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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Test that a group of probabilities is different from chance - in either direction

Suppose I have subjects sort 10 images into the categories "Group A" or "Group B". I want the null hypothesis to be that subjects are randomly assigning the images, and the alternate hypothesis that ...
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4 views

How to test hypothesis on the composition of CAPM portfolios

I'm facing two different portfolios in CAPM framework derived as $$\hat{\omega}_P=\hat{\Sigma}^{-1}\frac{E(r)-r_f}{H}(\hat{\mu}-\iota'r_f)$$ on the same assets but, for example, on different time ...
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5 views

convergent and discriminant validity test

Is it correct to do convergent and discriminant validity test (factor analysis, KMO, Pattern Matrix) of my research instrument only on independent variables? I use TAM in my study and found, that it ...
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0answers
4 views

Test MAPE < Train MAPE using auto.arima()

I am trying to build a forecasting model for the passenger vehicles registrations in a given country, and I wanted to use $auto.arima$ function from the $forecast$ package to estimate a simple ARIMA ...
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19 views

How to find p value range for two sample test given only sample size and standard deviation?

Given the sample size of two samples and their standard deviations, I could not find their exact p score, but should be able to find a range. However, I am having a very hard time determining how to ...
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25 views

Classifying groups using statistical significance

I am really struggling to get my head around some sample questions of my quant class. The exam is looming and I cant grasp what must be a basic concept. Sample A service provider has identified ...
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71 views

Comparison between regression of $a = bc^t$ and $\log a = \log b +t \log c$

This question is more qualitative then about the maths behind the equation. Variables: a = month (1, 2, 3, ) t = shipments of a product in that month You wish to derive the relationship between $a$ ...
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1answer
59 views

How to test if a percentage is significantly higher than 0?

I have asked people to rate different items between 0 and 100. On one condition, most of the items were rated very low. Therefore, the distribution of the result looks like an negative exponential. ...
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1answer
27 views

When is a Ljung-Box test significant?

I have trouble understanding the output of the Ljung-Box test due to conflicting information: The R documentation doesn't actually say how to interpret the output. This site states that small ...
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1answer
28 views

Chi Square independence test for continuous measure (not counts)

Suppose I do A/B testing and I collect many observations. An observation is the visit of a client into the store. I collect if the client bought something, the value of the eventual purchase, if the ...
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1answer
33 views

What statistical test would be appropiate for determining the preferences of lottery players?

I'm trying to conduct a simple study: to find out if there is a significant relationship between the time perspective of a person and his propensity to buy lottery. So to keep it simple, my ...
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14 views

Finding the power of a value [on hold]

You want to conduct a hypothesis test about the home prices in California using the housing data file: housing.mpj. a. At the 1% significance level, design the test the hypothesis that the mean ...
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1answer
34 views

likelihood ratio test with constrained null hypothesis

I am trying to understand a fundamental property of the Likelihood Ratio Test (LRT). For simplicity, the following example is framed as binomial data, which of course could be solved using a simple ...
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1answer
69 views

How do you calculate the test statistic of a hypothesis test with more than 1 parameter?

I am interested in testing the following hypothesis: \begin{align} \newcommand{\var}{\rm Var} \newcommand{\cov}{\rm Cov} \newcommand{\se}{\rm se} H_0\!:\ B_2 + B_3 &= 1 \\ H_1\!:\ B_2 + B_3 ...
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0answers
17 views

What to display for differences of medians of discrete variables?

I am using the Mann-Withney U test to compare two samples of count data. In several situations, I find that there is a significant difference between the populations, but when I estimate the CI for ...
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1answer
52 views

Unknown writing system: different letters or variants of the same letter?

In a fictitious language, there are 4 graphic variants of what is commonly believed to be the same letter "a": a1, a2, a3, a4. In a corpus of texts, any word containing "a" (Xa, Ya, Za, etc.) can be ...
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2answers
43 views

Student's t-test with a covariate?

I am testing the different between some variables $X$ and $Y$ using the Student's t-test. I suspect that there might be a latent variable $Z$ that has an effect on both $X$ and $Y$. How could I ...
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2answers
90 views

Aside from Durbin-Watson, what hypothesis tests can produce inconclusive results?

The Durbin-Watson test statistic can lie in an inconclusive region, where it is not possible either to reject or fail to reject the null hypothesis (in this case, of zero autocorrelation). What other ...
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2answers
48 views

Comparing frequencies

I'm trying to find the right test to use to compare 3 frequencies. Basically, in my research, 3 separate user interface prototypes were given to the same sample (10 people) and particular tasks needed ...
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1answer
40 views

Equivalent of z-score in exponential distribution

I have an exponentially distributed set of data, but there are a number of outliers at the margin. If I want to identify samples above the mean that I am 99.9+% confident are not the result of ...
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0answers
11 views

Statistically test difference based on time series

Usually in statistical hypothesis testing, we randomly split some unit into treatment group and control group, and we test if there are difference between treatment group and control group based on a ...
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1answer
51 views

Applying the T-test [on hold]

So far I have calculated the sample means $\overline{A} = 0.75$ and $\overline{B} = 2.33$. Using these I computed the sample variances: $S_A^2 \approx \frac{28.805}{9} = 3.2005$ and $S_B^2 = ...
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2answers
25 views

Help find a statistical test for proportion of a binary outcome with repeated measures

Here is an illustration of my problem: I have two stimuli (A and B) given to a number of subjects. Each subject is sequentially subjected to both stimuli 5 times (AAAAABBBBB or BBBBBAAAAA, but not ...
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1answer
25 views

Bonferroni Correction for Post Hoc Analysis in ANOVA & Regression

As we know, if we are doing many tests or multiple comparison, we don't use the same $\alpha$ value and use some $\alpha$ correction methods like Bonferroni. This is done because when we do multiple ...
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25 views

Likelihood of burning for a type of vegetation - which test to use?

I have six categories of vegetation, their total surface and the percentage of surface that has burned. I want to say eg. "coniferous vegetation burns more often on a statistically significant level". ...
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11 views

Non-existence of a UMP test in two-sided hypothesis [closed]

Good evening, I need some help: Prove that a uniformly most powerful test for a level $\alpha\in(0,1)$ doesn't exist for the test $H_0:\mu=\mu_0$ versus $H_1:\mu\neq\mu_0$, while ...
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21 views

Hypothesis formuation? [closed]

Dear expert community, I would like to ask about how do we explain the results in case we get that all my hypothesis were in negative forms ?! In other words, in my study i have do a hypothesis ...
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1answer
15 views

How should I test for multivariate ARCH effects in R?

I want to test for conditional heteroskedasticity in the form of ARCH effects in a multivariate time series. In the univariate setting, an ARCH-LM test can be used. A natural extension for the ...
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2answers
42 views

Hypothesis test null hypothesis equality

If we want to test whether the sample mean is at least 5 meters, how should we state the null hypothesis and alternative hypothesis? Here is what I think: H0: µ>=5 H1: µ<5 But when determining the ...
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33 views

Proper test for comparing two means from different distributions? (with limited data)

I have some data on frog weights for a small sample ($n \approx 30$). I need to compare the mean frog weight from this sample $\mu_s$ to the mean of another, much larger sample of frog weights $\mu_r$ ...
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17 views

hypothesis testing with uncertainty in variables

This is one of those questions that are easier to be explained with an example. Suppose we have the following data (made in R) ...
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5 views

General question about generating data, using GEE and testing the results

I am new to GEE and try to understand it by using it. Now I have troubles to understand how the "gee" package in R works. I start by explaining what I intended to generate and what my questions are. ...
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2answers
74 views

Bayesian analysis: Estimate whether a parameter is 0 or not

I have the following problem: I need to assess whether a given parameter $B$ is equal to 0. Let's consider the following model (my problem is more complicated but I think that this example is ...
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1answer
34 views

Hypothesis test of 2 proportions, with $np < 5$

We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$). However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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1answer
31 views

Test to compare distributions using the intersection area of the densities

I have to compare several distributions, but I don't want to use Kolmogorov-Smirnov test, since I'm dealing with big data ($N > 10^{6}$) and traditional hypothesis tests end up with detecting the ...
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14 views

Confidence interval for exponential moving average and variance

There are well known formulas for the exponential moving average and variance. Just for the completeness of the question, for each new x in a series of X(1..n) online EMA and EMVar can be estimated as ...
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3answers
55 views

Chi-squared vs ANOVA test

My study consists of three treatments. One treatment group has 8 people and the other two 11. Each person in the treatment group received three questions and I want to compare how many they answered ...
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12 views

how to use t test to my data. which type of t test to be used [closed]

my topic is inpatient satisfaction(hospital)using likert scale(5 point) i calculated mean score for reception(mean3.9), nursing care(4.10), doctors care(3.55) etc for 10 criteria. how to apply t test ...
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1answer
30 views

Wald Test and Z Test

The "z" hypothesis test is derived from the fact the mean estimator $\hat\Theta$ is distributed normally. If we don't know the variance, we just estimate it ($\widehat{se}$). The Wald test, derived ...
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12 views

BayesFactor Error Output in R

I am an R novice and I am trying to perform a Bayesian ANOVA (one-way) using R with the BayesFactor package. I want to test the null hypothesis that scores on a test do not differ between three groups ...
4
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0answers
18 views

how to test equality of proportions at different times

Here is my question. 20 (worm) mothers produce males + females and hermafrodites (many every hour). I want to test if the proportion of males + females born on day #1 is the same as in days #2 and ...
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2answers
21 views

How to compute Shapiro-Wilk test power?

I test normality of 12 residuals that are obtained from resid(lm(...)) command via shapiro.test. Thus I know variance, mean, ...
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0answers
18 views

Intuition behind Whites reality check

Assume you mined some strategy following a simple rule based approach with positive performance measures over the last 30 years from a giant parameter space. Now you want to find out how likely it is ...
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32 views

What is Frequentist Inference?

Frequentist Inference is defined as (according to the tag wiki) : In the frequentist approach to inference , statistical procedures are assessed by their performance over a hypothetical long run ...
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18 views

which test to use for showing shift from one category to another?

I have a data set where certain training is conducted and pre -post test scores are calculated. The scores are divided in low, medium and high (in percentages 0-33,34-66,67-100) coded 1,2,3 ...
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21 views

How would I calculate the t-statistic for this data and then determine if it's significant?

Say we want to test the hypothesis that a control group of cancer patients would report higher mean pain ratings than an experimental group receiving special massage treatments. Group 1: Mean = 78.1 ...
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1answer
25 views

Hypothesis testing on an empirical distribution

This may be a basic question, so please pardon me: given a vector of univariate data, and an individual observation from the said univariate data, I would like to derive some probability of observing ...
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1answer
49 views

I want to take a decision on two gaussian distributions, what approach can I take?

I observe a one dimensional random source, which could be any of two Gaussian distributions with a different set of parameters that do not change over time. They have a the same variance and a ...
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28 views

What kind of feature selection can Chi square test be used for?

Here I am asking about what others commonly do to use chi squared test for feature selection wrt outcome in supervised learning. If I understand correctly, do they test the independence between ...
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21 views

How to call extreme samples in a Monte Carlo simulation for hypothesis testing?

For many hypothesis tests, Monte Carlo methods are used to estimate the empirical $p$-value which is defined as $$p=\#{(T_{sample} > T_{observed})}/N.$$ Is there a name for the samples with ...