Abstract:
A review study of NIST Statistical Test Suite is undertaken with a motivation to understand all its test algorithms and to write their C codes independently without looking at various sites mentioned in the NIST document. All the codes are tested with the test data given in the NIST document and excellent agreements have been found. The codes have been put together in a package executable in MS Windows platform. Based on the package, exhaustive test runs are executed on three PRNGs, e.g. LCG by Park & Miller, LCG by Knuth and BBSG. Our findings support the present belief that BBSG is a better PRNG than the other two.

Abstract:
It is well known that the NIST statistical test suite was used for the evaluation of AES candidate algorithms. We have found that the test setting of Discrete Fourier Transform test and Lempel-Ziv test of this test suite are wrong. We give four corrections of mistakes in the test settings. This suggests that re-evaluation of the test results should be needed.

Abstract:
We checked the statistical analysis behind the original paper's tests of equiprobability.The original paper tested equiprobability with the Kolmogorov-Smirnov test outside its regime of validity. Correct tests find no statistically significant deviations from equiprobability for the statistical values in Nature.Statistical tests should be used correctly.A recent paper concluded that "statistical practice is generally poor, even in the most renowned scientific journals" [1]. The paper prompted significant attention in the popular press, and serious concern within the scientific community [2-7]. It led the editors of Nature Medicine to review their statistical practices, ultimately resulting in new statistical guidelines for all Nature Research Journals [3].One of the two main results of [1] was that terminal digits of statistical values in Nature deviated significantly from an equiprobable distribution, indicating errors or inconsistencies in rounding. The authors of [1] collected random samples of test statistics and p values published in Nature, and looked at the terminal digits of these numbers. Their raw data is shown in tables 1 and 2. They argued that these terminal digits should be spread evenly among the ten possible digits. Applying the Kolmogorov-Smirnov test with SPSS for Windows, they obtained Z = 2.7, p < 0.0005, for the 610 test statistics, and Z = 1.4, p = 0.043, for the 181 p values. They thus concluded that the terminal digits suffered from errors, most likely due to poor rounding procedures. We point out that the original paper's test of equiprobability was based on invalid use of the Kolmogorov-Smirnov test on categorical data and that correct statistical testing finds no statistically significant deviations from equiprobability.The authors of [1] also found a number of cases where p values in Nature and the British Medical Journal were reported incorrectly, based on comparison with the reported test statistics. That finding is unaffected by our an

Abstract:
The use of routine laboratory tests in diagnosing disease is becoming of increasing importance. This emphasizes to test the efficiency of diagnostic tests, since relatively few diagnostic tests correctly classify all subjects tested as diseased or well. The more usual situation is one in which some well subjects are classified as diseased and some diseased subjects classified as well. In this type of situation, Diagnostics and prognostic models serve the purpose. Diagnostic models are usually used for classification and quite commonly used in medical field. In this paper, importance of statistical classification procedures are highlighted which helps in the evaluation of diagnostic tests.

Abstract:
symmetries and statistical properties in nuclei are closely related. the most striking example is the extremely large enhancement of parity violation in neutron resonances. statistical distributions can provide information about the underlying character of nuclear properties. level statistics and electromagnetic transition distributions have been used successfully to provide unique tests of predictions of random matrix theory.

Abstract:
Being given the conditions of an ever increasing competition between the offerers of touristic products at internal and international level, an important factor is represented by the formation of stable customers who should also ensure the promotion of the touristic product among the possible clients on different markets. This supposes the achievement of some high quality touristic services which should generate favorable and long-lasting impressions. The paper is meant to build an analysis model of the data resulted from sounding research based by applying statistical tests.

Abstract:
The variation in sizes of chondrules from one chondrite to the next is thought to be due to some sorting process in the early solar nebula. Hypotheses for the sorting process include chondrule sorting by mass and sorting by some aerodynamic mechanism; one such aerodynamic mechanism is the process of turbulent concentration (TC). We present the results of a series of statistical tests of chondrule data from several different chondrites. The data do not clearly distinguish between various options for the sorting parameter, but we find that the data are inconsistent with being drawn from lognormal or (three-parameter) Weibull distributions in chondrule radius. We also find that all but one of the chondrule data sets tested are consistent with being drawn from the TC distribution.

Abstract:
Nonparametric statistical tests are useful procedures that can be applied in a wide range of situations, such as testing randomness or goodness of fit, one-sample, two-sample and multiple-sample analysis, association between bivariate samples or count data analysis. Their use is often preferred to parametric tests due to the fact that they require less restrictive assumptions about the population sampled. In this work, JavaNPST, an open source Java library implementing 40 nonparametric statistical tests, is presented. It can be helpful for programmers and practitioners interested in performing nonparametric statistical analyses, providing a quick and easy way of running these tests directly within any Java code. Some examples of use are also shown, highlighting some of the more remarkable capabilities of the library.

Abstract:
The previous discussion emphasized statistical significance testing. But there are various reasons to expect departure from the uniform distribution in terminal digits of p-values, so that simply rejecting the null hypothesis is not terribly informative. Much more importantly, Jeng found that the original p-value of 0.043 should have been 0.086, and suggested this represented an important difference because it was on the other side of 0.05. Among the most widely reiterated (though often ignored) tenets of modern quantitative research methods is that we should not treat statistical significance as a bright line test of whether we have observed a phenomenon. Moreover, it sends the wrong message about the role of statistics to suggest that a result should be dismissed because of limited statistical precision when it is so easy to gather more data.In response to these limitations, we gathered more data to improve the statistical precision, and analyzed the actual pattern of the departure from uniformity, not just its test statistics. We found variation in digit frequencies in the additional data and describe the distinctive pattern of these results. Furthermore, we found that the combined data diverge unambiguously from a uniform distribution. The explanation for this divergence seems unlikely to be that suggested by the previous authors: errors in calculations and transcription.In 2004, Garcia-Berthou and Alcaraz [GBA] published "Incongruence between test statistics and P values in medical papers [1]." This article reported that last digits of published test statistics and p-values in a sample of consecutive articles from Nature deviated from a uniform distribution more than would be expected by chance. The article, which also examined incongruence between reported statistics and p-values, attracted a great deal of attention among journal editors, the popular press, and a large number of readers [2]. In 2006, however, Jeng pointed out that the GBA analysis of last digi

Abstract:
NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to construct functions that are considered as GOOD pseudorandom generators by NIST SP800-22 test suite though the output of these functions are easily distinguishable from the uniform distribution. Thus these functions are not pseudorandom generators by definition. On the other hand, NIST SP800-22 does not cover some of the important laws for randomness. Two fundamental limit theorems about random binary strings are the central limit theorem and the law of the iterated logarithm (LIL). Several frequency related tests in NIST SP800-22 cover the central limit theorem while no NIST SP800-22 test covers LIL. This paper proposes techniques to address the above challenges that NIST SP800-22 testing suite faces. Firstly, we propose statistical distance based testing techniques for (pseudo) random generators to reduce the above mentioned Type II errors in NIST SP800-22 test suite. Secondly, we propose LIL based statistical testing techniques, calculate the probabilities, and carry out experimental tests on widely used pseudorandom generators by generating around 30TB of pseudorandom sequences. The experimental results show that for a sample size of 1000 sequences (2TB), the statistical distance between the generated sequences and the uniform distribution is around 0.07 (with $0$ for statistically indistinguishable and $1$ for completely distinguishable) and the root-mean-square deviation is around 0.005.