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Hypothesis testing assesses whether data are inconsistent with a given hypothesis (usually a null hypothesis of no effect).
2
votes
0
answers
381
views
Converting a chi2 to a sigma value
I am working in astronomy. I fit a theoretical model to some data. The model takes input parameters (like the mass and age) and produces some outputs that I compare with the data.
I measured the goodn …
1
vote
1
answer
73
views
Sampling from the null distribution for a t-test
I am trying to apply the Dietterich 5x2 cv t-test to test whether one statistical model is better than another on a particular data set.
In order to apply this test, one must assume that under the n …
2
votes
0
answers
199
views
Paired non-parametric test for a difference in variance
I have $N = 391$ paired data points $\mathbf a = a_1, \ldots a_N$ and $\mathbf b = b_1, \ldots b_N$.
Both $\mathbf a$ and $\mathbf b$ are approximately normally distributed with a mean of zero.
I …
2
votes
1
answer
437
views
Hypothesis testing with regression models
I have two regression models: a linear model with one variable, and a neural network with many. I want to test whether the neural network is better than the linear model.
I am wondering the best way …
2
votes
1
answer
2k
views
Dietterich's 5x2cv paired t-test for regression problems
In 1998 Dietterich proposed an algorithm for comparing classification algorithms using a series of cross validated t-tests:
Dietterich, Thomas G. "Approximate statistical tests for comparing supervi …
1
vote
1
answer
2k
views
Statistical test for the difference in mean for two normal distributions
I have measured $x$ and $y$ and estimated their uncertainty. They are both distributed normally. I found $x = 5 \pm 0.25$ and $y = 7 \pm 0.5$.
I want to know if these estimates are statistically dif …
3
votes
2
answers
100
views
Assessing significance when measurements are correlated
I am trying to estimate a function $f(x)$ at $x=0.1, 0.2, 0.3, 0.4, 0.5$.
I make this estimate through some complex procedure based on a set of independent but noisy data (with known uncertainties). …
1
vote
0
answers
46
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Does the $\chi^2$ test of variance rely on homoskedasticity? [closed]
I have a linear model $y=ax+b$. I have fit the relations using two data sets. I have found that estimate of $a$ from the two data sets are similar, but that the uncertainty of $a$ is much larger in on …
0
votes
0
answers
46
views
Showing that an increase in uncertainty is significant
I have a linear model $y = ax+b$ and I estimate the coefficients $a$ and $b$ in the ordinary way.
I have found out that all of my values of $x$ were systematically overestimated, and also that they …
1
vote
0
answers
33
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Testing if slopes differ using data with different uncertainties?
I have two data sets that each have the following form:
x y sigma
13 1495.00 0.07
15 1700.91 0.09
...
basically where $x$ and $y$ are given, but also the uncertainty of $y$, denoted $\sigm …
1
vote
1
answer
90
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How to show whether the average coefficients of determination from one regression technique ...
I have 50,000 objects on which I have performed two different types of regression. Using cross validation, I obtained the average $R^2$ score from each model on each of the objects. So now I have a li …
3
votes
1
answer
83
views
What does "(scores mapped into 1:m using rounded scores)" from the 1-sample permutation test...
I'm trying to do an exact paired permutation test. What does this "mapping" mean?
> library(exactRankTests)
> perm.test(rnorm(10), rnorm(10), paired=TRUE, exact=TRUE)
1-sample Permutation Test ( …
2
votes
2
answers
111
views
Obtaining error bars for a difference
I have a pair of data sets, and I want to know whether the medians of these two sets differ significantly. I've calculated the median of each set and subtracted them from each other. How can I determi …