![]() There are at most $n \cdot (n - 1)$ permutations of $\mathbb Z/n\mathbb Z$ of the form $x \mapsto ax + b$: if $n$ is prime, there are $n - 1$ choices for $a$ and $n$ choices for $b$ under which this is a permutation. So the question is: if I found some "hidden" structure in "random" object, does it indicate that the object is very unlikely to be random or I can always find structure in every object that friend gives to me? How this "suspiciousness" can be quantified in the rigorous mathematical sense? But this does not indicate that the permutation is not random. And my friend is telling me: well you can always invent some tricky formula and get every my permutation. But the structure can be more tricky (for example, k-round Feistel network over some group with some round functions or the like). I can try to say something like : well, there is a structure, and a chance that random permutation will have this structure is really small. Is there any strategy using which I can rigorously state (as a mathematical statement) that this event is very unplausible? Of course it is not possible for me to actually prove that permutation is not random, because we always can generate this one by chance. My friend said to me that it happens by chance. ![]() I'm suspicious and worried, because the permutation (for instance) looks like: $\pi(x) = ax + b \pmod n$ for some $a$, $b$. He pretends that the permutation was generated completely random. Singleton dimensions are prepended to samples with fewer dimensionsīefore axis is considered.Imagine that my friend gives me the permutation $\pi$. If samples have a different number of dimensions, The axis of the (broadcasted) samples over which to calculate the The observed test statistic and null distribution are returned inĬase a different definition is preferred. The convention used for two-sided p-values is not universal Test statistic is always included as an element of the randomized Interpretation of this adjustment is that the observed value of the The numerator and denominator are both increased by one. That is, whenĬalculating the proportion of the randomized null distribution that isĪs extreme as the observed value of the test statistic, the values in Rather than the unbiased estimator suggested in. Note that p-values for randomized tests are calculated according to theĬonservative (over-estimated) approximation suggested in and 'two-sided' (default) : twice the smaller of the p-values above. ![]() Less than or equal to the observed value of the test statistic. 'less' : the percentage of the null distribution that is Greater than or equal to the observed value of the test statistic. 'greater' : the percentage of the null distribution that is The alternative hypothesis for which the p-value is calculated.įor each alternative, the p-value is defined for exact tests as If vectorized is set True, statistic must also accept a keywordĪrgument axis and be vectorized to compute the statistic along the statistic must be a callable that accepts samplesĪs separate arguments (e.g. Statistic for which the p-value of the hypothesis test is to beĬalculated. ![]() Parameters : data iterable of array-likeĬontains the samples, each of which is an array of observations.ĭimensions of sample arrays must be compatible for broadcasting except That the data are paired at random or that the data are assigned to samplesĪt random. Randomly sampled from the same distribution.įor paired sample statistics, two null hypothesis can be tested: Performs a permutation test of a given statistic on provided data.įor independent sample statistics, the null hypothesis is that the data are permutation_test ( data, statistic, *, permutation_type = 'independent', vectorized = None, n_resamples = 9999, batch = None, alternative = 'two-sided', axis = 0, random_state = None ) # ![]()
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