All Questions
Tagged with hypothesis-testing goodness-of-fit
136 questions
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Reading the chi-square table
For solving problems involving the chi-square distribution in my syllabus, we use this $\chi^2$ statistical table. However, I have a doubt in reading it.
Suppose there is an experiment where a die is ...
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7
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20k
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Appropriate normality tests for small samples
So far, I've been using the Shapiro-Wilk statistic in order to test normality assumptions in small samples.
Could you please recommend another technique?
- 1,539
1
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0
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137
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Convergence rate of test-statistic to chi-square distribution
I know that the to test whether $\Sigma=\Sigma_0$ against $\Sigma\ne\Sigma_0$ for an $n\times p$ data matrix, the test statistic is $np(a-1-\log g)$ where $a$ and $g$ are the AM and GM of the eigen ...
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Choosing bins for chi-square testing distributional fits for distribution similar to normal/heavy-tailed
Chi-squared test can be used to check the hypothesis, that given sample
is from the given theoretical distribution.
If the distribution is continuous then we should properly choose bins.
Question 1 : ...
- 82.8k
2
votes
0
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goodness of fit for psychometric data (perceptual threshold)
I'm running an experiment on perceptual thresholds in audio. I'll try not to bog you down with too many details:
The experiment is about vibrato speed; specifically, when can you tell the difference ...
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4
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1
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236
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Is there a G-test equivalent for continuous variables?
The G-test is similar to the chi-square test for goodness of fit. It is proportional to the kl-divergence.
I am wondering if there is a similar test that is applicable to continuous variables. Since ...
- 82.8k
1
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1
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57
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Most appropriate statistical test to compare frequencies within and between treatments
I am working with a dataset that includes demographic variables (age and sex) and purchase details for services related to body ornamentation (tattoo location, piercing location, tattoo type, etc.) ...
CommunityBot
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0
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Determining trend statistic for two time series
I have two time series: one with reported scatter plot points, and a solid line that represents a fit to the data based on other variables. Here:
https://docs.google.com/document/d/1gizOAV8ZjaATLm-...
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253
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Chi-squared test, Poisson distribution, type I error overestimated - well-suited test for discrete distributions?
UPDATE I edited my original question to make it as clear as possible.
My goal is to find a reliable goodness-of-fit test for Poisson-distributed samples. There are a few discussions here related to ...
- 126
1
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1
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159
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goodness-of-fit and bootstrap
Assume one has two data samples: $X = \{ x_{1}, \dots, x_{n} \}$ and $Y = \{y_{1}, \dots, y_{m}\}$. Next, we aim to check if the data $Y$ was generated by the same data generating process (DGP) as $X$ ...
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Is it possible to calculate a p-value from a modified test?
I was asked to fit a distribution to some data and calculate the goodness-of-fit and a corresponding p-value. I've been using Pearsons chi-squared test (chi2gof in matlab) to do this but my advisor ...
- 532
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1
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53
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Wrong answer in basic goodness-of-fit test
I am following my lecture notes on this test:
However, when I calculate the expression $2\log \Lambda$ (Python script attached below), I get $21.8$ instead of $44.9$, which is quite far off. The ...
- 7,752
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218
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Goodness of fit that puts high weight towards the tail of the distributions
I have two distributions A and B and I am looking for a goodness of fit test that measures how much the tail of A matches (or fail to match) the tail of B. Alternatively, I am looking for a test that ...
- 385
1
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1
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Comparing two discrete paired datasets
The problem: I am studying the estimated number of cases of malaria in regions of the world and found that both the WHO and IHME have their own estimates. I want to find if the difference between the ...
- 2,318
2
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1
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Statistical test to detect regional excess of observations compared to background observations
I have data on the protein position of genetic variants. I want to determine whether there is a region of the proteins with a significant excess of variants relative to controls.
Consider this ...
- 5,130
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How to decide between goodness of fit tests
I have a question on BIC and AIC.
I have a data set and I need to test this data set if it fits various distributions (for example, Gamma or Poisson, etc.) I need to use AIC and BIC statistics for ...
- 5,114
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What does goodness of fit tell us with skewed data?
"The goodness of fit test is a statistical hypothesis test to see how well sample data fit a distribution from a population with a normal distribution. Put differently, this test shows if your sample ...
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Why there's never a good reason to use the Jarque-Bera test
This question was inspired by a comment made by @whuber in response to this question regarding the use of distributional tests.
The comment stated there is never any reason to use [the Jarque-Bera ...
- 3,048
2
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Goodness of Fit Test vs Testing RMSE
I have a bit of a broad question. It seems to be that there are two different approaches (Borrowing a bit of Breiman's Two Culture's paper) when it comes to testing if our data looks like our model.
...
- 625
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1
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342
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Goodness of fit for two samples with uneven different sizes
I have 2 different samples and would like to test a hypothesis about some aspect of their distribution. The first sample has 11,000 observations but the second is just 150 outcomes.
From graphically ...
- 1,622
2
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1
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Good Text for Shapiro-Wilk Test
I was wondering if anyone can give me some good texts for understanding the Shapiro-Wilk test.
I'm searching for an intermediate level text, not too simple like the wikipedia page (it gives very ...
- 290k
2
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1
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2k
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chi squared goodness of fit test to check for normality
I have the following data:
I would like to use the chi-squared goodness of fit test to test whether it comes from a normal distribution. How shall I go about it?
In particular,
I would like to know ...
- 57.6k
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How do I determine goodness of fit for a test of n binary decisions?
Let's say I have $n$ pairs of items. For each pair I select one item over another due to some perceived trait. This could be anything, for example, identifying which image is brighter than the other ...
- 111
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236
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F test to determine lack of fit
Perform the F test to determine whether or not there is lack of fit of a linear regression function; use a significant level of 0.025. Compute the test statistic, reject region, and estimate the p-...
- 447
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1
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43
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Goodness of fit test for a normal distribuition
I have the following exercise that shows $n=6$ numbers:
$$ 1.40, 1.55, 1.35, 1.50, 1.29, 1.64 $$
Is data normally distributed at the 5% significance level?
Surely $\overline{x} = 1.455$, $s=0....
- 57.6k
5
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1
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7k
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Test if two gamma distributed populations are different
I have data from two populations of different sizes. Both have Gamma distributions with different shapes and scales (as estimated in R):
...
- 82.8k
2
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1
answer
1k
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Deviance Statistic in HLM analysis
I am analyzing a multilevel model using the software HLM. I am trying to find out more about the Deviance statistic that I increasingly see being reported as a measure of the explanatory value/effect ...
CommunityBot
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4
votes
1
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Bootstrap for goodness of fit
Suppose I want to test whether a die is fair. I toss 60 times with outcome $X = (40,20,0,0,0,0)$ where $i$th coordinate denotes times of $i$th face occurs.Consider Hypothest test($\alpha = 0.05$):
$$...
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Can I test for inequality in H0 using chi square test?
Let's say I want to test whether an $n$-sided dice is not too unfair. In the standard chi-square test we test the zero-hypothesis
$$
H_0\colon (p_1,\dots p_n) = (1/n,\dots,1/n)
,\quad\text{i.e.,}\quad
...
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70
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Goodness Of Fit Testing When Multiple Parameters Are Estimated
I am working with independent data points $X_1,...,X_N$ each of which, under my model assumptions, is a sum of exponential waiting times with different rates, and so should come from gamma ...
4
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1
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2k
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Chi squared test for goodness of fit
I have a signal coming from a measurement device (e.g., Volt vs., time) and perform a fit to the signal. I would like to do a goodness of fit test like the chi-squared test. However, I am not sure ...
CommunityBot
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1
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909
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A statistical test to check whether a set of data are Pareto distributed
I need to construct a statistical test which outputs the p value for the hypothesis, H0: Data are Pareto distributed Vs H1: Data are not Pareto distributed.
I found a test in stack exchange, but it's ...
- 64.8k
1
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0
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36
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Goodness-of-fit test when the sample space is monotonically increasing [closed]
I came across this paper which develops a GoF test on data drawn from a circular sample space (i.e. it has cyclical support).
I am now wondering if there is a parallel to monotonic supports (or if ...
- 989
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0
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22
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Goodness-of-fit test applied to tuples in sequences/samples, instead of raw data
High level problem:
I have two sequences of data. The first one is the reference, the truth, the second is one which contains missed values (due to measurement errors). I want a test which can ...
- 128k
0
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1
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136
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A test of whether a sample has a specified distribution
Suppose we have an iid sample $X_1, \dots, X_n$. We want to test if it has a standard normal distribution.
One test statistic I learned from Brockwell and Davis's Introduction to Time Series and ...
- 82.8k
0
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0
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284
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How do I interpret the p-value from a Shapiro-Francia Test?
I have a situation where I have more than 50 samples in a given set of inputs and I cannot use the Shapiro-Wilk test as I don't have the numbers for the pyramid for $n>50$. I was then asked to use ...
2
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1
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How to compare two variables with different distributions?
I want to compare 2 independent variables, but the problem is that the first variable is normally distributed, while the second variable is not. What is the appropriate test in this case? Can I use an ...
- 82.8k
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0
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Chi square test of goodness of fit with unknown parameters
$\chi^2$ test of good fit for multinomial distribution with known parameters uses test statistics
$$
\sum\limits_{k=1}^K \frac{\left( X_k -n p_k^0 \right)^2}{np_k^0},
$$
where $K$ is number of ...
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1
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A powerful test for any distribution
Simulations by Razali et al (2011) showed that the Shapiro-Wilk test of normality provided the most power (at a fixed significance level) when compared to Anderson-Darling, Kolmogorov-Smirnov, etc. My ...
- 290k
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Test which one of two (mechanistic / non-regression) models fits the observations better
There's a large number of similar questions, but they mostly seem to be about regression models and deal with cross validation, comparison of nested statistical models via likelihood-ratio, etc. ...
- 47.3k
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Why do I get this p-value doing the Jarque-Bera test in R?
Doing a Jarque Bera test in R I get this result:
jarque.bera.test(rnorm(85))
data: rnorm(85)
X-squared = 1.259, df = 2, p-value = 0.5329
Does it mean that the ...
CommunityBot
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126
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What criteria to use for goodness-of-fit test for normal distribution ?
There are several goodness of fit tests, may be chi-squared is most famous one, however it seems it is not a preferable choice to be used in the case of continous variables.
There is an excellent ...
11
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1
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14k
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D'Agostino-Pearson vs. Shapiro-Wilk for normality
In the field I work in, there is a large amount of impetus to use Shapiro-Wilk testing as the default normality test (possibly due to NIST and some pubmed papers). I understand that one weakness of SW ...
- 290k
1
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0
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56
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Test for positional amino acid enrichment
I have a question about which statistical test to use for a particular research question. I am studying protein binding motifs (amino acid sequences that other proteins bind to), typically these ...
- 11
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0
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35
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Compare the quality of distribution fits
I have two random variables $A$ and $B$ they are of different size. Both are well fitted as $\gamma$ distributions. My question is to find which one is more gamma like.
Could You help me to solve ...
- 718
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427
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Anderson-Darling test for any distribution with unknown parameters
I have been spending the last two days trying to construct a solid answer to the question:
What is the distribution that best describes my sample?
I did the following:
Plot the histogram (nomalized ...
- 1,270
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2
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Post-hoc test for chi-square goodness-of-fit test
I'm conducting a chi-square goodness-of-fit (GOF) test with three categories and specifically want to test the null that the population proportions in each category are equal (i.e., the proportion is ...
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0
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617
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Is the Pearson goodness-of-fit test parametric or non-parametric?
In this question there was an interesting discussion concerning the Pearson goodness-of-fit test going on which was far from conclusive: Is there any statistical test that is parametric and non-...
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1
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Get p-value from fitdistrplus
Starting from this question How can I test if my observed PDF follows a binomial distribution?
I have got the following binomial distribution:
...
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Normality Test for a Random Sample on SPSS
I have created a random sample of 100 values in SPSS and need to now test for normality with an appropriate goodness of fit test.
I am trying to do a One-Sample t-test via Analyze -> Compare Means -> ...
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