LIMO EEG: A Toolbox for hierarchical LInear MOdeling of ElectroEncephaloGraphic data

Magnetic- and electric-evoked brain responses have traditionally been analyzed by comparing the peaks or mean amplitudes of signals from selected channels and averaged across trials. More recently, tools have been developed to investigate single trial response variability (e.g., EEGLAB) and to test differences between averaged evoked responses over the entire scalp and time dimensions (e.g., SPM, Fieldtrip). LIMO EEG is a Matlab toolbox (EEGLAB compatible) to analyse evoked responses over all space and time dimensions, while accounting for single trial variability using a simple hierarchical linear modelling of the data. In addition, LIMO EEG provides robust parametric tests, therefore providing a new and complementary tool in the analysis of neural evoked responses

A Project Based Approach to Statistics and Data Science

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills

A comparison of efficient permutation tests for unbalanced ANOVA in two by two designs--and their behavior under heteroscedasticity

We compare different permutation tests and some parametric counterparts that are applicable to unbalanced designs in two by two designs. First the different approaches are shortly summarized. Then we investigate the behavior of the tests in a simulation study. A special focus is on the behavior of the tests under heteroscedastic variances.Comment: 20 pages, 9 figures, Working Paper of the Department of Management And Enigineering of the University of Padov

Impact of unbalancedness and heteroscedasticity on classic parametric significance tests of two-way fixed-effects ANOVA tests

Classic parametric statistical tests, like the analysis of variance (ANOVA), are powerful tools used for comparing population means. These tests produce accurate results provided the data satisfies underlying assumptions such as homoscedasticity and balancedness, otherwise biased results are obtained. However, these assumptions are rarely satisfied in real-life. Alternative procedures must be explored. This thesis aims at investigating the impact of heteroscedasticity and unbalancedness on effect sizes in two-way fixed-effects ANOVA models. A real-life dataset, from which three different samples were simulated was used to investigate the changes in effect sizes under the influence of unequal variances and unbalancedness. The parametric bootstrap approach was proposed in case of unequal variances and non-normality. The results obtained indicated that heteroscedasticity significantly inflates effect sizes while unbalancedness has non-significant impact on effect sizes in two-way ANOVA models. However, the impact worsens when the data is both unbalanced and heteroscedastic.StatisticsM. Sc. (Statistics

Markups, entry regulation, and trade - Does country size matter?

Actual, and potential competition is a powerful source of discipline on the pricing behavior of firms with market power. The authors develop a simple model that shows that the effects of new entry, and import competition on industry price-cost markups, depend on country size. The authors predicted that barriers to domestic entry would have a stronger anti-competitive effect in large countries, while barriers to foreign entry (imports) would have a stronger effect in small countries. After estimating markups for manufacturing sectors in forty-one industrial, and developing countries, they test these hypotheses, and find that the hypotheses cannot be rejected by the data. For example, although Indonesia, and Italy impose the same number of regulations on the entry of new firms, the effect of the regulations on manufacturing markups is twenty percent greater in Italy because of its larger size. Similarly, while Chile and Zimbabwe have the same import penetration ration, the market discipline effect of imports is thirteen percent greater in Zimbabwe because of its smaller size.Water Treatment&Quality,Roads&Highways,Montreal Protocol,Water Conservation,Coastal and Marine Resources,Environmental Economics&Policies,Economic Theory&Research,Water and Industry,Trade and Regional Integration,Banks&Banking Reform

H-statistic with winsorized modified one-step M-estimator as central tendency measure

Two-sample independent t-test and ANOVA are classical procedures which are widely used to test the equality of two groups and more than two groups respectively. However, these parametric procedures are easily affected by non-normality, becoming more obvious when heterogeneity of variances and unbalanced group sizes exist. It is well known that the violation in the assumption of the tests will lead to inflation in Type I error rate and decreasing in the power of test. Nonparametric procedures like Mann-Whitney and Kruskal-Wallis may be the alternative to the parametric procedures, however, loss of information occur due to the ranking data. In mitigating these problems, robust procedures can be used as the other alternative. One of the procedures is H-statistic. When used with modified one-step M-estimator (MOM), the test statistic (MOM-H) produces good control of Type I error rate even under small sample size but inconsistent under certain conditions investigated. Furthermore, power of test is low which might be due to the trimming process. In this study, MOM was winsorized (WMOM) to retain the original sample size. The Hstatistic when combines with WMOM as the central tendency measure (WMOM-H) shows better control of Type I error rate as compared to MOM-H especially under balanced design regardless of the shape of distributions. It also performs well under highly skewed and heavy tailed distribution for unbalanced design. On top of that, WMOM-H also generates better power value, as compared to MOM-H and ANOVA under most of the conditions investigated. WMOM-H also has better control of Type I error rates with no liberal value (>0.075) compared to the parametric (t-test and ANOVA) and nonparametric (Mann-Whitney and Kruskal-Wallis) procedures. In general, this study demonstrates that winsorization process (WMOM) is able to improve the performance of H-statistic in terms of controlling Type I error rate and increasing power of test