent $\chi^2_1$. i.e. some test statistics $T_n$ is ...
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How to calculate sample size for testing H0: Y is related to X by a sigmoidal function?

I'm assuming I would need to specify a given functional form and conditional standard deviation for Y at each X. That would give me some parameters to be estimated and I would need to set a threshold ...
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19 views

What statistical methods should I use to assess the influence of a nurses's demographic profile on their attitudes and practice?

Im trying to prove my hypothesis: The demographic profile (age, sex, length of nursing service, religion, area of assignment, and relevant education on the care of dying (answerable by yes/none) ...
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20 views

Multiple comparison FDR for positively correlated p-values and test statistics

I have the following scenario: I have sampled two subjects on three days. I am looking for a consistent and statistically significant difference between two collections of measurements (call them A ...
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10 views

Chi squared test on multiple survey responses?

I have completed a questionnaire using a variety of categories (i.e. some questions are yes/no, some are a different categories etc.). I want to find out whether there is a relationship between age ...
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18 views

Hints to find the confidence interval

Que. Consider a normal population with unknown mean $\mu$ and variance $\sigma^2=9$. To test $H_{0}:\mu=0 $against $H_{1}:\mu\ne0$, a random sample of size 100 is taken. Based on this sample, the test ...
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15 views

Test for Equality of Parameters in Beta-Binomial Distribution

With binomially distributed data, it's straightforward to test the null hypothesis of equiprobable responses, $H_0: p=0.5$, but say you want to test the analogue in a Beta-Binomial model fit to ...
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21 views

Proper way to test hypothesis of random selection?

Suppose I have $N$ urns, each containing various mixes of red and green balls. A subject is to make a random selection without replacement of $M$ balls from each of the urns, whereupon a count is made ...
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29 views

confidence intervals for one sided test of proportions

I am interested in running A/B tests on differences in proportions and reporting the confidence intervals to convey the precision of the test. Tests would be of the form $H_{o}: p(a) \geq p(b)$ vs ...
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12 views

Gap Test Random Numbers: Special Case

How many gaps can I consider for a number like |10121| or a number like "|01111|"? I'm using the gap test by digits, so for the first number I consider 3 gaps or only one, and for the second number I ...
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18 views

Minimum sample size for 1-tailed hypothesis testing

Let's say we have some endangered species of animals, whose population is 10,000 and dwindling due to some disease they all carry. And say I want to be able to test the efficacy of some new drug (with ...
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15 views

A/B Testing and statistical significance [duplicate]

I often read that when you are running a website conversion a/b test, if you see a 5% significance level before you hit your sample size, you should discount it, and that the more often you compare ...
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10 views

How to avoid a high familywise error rate in case i can't favor between tests?

If i can't favor between tests , what should i do to avoid high familywise error rate. For example, I am doing a meta-analysis i believe that some variables might explain the heterogeneity like Year ...
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42 views

How do I get which experiment is doing better using the Mann-Whitney U Test?

The material I got only described how to test if there is difference (null hypothesis: H0 = H1). However, what I want to test is if the test version is doing better than control: null hypothesis: H0 ...
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Testing for the ordering of several means

We have delineated 4 groups into a population and have a theory according to which the distributions of a certain characteristic of this popular are ordered in the sense that $\mu_i > \mu_{i+1}$ ...
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1answer
71 views

Sexuality of Dog Owner

My girlfriend told me a weird thing. She said "All of my friend who have a chihuahua dog is gay." and "I think a gay guy likes that dog." The story about her friends seemed true, and I got bit ...
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22 views

Comparing variances of forecast errors

I am forecasting a weekly commodity price series. I use a rolling window for estimating my model, and from each window I make point forecasts for one and two steps ahead. I want to investigate ...
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2answers
44 views

How to assess difference in binary variable between two groups

I have $3$ groups ($n_1 = 30$, $n_2 = 20$, $n_3 = 5$), and I am looking at anxiety scores, which is binary (0 = no anxiety, ...
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1answer
18 views

Best critical region and Neyman-Pearson lemma?

I'm reading an online course and I'm really confused about the Neyman-Pearson lemma. It states From my understanding, does it mean that critical region could be any region like (a,b) and (c,+00)? ...
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23 views

Bayes factor from posterior odds

I tried to answer my own question Comparing two Bayesian models under disjoint prior supports using MCMC. Here is my intent. I am not confident in what I wrote so prefer to post it as a question : Is ...
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27 views

How can I compare two datasets statistically with using distribution of the numbers in each class

I have datasets ordered based on the date in each class. Consider each number represents a company and each list is a specific customer`s visit pattern. For example customer a1 visited company ...
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16 views

Which test(s) can be used to capture a change in non-linear correlation over time?

Is there a test that can capture a change of correlation in a part of the dataset, i.e. year on year? Essentially I would like to understand and measure if the "local" correlation increases in a ...
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interpretation of CAPM test

the CAPM is the Capital Asset Pricing Model. If i test the null hyphotesis that all intercepts of a multiple regression (where the dipendent variable is a equity and the indipendent is the market ...
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46 views

Can BIC be Used for Hypothesis Testing

Define the Bayesian information criterion as $$ \mathrm{BIC} = {-2 \cdot \ln{\hat L} + k \cdot (\ln(n) - \ln(2 \pi))} $$ (I do not drop the constant, $ - \ln(2 \pi)$, to avoid issues when equating to ...
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22 views

How to compare the feature importances produced by two different classifiers?

In one study, I am using two different classifiers. I want to compare the feature importances produced by two classifiers. Is there a statistical technique to measure the similarity between the two ...
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G test with small observed counts (~zero)

I have an experiments that counts how many events happened during a certain period of time. The experiments is repeated many times in different "runs" (I have 65 runs). Here for example the list of ...
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1answer
30 views

Clustering and A/B testing

My question is the following: Let's imagine I've defined clusters in my data (different segments of customers) and I run an A/B test. Can I compare the performances of the different clusters on the ...
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1answer
28 views

Check population randomness in an A/B test?

I am fairly new to A/B testing and I don't really understand some points that my colleagues make. On our website users are randomly assigned to A or B when their session start (by randomly assigned, ...
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20 views

Crossover study, multiple measure

I'm trying to analyze data from a crossover study, where two treatments ($A$ and $B$) are applied to $n$ patients (each patient receive both treatments). For each treatment I have an outcome with ...