Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [goodness-of-fit]

Goodness of fit tests indicate whether or not it is reasonable to assume that a random sample comes from a specific distribution.

"They are a form of hypothesis testing where the null and alternative hypotheses are:

H0: Sample data come from the stated distribution
HA: Sample data do not come from the stated distribution

These tests are sometimes called omnibus tests.

Reference:

Ricci, V. (2005). Fitting distributions with R.
Retrieved from: http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf
page 16.

1176 questions
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Norm of residuals to measure goodness of fit

I used a least squares method on my data set, using the lsqr Matlab function. I know that the norm of residuals is a measure of the goodness of fit, but how can I assess whether the value of the norm of residuals is "good"? Which is the range of…
giovanna
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Most powerful GoF test for normality

It's well established that both Anderson-Darling and Shapiro-Wilk have a much higher power to detect departures from normality than a KS-Test. I have been told that Shapiro-Wilk is usually the best test to use if you want to test if a distribution…
Christopher Aden
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is Shapiro Wilk test insensitive on the tails?

Is Shapiro Wilk test insensitive on the tails of sample distribution? I've read such statement on a paper but I cannot figure out why from its test statistic W. Could someone help me understand this?
Joy
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Multi-dimensional goodness of fit

I have two (soon to be three) dimensional spatial data and I what to compare the goodness of fit between my model and reality. As the data is continuous and not categorial I can't really use the Chi-squared test. I have considered trying to…
Bowler
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Anderson Darling exponential distribution

I need a goodness of fit test for the exponential distribution. I understand that Kolmogorov-Smirnov is not generally regarded as very powerful and that Anderson-Darling is regarded as superior. However I have two problems. None of the literature…
Simd
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Goodness of fit of sorted data

Say I have a list of 10000 sorted counts $\ge 0$ that sum to 20000 and I want to determine that they came from placing 20000 balls randomly, independently and uniformly into 10000 cells. A straight Chi-squared test would be reasonable if I assume…
deinst
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Goodness-of-fit for Lomax distribution

I have some data n > 3000 https://drive.google.com/file/d/1gwB_U_TOX-IQHZJJDX-WeErLzrZZFoXu/view?usp=sharing (Third column) that I believe based on my physical theory should follow a Lomax distribution. $$ f(x) = \frac{ks^k}{(k + x)^{s+1}}…
Reza Afra
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Are goodness of fit and lack of fit the same?

Are goodness of fit and lack of fit the same? If they are tests, is one's null the other's alternative?
Tim
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Comparing $R^2$ values that measure different predictions

I have a question regarding $R^2$. Say, a model A predicts $y$ based on $x$, and a model B predicts $x$ based on y. I want to test which model is a better fit to the data. Since model A predicts $y$, the $R^2$ for that model will compare $\hat{y}$ …
Erik
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Use cases for chi square goodness of fit tests

In the answer to the question: Chi squared goodness of fit test, user glen_b comments that: The circumstances where it really makes much sense to formally test goodness of fit are surprisingly few. Perhaps the reason for this that in a lot…
sntx
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How to measure the goodness of fit of a 3D line?

I have data points in 3D space, and I'd like to quantify how well they conform to a straight line. Specifically, this is a body tracking problem. I have multiple options available for the 3D positions of body parts. For example, there are points for…
Vermillion
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What does goodness of fit mean in context of linear regression

I am having trouble understanding the concept of 'goodness of fit' w.r.t linear regression. The name suggests that the goodness of fit test is used to determine how well a model fits the data. But the linear model is already the 'best' fit since we…
Victor
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What's the best way to test the uniformity of location data?

I'd like a test to determine whether a number of collected 2D points (say, x,y in (0,1]) are distributed uniformly across the space. The points will be one or more 'paths' through the space - collections of points resembling movement through the 2D…
dfb
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Calculating goodness of fit for a physics-based model

I have a physics based mathematical model that predicts water quality metrics based on end-member mixing. It makes several simplifying assumptions such as constant values of the end-members and continuous mixing that are not perfectly met in the…
C. Denney
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Proportions of different types of nuts in bags of mixed nuts

Say I wanted to investigate the proportion of different types of nuts in bags of mixed nuts. So I weigh the nuts by type. Would I be able to use the information on weights and the Chi-squared test to analyze the nuts?
BOB
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