Conducting and Interpreting Appropriate Hypotheses Tests (Part 2)

Catherine Comiskey CI and Hypothesis tests part 2 Hypothesis Testing   - Developing Null and Alternative Hypotheses   - Type I and Type II Errors   - Population Mean:  s Known   - Population Mean:  s Unknown   - Population Proportion  

Conducting and Interpreting Appropriate Hypotheses Tests

Catherine Comiskey CI and Hypothesis tests part 1 Hypothesis Testing   -  Developing Null and Alternative Hypotheses   -  Type I and Type II Errors   -   Population Mean:  S Known   -  Population Mean:  S Unknown   -  Population Proportion  

Cluster recognition in spatial-temporal sequences: The case of forest fires

Forest fire sequences can be modelled as a stochastic point process where events are characterized by their spatial locations and occurrence in time. Cluster analysis permits the detection of the space/time pattern distribution of forest fires. These analyses are useful to assist fire-managers in identifying risk areas, implementing preventive measures and conducting strategies for an efficient distribution of the firefighting resources. This paper aims to identify hot spots in forest fire sequences by means of the space-time scan statistics permutation model (STSSP) and a geographical information system (GIS) for data and results visualization. The scan statistical methodology uses a scanning window, which moves across space and time, detecting local excesses of events in specific areas over a certain period of time. Finally, the statistical significance of each cluster is evaluated through Monte Carlo hypothesis testing. The case study is the forest fires registered by the Forest Service in Canton Ticino (Switzerland) from 1969 to 2008. This dataset consists of geo-referenced single events including the location of the ignition points and additional information. The data were aggregated into three sub-periods (considering important preventive legal dispositions) and two main ignition-causes (lightning and anthropogenic causes). Results revealed that forest fire events in Ticino are mainly clustered in the southern region where most of the population is settled. Our analysis uncovered local hot spots arising from extemporaneous arson activities. Results regarding the naturally-caused fires (lightning fires) disclosed two clusters detected in the northern mountainous area.

Statistical Analysis of Eco-Toxicologic Data of Mammals from a Polluted Area

Several eco-toxicological studies have shown that insectivorous mammals, due to theirfeeding habits, easily accumulate high amounts of pollutants in relation to other mammal species. To assess the bio-accumulation levels of toxic metals and their in°uenceon essential metals, we quantified the concentration of 19 elements (Ca, K, Fe, B, P,S, Na, Al, Zn, Ba, Rb, Sr, Cu, Mn, Hg, Cd, Mo, Cr and Pb) in bones of 105 greaterwhite-toothed shrews (Crocidura russula) from a polluted (Ebro Delta) and a control(Medas Islands) area. Since chemical contents of a bio-indicator are mainly compositional data, conventional statistical analyses currently used in eco-toxicology can givemisleading results. Therefore, to improve the interpretation of the data obtained, weused statistical techniques for compositional data analysis to define groups of metalsand to evaluate the relationships between them, from an inter-population viewpoint.Hypothesis testing on the adequate balance-coordinates allow us to confirm intuitionbased hypothesis and some previous results. The main statistical goal was to test equalmeans of balance-coordinates for the two defined populations. After checking normality,one-way ANOVA or Mann-Whitney tests were carried out for the inter-group balances

Altruism, Equity, and Reciprocity in a Gift-Exchange Experiment: An Encompassing Approach

Considerable experimental evidence suggests that non-pecuniary motives must be addressed when modeling behavior in economic contexts. Recent models of non-pecuniary motives can be classified as either altruism- based, equity-based, or reciprocity-based. We estimate and compare leading approaches in these categories, using experimental data. We then offer a flexible approach that nests the above three approaches, thereby allowing for nested hypothesis testing and for determining the relative strength of each of the competing theories. In addition, the encompassing approach provides a functional form for utility in different settings without the restrictive nature of the approaches nested within it. Using this flexible form for nested tests, we find that intentional reciprocity, distributive concerns, and altruistic considerations all play a significant role in players' decisions.

A new method for constructing exact tests without making any assumptions

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes.This method separates the search for an exact test from the goal to create a non-randomized test. Randomization is used to extend any exact test relating to meansof variables with finitely many outcomes to variables with outcomes belonging to agiven bounded set. Tests in terms of variance and covariance are reduced to testsrelating to means. Randomness is then eliminated in a separate step.This method is used to create confidence intervals for the difference between twomeans (or variances) and tests of stochastic inequality and correlation.

Strong minimax lower bounds for learning

Minimax lower bounds for concept learning state, for example, thatfor each sample size $n$ and learning rule $g_n$, there exists a distributionof the observation $X$ and a concept $C$ to be learnt such that the expectederror of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimensionof the concept class. However, these bounds do not tell anything about therate of decrease of the error for a {\sl fixed} distribution--concept pair.\\In this paper we investigate minimax lower bounds in such a--stronger--sense.We show that for several natural $k$--parameter concept classes, includingthe class of linear halfspaces, the class of balls, the class of polyhedrawith a certain number of faces, and a class of neural networks, for any{\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distributionof $X$ and a fixed concept $C$ such that the expected error is larger thana constant times $k/n$ for {\sl infinitely many n}. We also obtain suchstrong minimax lower bounds for the tail distribution of the probabilityof error, which extend the corresponding minimax lower bounds.

The minimax distortion redundancy in empirical quantizer design

We obtain minimax lower and upper bounds for the expected distortionredundancy of empirically designed vector quantizers. We show that the meansquared distortion of a vector quantizer designed from $n$ i.i.d. datapoints using any design algorithm is at least $\Omega (n^{-1/2})$ awayfrom the optimal distortion for some distribution on a bounded subset of${\cal R}^d$. Together with existing upper bounds this result shows thatthe minimax distortion redundancy for empirical quantizer design, as afunction of the size of the training data, is asymptotically on the orderof $n^{1/2}$. We also derive a new upper bound for the performance of theempirically optimal quantizer.

Exact tests for correlation and for the slope in simple linear regressions without making assumptions

We present an exact test for whether two random variables that have known bounds on their support are negatively correlated. The alternative hypothesis is that they are not negatively correlated. No assumptions are made on the underlying distributions. We show by example that the Spearman rank correlation test as the competing exact test of correlation in nonparametric settings rests on an additional assumption on the data generating process without which it is not valid as a test for correlation.We then show how to test for the significance of the slope in a linear regression analysis that invovles a single independent variable and where outcomes of the dependent variable belong to a known bounded set.

A note on robust detection

We introduce a simple new hypothesis testing procedure, which,based on an independent sample drawn from a certain density, detects which of $k$ nominal densities is the true density is closest to, under the total variation (L_{1}) distance. Weobtain a density-free uniform exponential bound for the probability of false detection.

Altruism, equity and reciprocity in a gift-exchange experiment: An encompassing approach

Considerable experimental evidence suggests that non-pecuniary motivesmust be addressed when modeling behavior in economic contexts. Recentmodels of non-pecuniary motives can be classified as either altruism-based, equity-based, or reciprocity-based. We estimate and compareleading approaches in these categories, using experimental data. Wethen offer a flexible approach that nests the above three approaches,thereby allowing for nested hypothesis testing and for determiningthe relative strength of each of the competing theories. In addition,the encompassing approach provides a functional form for utility in different settings without the restrictive nature of the approaches nested within it. Using this flexible form for nested tests, we findthat intentional reciprocity, distributive concerns, and altruisticconsiderations all play a significant role in players' decisions.

The evolutionary host switches of Polychromophilus: a multi-gene phylogeny of the bat malaria genus suggests a second invasion of mammals by a haemosporidian parasite.

BACKGROUND: The majority of Haemosporida species infect birds or reptiles, but many important genera, including Plasmodium, infect mammals. Dipteran vectors shared by avian, reptilian and mammalian Haemosporida, suggest multiple invasions of Mammalia during haemosporidian evolution; yet, phylogenetic analyses have detected only a single invasion event. Until now, several important mammal-infecting genera have been absent in these analyses. This study focuses on the evolutionary origin of Polychromophilus, a unique malaria genus that only infects bats (Microchiroptera) and is transmitted by bat flies (Nycteribiidae). METHODS: Two species of Polychromophilus were obtained from wild bats caught in Switzerland. These were molecularly characterized using four genes (asl, clpc, coI, cytb) from the three different genomes (nucleus, apicoplast, mitochondrion). These data were then combined with data of 60 taxa of Haemosporida available in GenBank. Bayesian inference, maximum likelihood and a range of rooting methods were used to test specific hypotheses concerning the phylogenetic relationships between Polychromophilus and the other haemosporidian genera. RESULTS: The Polychromophilus melanipherus and Polychromophilus murinus samples show genetically distinct patterns and group according to species. The Bayesian tree topology suggests that the monophyletic clade of Polychromophilus falls within the avian/saurian clade of Plasmodium and directed hypothesis testing confirms the Plasmodium origin. CONCLUSION: Polychromophilus' ancestor was most likely a bird- or reptile-infecting Plasmodium before it switched to bats. The invasion of mammals as hosts has, therefore, not been a unique event in the evolutionary history of Haemosporida, despite the suspected costs of adapting to a new host. This was, moreover, accompanied by a switch in dipteran host.

Emotion expression in body action and posture

Emotion communication research strongly focuses on the face and voice as expressive modalities, leaving the rest of the body relatively understudied. Contrary to the early assumption that body movement only indicates emotional intensity, recent studies show that body movement and posture also convey emotion specific information. However, a deeper understanding of the underlying mechanisms is hampered by a lack of production studies informed by a theoretical framework. In this research we adopted the Body Action and Posture (BAP) coding system to examine the types and patterns of body movement that are employed by 10 professional actors to portray a set of 12 emotions. We investigated to what extent these expression patterns support explicit or implicit predictions from basic emotion theory, bi-dimensional theory, and componential appraisal theory. The overall results showed partial support for the different theoretical approaches. They revealed that several patterns of body movement systematically occur in portrayals of specific emotions, allowing emotion differentiation. While a few emotions were prototypically encoded by one particular pattern, most emotions were variably expressed by multiple patterns, many of which can be explained as reflecting functional components of emotion such as modes of appraisal and action readiness. It is concluded that further work in this largely underdeveloped area should be guided by an appropriate theoretical framework to allow a more systematic design of experiments and clear hypothesis testing.

Methods for Region Based Paper Surface Roughness Measurement

Paperin pinnan karheus on yksi paperin laatukriteereistä. Sitä mitataan fyysisestipaperin pintaa mittaavien laitteiden ja optisten laitteiden avulla. Mittaukset vaativat laboratorioolosuhteita, mutta nopeammille, suoraan linjalla tapahtuville mittauksilla olisi tarvetta paperiteollisuudessa. Paperin pinnan karheus voidaan ilmaista yhtenä näytteelle kohdistuvana karheusarvona. Tässä työssä näyte on jaettu merkitseviin alueisiin, ja jokaiselle alueelle on laskettu erillinen karheusarvo. Karheuden mittaukseen on käytetty useita menetelmiä. Yleisesti hyväksyttyä tilastollista menetelmää on käytetty tässä työssä etäisyysmuunnoksen lisäksi. Paperin pinnan karheudenmittauksessa on ollut tarvetta jakaa analysoitava näyte karheuden perusteella alueisiin. Aluejaon avulla voidaan rajata näytteestä selvästi karheampana esiintyvät alueet. Etäisyysmuunnos tuottaa alueita, joita on analysoitu. Näistä alueista on muodostettu yhtenäisiä alueita erilaisilla segmentointimenetelmillä. PNN -menetelmään (Pairwise Nearest Neighbor) ja naapurialueiden yhdistämiseen perustuvia algoritmeja on käytetty.Alueiden jakamiseen ja yhdistämiseen perustuvaa lähestymistapaa on myös tarkasteltu. Segmentoitujen kuvien validointi on yleensä tapahtunut ihmisen tarkastelemana. Tämän työn lähestymistapa on verrata yleisesti hyväksyttyä tilastollista menetelmää segmentoinnin tuloksiin. Korkea korrelaatio näiden tulosten välillä osoittaa onnistunutta segmentointia. Eri kokeiden tuloksia on verrattu keskenään hypoteesin testauksella. Työssä on analysoitu kahta näytesarjaa, joidenmittaukset on suoritettu OptiTopolla ja profilometrillä. Etäisyysmuunnoksen aloitusparametrit, joita muutettiin kokeiden aikana, olivat aloituspisteiden määrä ja sijainti. Samat parametrimuutokset tehtiin kaikille algoritmeille, joita käytettiin alueiden yhdistämiseen. Etäisyysmuunnoksen jälkeen korrelaatio oli voimakkaampaa profilometrillä mitatuille näytteille kuin OptiTopolla mitatuille näytteille. Segmentoiduilla OptiTopo -näytteillä korrelaatio parantui voimakkaammin kuin profilometrinäytteillä. PNN -menetelmän tuottamilla tuloksilla korrelaatio oli paras.

Is the matching function Cobb-Douglas?

[cat] Estudiem les propietats teòriques que una funció d.emparellament ha de satisfer per tal de representar un mercat laboral amb friccions dins d'un model d'equilibri general amb emparellament aleatori. Analitzem el cas Cobb-Douglas, CES i altres formes funcionals per a la funció d.emparellament. Els nostres resultats estableixen restriccions sobre els paràmetres d'aquests formes funcionals per assegurar que l.equilibri és interior. Aquestes restriccions aporten raons teòriques per escollir entre diverses formes funcionals i permeten dissenyar tests d'error d'especificació de model en els treballs empírics.