All Questions
Tagged with hypothesis-testing normal-distribution
279 questions
6
votes
1
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404
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Distinguishing two Gaussians
Assume we have two Gaussians $N_0 = \mathcal{N}(0, \Sigma_0)$ and $N_1 = \mathcal{N}(0,\Sigma_1)$ where $\Sigma_0$ and $\Sigma_1$ are two $n\times n$ covariance matrices.
What are the optimal test ...
- 195
-1
votes
1
answer
38
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Paramaterization of the Normal Distribution in Hypothesis Testing
When looking at how a z-statistic fits into the normal distribution $f(x) = \frac{1}{\sigma \sqrt{2\pi} } e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$ my intuition was always that it was just ...
- 3
2
votes
2
answers
215
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Is it possible for some p-values to be impossible? (because statistic generated by parametric bootstrap is mostly the same value.)
I am using a parametric bootstrap/monte carlo hypothesis testing method to generate the null distribution of the log likelihood ratio statistic. However, I am worried I might be doing it wrong ...
- 425
2
votes
0
answers
39
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Testing for Gaussian Mixtures
Suppose I observe data from a univariate distribution $\mathcal{D}$ with zero mean, and unit variance. We know that either $\mathcal{D} = \mathcal{D}_0 = \mathcal{N}(0,1)$ is standard Gaussian or $\...
- 318
0
votes
0
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58
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Testing difference between regression coefficients for different greoups
I am aware that this questions was addressed several times in this site and that there are certain papers discussing this issue for instance 1, 2.
USING THE CORRECT STATISTICAL TEST FOR THE EQUALITY ...
- 431
1
vote
1
answer
51
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Questions on Basic Data Cleansing For Linear Regression
I'm following some tutorials on doing some linear regression and as I was building my notebook, I'm working on outlier detection and amongst the techniques described for doing outlier detection, one ...
- 163
5
votes
2
answers
501
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Detect rare high-value measurements in a series of measurements
We do a measurement on 1000 samples to detect if a chemical element A is present, and for each measurement, two cases can happen :
the element A is not present, and the values we get are a "...
- 622
5
votes
4
answers
193
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Distribution of $Z^2 \cdot I(Z > 0)$ where $Z \sim \text{N}(0,1)$
When using the Likelihood Ratio test for testing particular hypotheses and attempting to obtain an size-$\alpha$ test, I run into the expression
$$ \mathbb{P}\left( Z^2 \cdot I(Z > 0) > c \right)...
0
votes
0
answers
34
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Binomial Test for data with normally distributed messurement error
I have a series of measurements and I want to perform a binomial test to see if the chance of exceeding some value $a$ is less or equal to some $p_0$. The measurement has some error which is normally ...
- 63
7
votes
1
answer
279
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Power of two-sample z-test
In a pilot study with two groups, the control distribution has the Mean1 = 90, SD1 = 5 and the treatment distribution has Mean2 = 85, SD2 = 5. The null hypothesis of the test is that the sample ...
- 193
0
votes
0
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72
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Sample size required for normal approximation - null hypothesis or estimate?
Consider a simple hypothesis test with a binomial distribution $Bin(p,n)$:
$$
H_0: p = p_0, \\
H_a: p \neq p_0
$$
and my estimate for $p$ is $\hat{p}$.
If I wanna do a normal approximation, a common ...
- 143
1
vote
0
answers
30
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How to establish what distribution to compare my statistic to
Apologies for this poorly titled question, but I've been taking some statistics courses and sometimes when you try to learn too many things in too little time you want to take a step back to check if ...
- 11
1
vote
1
answer
102
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Difference between F-test and confidence intervals on variance estimates
Given n samples from a normally-distributed variable X, we estimate variance as $s^2=\frac{1}{n-1}\sum{(x_i - \bar{x})^2}$. We can also get a confidence interval for such a variance estimate as:
$$...
- 1,176
1
vote
0
answers
139
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Hypothesis testing of normal distribution, unknown mean unknown variance
Suppose that we make measurements of an effect, and we know that the values that we obtain follow a normal distribution. But we don't know the mean nor the variance. The hypothesis is that 95% of the ...
- 63
0
votes
1
answer
75
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Hypothesis testing - Newbie blockers - Update and more
Brief : I'm from manufacturing industry, a processing machine in our production line used to do pressing, polishing and QA one after the other. Now we have a new machine that will perform these at the ...
- 3
0
votes
0
answers
30
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How is it possible to compare powers of normality tests?
The famous paper [1] compares the power of several normality
tests. Regardless of its result, my immediate question is, "How
is that even possible?"
Well, the definition of power in this ...
- 235
0
votes
0
answers
36
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normality testing [duplicate]
Good day,
I am a medical student currently working on a thesis focused on metabolic syndrome. My sample size is 45 individuals. I have encountered multiple challenges in assessing the normality of my ...
3
votes
2
answers
391
views
Why is it the convention to take equal tails in a two-tailed test with a statistic following a symmetric distribution?
Is there a particular reason for conventionally dividing the tails equally in a two-tailed test? Consider an $\alpha$ level test with a statistic following standard normal distribution. Then, why do ...
- 385
5
votes
1
answer
266
views
What is the substantive meaning of one statistical test is more powerful than another?
There are some research claims that one statistical test is more powerful than another. For example, a highly cited study states:
Results show that the Shapiro-Wilk test is the most powerful ...
- 723
1
vote
0
answers
63
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Interpretation of Anderson–Darling test
Assume that I am using Anderson–Darling test to evaluate whether a given sample of data is drawn from a normal distribution with some mean and standard deviation.
If you accept the null hypothesis in ...
- 363
1
vote
0
answers
43
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Papers or documents about the central limit theorem and its possible extensions: what happen when the sample size is big? [closed]
The central limit theorem in its most popular form states that (without being too formal) for a set of random variables $X_1,X_2,...,X_n$ independent and identically distributed with mean $\mu$ and ...
- 472
2
votes
1
answer
109
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Testing correlation coefficient of two bivariate gaussian
I have datasets from two bivariate normal distributions, $\mathcal{N}(\mu_x, \Sigma_x)$, and $\mathcal{N}(\mu_y, \Sigma_y)$ respectively. Now we know the correlation coefficient for these two ...
- 173
0
votes
0
answers
26
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Can I use the Z-Test with estimators for mean and standard deviation?
I'm trying to select feature columns in a binary classification model.
I'd like to remove near-constant columns that don't predict the target column values very well. One way of defining this is the ...
- 667
3
votes
1
answer
141
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About the statistics for the hypothesis test of the mean of two normal population
Let $X = (X_1, ..., X_n)$ be an independent sample from $N(\mu_1, \sigma_1^2)$ and $Y=(Y_1,...,Y_m)$ an independent sample from $N(\mu_2, \sigma_2^2)$. Consider the following hypothesis test given ...
- 31
0
votes
1
answer
192
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Calculating the probability my observation, $Y_i$, is drawn from a random variable $X$?
If I sample a population distribution 2,000 times and get an estimator for the population mean, $\mu$, and the standard deviation, $\sigma$, how can I use these to get the probability that an ...
- 667
1
vote
0
answers
61
views
Bayesian AB Testing and Normal Distribution: How to Implement Posterior Variance Samples
I'm running an bayesian AB test to compare a normally distributed metric with unknown mean and variance between two groups. My goal is to compare the average value of the metric between the two groups,...
- 331
0
votes
0
answers
23
views
Sampling from either a known or unknown Gaussian
Suppose I have two Gaussian distributions $N(\mu_0, \sigma), N(\mu_1, \sigma)$ with identical variance, where $\mu_0, \sigma$ are known and $\mu_1$ is unknown. Suppose I realize a sample $x$ from one ...
- 1
2
votes
0
answers
151
views
Which distributions are valid for Student's t-test?
When I read Wikipedia - Student's t-test I can see it assumes that:
The sample mean follows a Gaussian distribution.
The sampled mean follows a chi square distribution.
Samples of Gaussian ...
- 277
0
votes
0
answers
63
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Fiding the test statistic, using wald test
Given the random sample $X_1,...,X_n \sim N(\mu, \sigma^2)$, I want to perform a Wald test for:
$\mathrm{H}_\mathrm{0}: \mu = \mathrm{\mu}_\mathrm{0}$
$\mathrm{H}_\mathrm{1}: \mu \neq \mathrm{\mu}_\...
- 553
0
votes
0
answers
74
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Frequentists tests to check for normality
Let $X_1,...,X_n\sim X$ be $n$ i.i.d. random variables. I want to to test if they follow a normal distribution, in other words, check if their distribution belongs to the Gaussian family.
These are ...
- 107
1
vote
0
answers
31
views
Confusion on using Z-distribution or Chi-squared
I have two questions in front of me, first is :
A random sample of size 35 is selected from a population that is normally distributed. If the mean and the standard deviation of the sample is 75 and 8....
1
vote
1
answer
278
views
Can we compare statistically z-scores? Isn't their mean is always zero?
Let's say I have two variables of any distribution for which the population average and variance is assumed/known/fixed for some topic (common in psychology). Using this I can calculate z-scores for ...
0
votes
0
answers
160
views
Proof Maximum likelihood ratio test to be a $\chi^2$ distribution
I have been struggling with this demonstration and I can not finish it, I want to demonstrate that for Gaussian samples (of $\sigma$ and $\mu$) the maximum likelihood ratio test holds for a $\chi^2$ ...
- 123
1
vote
1
answer
52
views
Test linear regression coeficient significance if the residuals are not normally distributed
I have a linear regression with 51 data points, and I would like to get the confidence intervals and to test the coeficient's significance, but the problem is that the residuals are not normally ...
-1
votes
1
answer
298
views
Testing the difference between two ratios of Poisson variables
I have two ratios of four independent Poisson variables $R_1=\frac{\large Po(\mu_1)}{\large Po(\gamma_1)}, R_2=\frac{\large Po(\mu_2)}{\large Po(\gamma_2)}$.
The Poisson variables are tallies, they ...
- 161
5
votes
3
answers
242
views
How to check the data is generated by machine or human?
I have a bunch of data points (about 300 samples in total), each sample is a number from 1 to 3 (from {1, 2, 3}).
These numbers are supposed to come from a survey. Are there any statistical methods to ...
- 195
2
votes
3
answers
559
views
Compare single observed value to simulated distribution
I have a distribution of values that I have simulated for a null hypothesis data generating process. I have a single real-world observation that is wayyyy outside the percentiles of this distribution. ...
- 41
0
votes
0
answers
25
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Normal and non-normal distribution of data?
I am quite an amateur in statistics. I have data where I would like to test if I can perform parametric or non-parametric testing depending on if the data is normally distributed or not. The data has ...
5
votes
1
answer
91
views
forming confidence ellipse versus using contrast
Suppose I am testing a hypothesis on data that is bivariate normal, $(x,y)\sim N(\mu,\Sigma)$ where $\Sigma$ is known but $\mu$ is not. My null hypothesis is a contrast $a^T\mu=a_1\mu_1+a_2\mu_2=0$. ...
- 311
0
votes
0
answers
93
views
Which statistical Test should I use/ Comparing 2 groups
I am new to statistics, can someone guide me regarding the test I should use to compare the foot dimensions of 9 subjects to footwear dimensions (we have 2 footwear brands).
So, to simplify, I have ...
2
votes
0
answers
62
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Does Central Limit Theorem (CLT) apply to Regression Coefficients? [duplicate]
The way I learned about Central Limit Theorem in school is illustrated in the following example:
Suppose you have a population of 100,000 basketball players. You are interested in knowing the average ...
1
vote
1
answer
723
views
In standard normal distribution table how I deal with value of Z greater than or equal to 5
How can I deal with sample distribution table when Z is greater or equal to 5?
For example:(-2.04 <z<-5.96)
Sample distribution table value for -2.04 will be 0.2018 then what will be the sample ...
0
votes
0
answers
63
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Testing for constant mean (stationarity)
I have a grayscale digital image with noise and I would like to test for uniformity in small neighborhoods.
One hypothesis says that the mean is independent of the spatial coordinates, against the ...
- 364
0
votes
1
answer
279
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Proof of the Student t-test for independent samples drawn from the same normal distribution when $\mu \neq 0$
I'm following the proof in Cramer's book Mathematical Methods of Statistics, $\S 29.4$. There it is assumed that we have two independent samples $x_1,\ldots, x_{n_1}$ and $y_1,\ldots,y_{n_2}$ drawn ...
- 101
0
votes
0
answers
77
views
Significance test for accuracy - normal assumption
I have a dataset with pre-defined labels. I trained two machine learning classifier methods A and B to predict the labels and calculated the accuracy for each. I varied the dataset a bit and thus got ...
- 564
2
votes
2
answers
269
views
Why use normality tests if we have goodness-of-fit tests?
What are the reason/s to use a nonparametric normality test (e.gr., Shapiro-Wilk, Jarque-Bera) instead of generic, parametric goodness-of-fit tests (good for any distribution including but not limited ...
- 213
1
vote
1
answer
84
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Showing that the given critical value (?) gives a test with significance level 0.05
So I have a maths problem that I'm struggling to understand... The original language isn't English, but I have done my best to translate the necessary background information into English.
Assume that ...
- 13
2
votes
1
answer
553
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t- test for non normally distributed sample
I am doing a statistical test (analysis) for the following case:
As part of a product aimed at improving the quality and speed of code writing for developers,
we have implemented a new feature that ...
- 31
4
votes
2
answers
162
views
Prediction interval: but instead, the probability that the next datum is above a fixed threshold?
I've been struggling with this problem, and I think I must be missing some important conceptual step. Imagine we observe $\theta_1 \sim N(\mu, \sigma^2)$, with unknown $\mu$ and known $\sigma^2$ (for ...
- 325
0
votes
0
answers
816
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Using z test or t test when $\sigma$ is unknown
Note: I realize similar questions have been asked here before but I couldn't find my specific doubt addressed (not in so many words, anyway).
In testing a large sample for the population mean if the ...
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