Statistical hypothesis testing

About: Statistical hypothesis testing is a research topic. Over the lifetime, 19580 publications have been published within this topic receiving 1037815 citations. The topic is also known as: statistical hypothesis testing & confirmatory data analysis.

Defending against statistical steganalysis

Abstract: The main purpose of steganography is to hide the occurrence of communication. While most methods in use today are invisible to an observer's senses, mathematical analysis may reveal statistical anomalies in the stego medium. These discrepancies expose the fact that hidden communication is happening. This paper presents improved methods for information hiding. One method uses probabilistic embedding to minimize modifications to the cover medium. Another method employs error-correcting codes, which allow the embedding process to choose which bits to modify in a way that decreases the likelihood of being detected. In addition, we can hide multiple data sets in the same cover medium to provide plausible deniability. To prevent detection by statistical tests, we preserve the statistical properties of the cover medium. After applying a correcting transform to an image, statistical steganalysis is no longer able to detect the presence of steganography. We present an a priori estimate to determine the amount of data that can be hidden in the image while still being able to maintain frequency count based statistics. This way, we can quickly choose an image in which a message of a given size can be hidden safely. To evaluate the effectiveness of our approach, we present statistical tests for the JPEG image format and explain how our new method defeats them.

Robust Performance Hypothesis Testing with the Sharpe Ratio

Abstract: Applied researchers often test for the difference of the Sharpe ratios of two investment strategies. A very popular tool to this end is the test of Jobson and Korkie (1981), which has been corrected by Memmel (2003). Unfortunately, this test is not valid when returns have tails heavier than the normal distribution or are of time series nature. Instead, we propose the use of robust inference methods. In particular, we suggest to construct a studentized time series bootstrap confidence interval for the difference of the Sharpe ratios and to declare the two ratios different if zero is not contained in the obtained interval. This approach has the advantage that one can simply resample from the observed data as opposed to some null-restricted data. A simulation study demonstrates the improved finite sample performance compared to existing methods. In addition, two applications to real data are provided.

The power of statistical tests in meta-analysis.

Abstract: Calculations of the power of statistical tests are important in planning research studies (including meta-analyses) and in interpreting situations in which a result has not proven to be statistically significant. The authors describe procedures to compute statistical power of fixed- and random-effects tests of the mean effect size, tests for heterogeneity (or variation) of effect size parameters across studies, and tests for contrasts among effect sizes of different studies. Examples are given using 2 published meta-analyses. The examples illustrate that statistical power is not always high in meta-analysis.

Statistical topological data analysis using persistence landscapes

Abstract: We define a new topological summary for data that we call the persistence landscape. Since this summary lies in a vector space, it is easy to combine with tools from statistics and machine learning, in contrast to the standard topological summaries. Viewed as a random variable with values in a Banach space, this summary obeys a strong law of large numbers and a central limit theorem. We show how a number of standard statistical tests can be used for statistical inference using this summary. We also prove that this summary is stable and that it can be used to provide lower bounds for the bottleneck and Wasserstein distances.

Eugene: A conceptual manual

Abstract: The study of international relations using quantitative analysis relies, in part, on the availability of comprehensive and easily manipulable data sets. To execute large‐n statistical tests of hypotheses, data must be available on the variables of interest, and those data must be manipulated into a suitable format to allow the inclusion of appropriate control variables as well as variables of central theoretical interest This paper introduces software designed to eliminate many of the difficulties commonly involved in constructing large international relations data sets, and with the unavailability of data on expected utility theories of war. In order to solve these two problems, we developed EUGene (the Expected Utility Generation and Data Management Program). EUGene is a stand‐alone Microsoft Windows based program for the construction of annual data sets for use in quantitative studies of international relations. It generates data for variables necessary to incorporate key variables from implementations...