Hot answers tagged fisher
26
You can turn the question around. Since the ordinary Pearson $\chi^2$ test is almost always more accurate than Fisher's exact test and is much quicker to compute, why does anyone use Fisher's test?
Note that it is a fallacy that the expected cell frequencies have to exceed 5 for Pearson's $\chi^2$ to yield accurate $P$-values. The test is accurate as long ...
26
This is a great question.
Fisher's exact test is one of the great examples of Fisher's clever use of experimental design, together with conditioning on data (basically on tables with the observed row and marginal totals) and his ingenuity at finding probability distributions (though this isn't the best example, for a better example see here). The use of ...
13
The only problem with applying Fisher's exact test to tables larger than 2x2 is that the calculations become much more difficult to do. The 2x2 version is the only one which is even feasible by hand, and so I doubt that Fisher ever imagined the test in larger tables because the computations would have been beyond anything he would have envisaged.
...
7
Your third item is the one I have seen the most often used as rigorous definition.
The others are interesting too (+1). In particular the first is appealing, with the difficulty that the sample size not being (yet) defined, it is harder to define the "from" set.
To me, the fundamental intuition of the likelihood is that it is a function of the model + its ...
6
I think I would call it something different. Likelihood is the probability density for the observed x given the value of the parameter $θ$ expressed as a function of $θ$ for the given $x$. I don't share the view about the proportionality constant. I think that only comes into play because maximizing any monotonic function of the likelihood gives the same ...
6
If you are concerned about sample size and significance, good concepts to start out with include effect size and power (while on the topic of CIs, you might want to include accuracy as well)
As noted previously, 95% CI refers not to probability but to confidence; it is not the likelihood that the current CI contains the population parameter, but that out of ...
6
An annotated Fisher would be an excellent resource!
I don't think that you will be able to understand Fisher without at the same time attempting to understand other major parts of the development of statistics and Fisher's interactions with the other important contributors. I found Statistics in Psychology: An Historical Perspective by Michael Cowles to be ...
5
You are correct to be suspicious and you are correct that problems arise from some of the low cell counts in this case. However, there is nothing wrong with Fisher's test itself. We just need to be careful in interpreting its results.
Let's review the data:
0 1 Total
Site 1 7 2 | 9
Site 2 95 9 | 104
Site 3 0 1 | 1
...
5
In 1946, geophysicist and Bayesian statistician Harold Jeffreys introduced what we today call the Kullback-Leibler divergence, and discovered that for two distributions that are infinitely close we can write their Kullback-Leibler divergence as a quadratic form whose coefficients are given by the elements of the Fisher information matrix. He interpreted this ...
5
The fiducial argument is to interpret likelihood as a probability. Even if likelihood measures the plausibility of an event, it does not satisfy the axioms of probability measures, which is one of the reasons this concept was never so successful.
Let's give an example. Imagine that you want to estimate a parameter, say the half-life $\lambda$ of a ...
4
The question asks for ways to display bivariate discrete data using Excel. Although that software is notoriously limited in graphical capabilities, it is still able to generate many different useful graphics. Let's use the example to illustrate. Here are the data, laid out as they might be in a spreadsheet:
X, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
Y, ...
4
Unless there is some specific reason for people being NA, and unless you are interested in that reason, then I would say to not include people who are missing.
You don't need an exact test here; all the cell sizes are reasonable.
However 1) Don't you want some form of regression instead? and 2) Why is Albumin dichotomized into low and high? Dichotomizing ...
3
Fisher's exact test is usually used for 2x2 tables. In such a table, you have a few choices for effect size.
One is the odds ratio, which can be calculated by hand pretty easily. If the four cells are $A_{11} A_{12} A_{21} $ and $A_{22}$ then the OR is $A_{11}*A_{22}/A_{21}*A_{12}$.
Another is the difference in proportions in the two rows or two columns: ...
3
You can use a Fisher exact test in your first example, though with so large a sample then a Chi-square test will give a similar result and without specialist software will be easier to calculate. Just looking at the numbers, it seems obvious you will reject your null hypothesis: E1 happens quite frequently in your observations of P2 and P4 but not at all ...
3
This page in MathWorld
explains how the calculations work. It points out that the test can be defined in a variety of ways:
To compute the P-value of the test,
the tables must be ordered by some
criterion that measures dependence,
and those tables that represent equal
or greater deviation from independence
than the observed table are the ones
...
3
Fisher uses p-values as a continuous measure of evidence against a null hypothesis?
Perhaps. What convinces you of this?
So a p-value of 0.06 would indicate that there is no difference and the null hypothesis is true?
Not at all. How did you go from 'continuous measure of evidence against' to 'there is no difference'?
3
i) First, a recommendation:
Use pchisq( -2*sum(log(p-values)), df, lower.tail=FALSE) instead of 1- ... - you're likely to end up with more accuracy for small p-values. To see that they're sometimes going to give different results, try this:
x=70;c(1-pchisq(x,1),pchisq(x,1,lower.tail=FALSE))
ii) Yes, it's one-sided. Small values of the chi-square ...
2
Generally speaking, the likelihood ratio and the ordinary Pearson $\chi^2$ tests are more accurate than Fisher's "exact" test. But for your situation you need an extremely heavy multiplicity adjustment thrown in, not matter which statistical test is used. Decision trees such as the one you are building require amazingly large datasets for their structure ...
2
The first test should read
> fisher.test(expData[,1], expData[,2])
Fisher's Exact Test for Count Data
data: expData[, 1] and expData[, 2]
p-value = 0.4857
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.001607888 4.722931239
sample estimates:
odds ratio
0.156047
as per the doc: x is the outcome ...
2
There's no reason you can't apply Fisher's exact test to this problem. Or you could use a standard chi-squared test for independence, as the expected cell counts aren't that small.
Neither approach will answer the question "what is the probability that these 39 times of seeing something is unevenly distributed between these 4 plants" though. That would ...
2
For many reasons, classification is not a good goal for most problems; prediction is. Logistic regression (LR) is a more direct probability model to use for prediction, with fewer assumptions. Linear discriminant analysis (LDA) assumes that X has a multivariate normal distribution given Y. Using Bayes' rule to get Prob(Y|X) you get a logistic model. So ...
2
Have a look at this work on the Tracklet Descriptor. In this case, they need to compute distances between time series of different lengths, and they use a nice dynamic time warping approach to inflate/deflate the two time series in question to find a minimum distance between them based on an idea of optimally distorting them. Outside of a reasonable set of ...
2
Including the ten in the analysis you get a significant result and without the 10 you don't get a significant result from prop.test in R. You can simulate your situation in R in order to see if you trust the approximate result:
# number of simulation replicates
n <- 10000
# variable to hold the output
is10 <- rep(NA, times = n)
for(i in 1:n){
# ...
2
There is a generalization of the Fisher Exact test for $2 \times2$ Tables to more general $R \times C$. In your case $R=2$ and $C=9$. The null hypothesis is that the column proportion is independent of the row. So it tests a null hypothesis that the proportions are the same for each configuration versus the alternative that they differ. So the test is ...
2
See the following paper for a very thourough, modern discussion:
Bjørnstad, J. F. (1996). On the Generalization of the Likelihood Function and the Likelihood Principle. Journal of the American Statistical Association 91: 791-806.
2
Here's an attempt at a rigorous mathematical definition:
Let $X: \Omega \to \mathbb R^n$ be a random vector which admits a density $f(x | \theta_0)$ with respect to some measure $\nu$ on $\mathbb R^n$, where for $\theta \in \Theta$, $\{f(x|\theta): \theta \in \Theta\}$ is a family of densities on $\mathbb R^n$ with respect to $\nu$. Then, for any $x \in ...
2
If you want to correlate X and Y, then you could consider point biserial correlation:
$R_{pb} = \frac{M_1 - M_0}{s_n}\frac{n_1n_0}{n*2}$ where $s_n$ is the standard deviation of (in your case) Y and the subscripts refer to the two groups as defined by X, if you are willing to posit that Y is "really" continuous (e.g. it's a marker on some latent scale).
If ...
2
Greater or less refers to a one sided test that compared to a null hypothesis that p1=p2 the alternative is p1>p2 in contrast to a two sided test where the alternative is that P1 not equla to p2. For your table the proportion of dieters that are male is 1/4 =0.25 (10 out of 40) in your sample. On the other hane the proportion of non-dieters that are male ...
2
Fisher's exact test tells you only about the probability of your or "more extreme" data given that the null hypothesis holds. It does not tell you about where in the table your data deviate from independence.
Pearson residuals are one way of expressing that. Try
chisq.test(x)$residuals to obtain them. Larger absolute values correspond to greater deviance ...
2
'N' or number of samples is usually the number of cases, this can be the number of subject (assuming you have one measurement of each feature per subject) or the number of measurements per feature. If you have multiple measurements per feature, per subject you will need to account for this.
Generally, EEG channels should be considered separately, as ...
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