All Questions
Tagged with variance hypothesis-testing
149 questions
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16
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Compare two variances
I am reading this paper
I have difficulty understanding Section 6: A Linear Time Statistic and Test.
At the beginning, they claim that $\text{MMD}^2_l$ has higher variance than $\text{MMD}^2_u$ (we ...
- 131
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50
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How to test for equal variances of correlated observations?
Let $r$ be a vector valued random variable with mean zero and variance $\Omega$.
Let $r_t$ denote a specific observation of $r$ at time $t$.
$\Omega$ is unknown but I have 2 estimates of it: $\Omega_a$...
- 1,275
2
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1
answer
51
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Why is the second assumption (i.e., known population variance) unrealistic when calculating Z-interval for a mean?
I'm learning the calculation of confidence interval about the mean by Z-interval. The lecture said that:
... the second assumption about the population variance being known is
unrealistic. After all, ...
- 1,075
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0
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10
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Detecting Volatility Clusters in Time Series, Stock Returns (%) in particular
My primary objective is to detect the presence of volatility clusters in financial time series, stock returns (%) in particular. So, it can be translated into the detection of "conditional ...
- 1
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0
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49
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Testing for Homoscedasticity - should Levene's and Brown-Forsythe use Welch's t-test/ANOVA?
This question just came up and I haven't seen any literature on the subject.
Background: When testing homoscedasticity for, say, a two-sample t-test, the F-test for equal variances is deprecated due ...
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12
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Testing equality of unconditional variance of two stationary AR times series?
Suppose I have two stationary AR time series:
$$
\begin{align}
y_{1,t} &= \phi_1 y_{1,t-1}+\varepsilon_{1,t} \\
y_{2,t} &= \phi_2 y_{2,t-1}+\varepsilon_{2,t}
\end{align}
$$
with $\varepsilon_{...
- 2,157
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56
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when focus on the pre-test for the normality test and ignore the pre-test for equality of variances?
When should a pre-test for normality only without a pre-test for equality of variances be performed before location tests like this paper did ((Rochon, J., Gondan, M. & Kieser, M. To test or not ...
4
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1
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282
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Standard deviation squared is variance. What is standard error of the mean squared? [closed]
Is it correct to say that there is a sample variance and a mean variance, and their square roots are the standard deviation and the standard error of the mean, respectively?
1
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0
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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
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1
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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
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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
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0
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143
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When A/B testing a two sample hypothesis test of means, should we always use the welch t-test? [duplicate]
The Welch t-test is best used when we cannot make an equal variance assumption between our treatment and control groups (our two samples).
However, in A/B testing, it's not clear to me how we could ...
8
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2
answers
523
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Why do we adjust for within-group variability in statistical testing of differences in group means?
I hope this question fits the forum. I'm not a statistician, but have received decent training in statistics and use statistical modeling in my daily work. I've been tasked to give a very condensed &...
- 2,815
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1
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89
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Variance test with survey weights
When not working with surveys, you do a variance test with var.test(). What do you do when you want to account for complex survey design?
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2
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35
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Need of hypothesis test when we know the population distribution & parameters
While studying about the hypothesis testing, I encountered the following case -
Consider a case where we are carrying out hypothesis testing for amount of perfume filled in the bottles:
NULL ...
2
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0
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124
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Statistically comparing the variance of two dependent samples
I have two dependent samples of data. Each sample contains N = 800 values (data points) and stem from the same human subjects, that is, sample one is the pre-experimental and sample two the post-...
- 307
4
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1
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186
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equal *population* variances in paired t test
I I want to perform a paired t-test to check if there's some effect, I have the distribution of "before" and the distribution of "after" the manipulation. Do I need to assume the ...
- 41
2
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1
answer
35
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Same mean, same SD, different spread
In an experiment I'm running, I'm trying to determine if my light brightnesses are "clumped" or not. During the experiment, stuff will change rapidly from light to dark in a random way, but ...
- 51
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1
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33
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Joint Hypothesis Testing-Variance
Got the following question:
Here is the provided answer:
I am confused about where the $9$ coefficient is coming from above. Any thoughts?
1
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0
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31
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Test statistic for whether variance is the same every month
I have a panel of observations, where there are $T$ days and each day there are $N$ observations. So the panel is $X \in R^{T \times N}$. The question I'm trying to answer is: is the cross-sectional ...
- 831
4
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1
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141
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Inferences about $\mu$ based on the sum of two dependent normal RVs
Given:
$X \sim \mathcal{N}(\mu, \sigma^2)$
$Y|X=x \sim \mathcal{N}(0, (\theta x)^2)$
$Z = X + Y$
I want to be able to make hypothesis tests or confidence intervals for $\mu$ using $Z$ and known $\...
0
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1
answer
60
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Why is the pooled variance calculated using the variation of the two tested groups?
When comparing between two populations, or two groups from the same population, a t-test assumes that both those groups have the same variance. However, a t-test works by using the pooled variance ...
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65
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Conditional variance $\hat{\beta}_1|x_1, x_2,\ldots, x_n$
Why do we need to estimate the variance of $\hat{\beta}_1|x_1, x_2,\ldots, x_n$ when we want to test a hypothesis about $\beta_1$?
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0
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858
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Derivation of the variance of the ${\hat{\beta}}$, why ${\frac{\hat{\beta} - \beta}{SE(\hat{\beta})}}$ follows t-distribution
Thank you so much for all the input and for pointing out my mistakes. I made some corrections and try to add more details but ended up trying to answer my problem based on other people's posts. Please ...
- 313
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1
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80
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How can one show the sum of observed variables is "zero"?
Let's assume one is collecting measurements $x_i(t)$ of "true" variables $\bar x_i(t)$, where $0\le i<n$ is the index identifying each variable and $t$ represents different sampling times....
1
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0
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20
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Standard error of regression coefficients? [duplicate]
I'm trying to test the hypothesis that $\beta_{1} = \beta_{2}$ for the SLR $y_{i} = \beta_{1} + \beta_{2}x_{i} + \epsilon_{i}.$ I start by letting $\delta = \beta_{2} - \beta_{1}$, so my null ...
- 11
3
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1
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160
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Why n-1 instead of n in pooled sample variance
I am currently self-learning hypothesis testing and am looking at the independent samples t-test whose test statistic involves the pooled sample variance (https://libguides.library.kent.edu/spss/...
- 85
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0
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20
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Can the F test be generalized for a null hyp where variances are unequal?
Sorry for the question, maybe this appears in a book a little more advanced than the ones I have seen.
Suppose we have two samples from normal distributions with sample variances $S_{n,1}^2$ and $S_{m,...
- 213
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1
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611
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Why is the Mean Square Between (MSB) used in 1-way ANOVA instead of total variance?
I'm having a hard time parsing the logic behind the formulas in the 1-way ANOVA. I'll first establish what I understand so far which will lead into my question.
The objective of a 1-way ANOVA is to ...
- 719
4
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1
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1k
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Is there such a thing as a paired-samples F-test?
I have paired data (from a pre/post-test) for which I assume that the variance differs between groups (again between pre/post). Visually, this assumption appears to check out and there is less ...
- 470
2
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2
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2k
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Computing a p-value of a 2-sided Chi-squared test for one variance
Below is a simple question from a textbook. I answer the question by computing the critical values for a critical region $\alpha = 0.05$ for a Chi-squared distribution (42.95, 86.83) and then ...
- 705
1
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1
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205
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Can I compare just some grades to see if they are statistically significantly different from one another?
I have grades of 25 students (for one test/exam) according to the German school system. The possible range of these grades is from 1 (very good) to 6 (insufficient). From my sample, 20 students got ...
- 11
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1
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101
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Standard convention for test statistic for F-test?
According to my textbook, Mathematical Statistics with Applications 7th. Ed, they write the test statistic in a F-test, that compares variances of two different populations, so that the larger ...
- 199
4
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1
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86
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Hypothesis Testing for the equality of 2 variances
Suppose I have 2 distributions:
$X\sim N(\mu_1,\sigma_1^2)$ and $Y\sim N(\mu_2,\sigma_2^2)$
such that $\sigma_1^2$ and $\sigma_2^2$ are unknown.
How do I test $H_0: \sigma_1^2 = 10\sigma_2^2$ and $ ...
- 43
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1
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473
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Significance test testing whether one variance is larger than the other
I feel like I am missing a key link and this tasks is quite easy:
I am given the following averages and standard deviations:
$\bar{x}_1 = 971$, $s_1 = 42$, $n_1 = 1000$
$\bar{x}_2 = 983.9$, $s_2 = 60....
- 13
1
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0
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145
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Hypothesis Test of 2 binomial distributions with unknown and unequal variances
I want to double check if my math and logic is correct in performing a hypothesis test of two sample means from binomial distributions with the assumption of unknown and unequal variances from the ...
1
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1
answer
490
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Normality test for circular data
I have some angles and I am wondering how can I test whether the distribution of my data is normal or not. In fact, I want something similar to KS test. Howver, I want to use it for circular data to ...
- 171
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0
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28
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Portion of variance explained by individual properties with ANOVA
I have used the ANOVA test to compare the expected values of three datasets. The data sets contain data about the lifespans of three brands of frying oils. I have used Excel to perform the test and I ...
- 123
3
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1
answer
1k
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How to interpret the Score-Based CUSUM test results?
Context
I'm doing an analysis of a price time series and checking for structural breaks (s.b. further on). One of these tests is the Score-Based CUSUM test. As far as I understand, this test is more ...
- 261
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1
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1k
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A/B test sample size formula confusion
I was trying to understand the math behind some commonly used calculators and formulas for A/B tests and it seems that there might be some variations. Ideally, I would like to understand how each of ...
- 206
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1
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429
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Can long run variance of a time series be used to test mean of the series?
Let $Y_t$ be a stationary time series with $Y_t \sim N(\mu, \gamma_0) \,\, \forall t$.
Further define, $$\bar Y_T \equiv (1/T)\sum\limits_{t=1}^TY_t$$
Further, let $\sigma^2_l$ be the long-run ...
- 2,611
4
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1
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96
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Does one need to test independence of variables first?
Suppose one is given the following data set $X$.
"8 5 12 4 11 6 8 7 7 12 7 3 11 14 11 9 6 6 5 6 10 14 4 5 5" Let $n$ be number of data points.
One wants to obtain 95% ...
- 1,465
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0
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22
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(Hypothesis testing of sum or count) standard error when underlying distribution is skewed and heavy tailed
I'm trying to perform hypothesis testing to check if there is a difference in two groups w.r.t. sum of X (continuous RV such as revenue) and sum of Y (integer RV such as count); Each sample in a group ...
- 21
2
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2
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448
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Ansari-Bradley Test Sensitivity to Median Differences: Should we subtract the median from each group?
The Ansari-Bradley test appears to be ineffective at detecting scale differences when the two distributions have markedly different medians. However, when I subtract the median of each group, I get ...
- 67.1k
2
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0
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71
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F test with inverted hypotheses
When using the F test to see whether pooled variance is appropriate, would it not be more useful to assume that the population variances are not equal and let the alternative hypothesis be that they ...
- 128
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31
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How to test that a sequence of variances rank ascendingly?
I am investigating forecast optimality. Diebold (2017, p. 334, list item d) indicates that one of the desirable properties of a good forecast is
Optimal forecasts have $h$-step-ahead errors with ...
- 69.5k
1
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0
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73
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How to perform a statistical comparison between these two groups?
How would I compare these two groups?
In this case, this would be a comparison between group A and B, where the first group would contain the first two violin plots, and the second group would be ...
- 11
1
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1
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148
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Good variance test when the distributions have different shapes but I really want to test the variance
Consider $X\sim N(1,1)$ and $Y\sim exp(1)$. The distributions are totally different, but they do have equal variance, so if I were to sample from these and test for unequal variance, I would not want ...
- 67.1k
1
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3
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803
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Test $H_0$ hypothesis that the population variances are equal
Here is the problem: Suppose you analyze potato prices in Brno and Prague. For Brno you analyze 18 shops and find sample variance
45. For Prague you analyze 27 shops and find sample variance 75. Test ...
- 229
1
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1
answer
2k
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$\chi^2$ test for the variance in Python [closed]
I am looking for a function in Python testing the hypothesis that the variance of a Gaussian sample is equal to a given value, to validate my own function.
I talk about this test:
https://www.itl.nist....
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