Rejection Of Null Hypothesis Research Articles

Investment Styles and Performance of Equity Mutual Funds in India

The study classified the 419 open-ended equity mutual fund schemes into six distinct investment styles, analysed the financial performance of select open-ended equity mutual fund schemes for the period 1st April 2005 - 31st March 2006 pertaining to the two dominant investment styles and tested the hypothesis whether the differences in performance are statistically significant. The variables chosen for analyzing financial performance are: monthly compounded mean return, risk per unit return and Sharpe ratio. A comparison of the financial performance of the 21 Open-ended Equity growth plans and 21 Open-ended Equity dividend plans was made in terms of the chosen variables. The analysis indicated that Growth plans have generated higher returns than that of Dividend plans but at a higher risk. Further, 17 Growth plans have generated higher returns than that of corresponding Dividend plans offered by the same Asset Management Companies (AMC) and only one Dividend plan could generate higher return than its corresponding Growth plan. However, three Growth plans and the corresponding Dividend plans had the same returns. Out of the 21 Growth plans, 4 Growth plans had higher Coefficient of Variation (Risk per unit Return) than the corresponding Dividend plans and 13 Dividend plans had higher Coefficient of Variation (Risk per unit Return) than the corresponding Growth plans offered by the AMC. Three Growth plans and three Dividend plans had almost equal Risk per unit return. A comparison of the Sharpe ratios of Growth plans and the corresponding Dividend plans indicated that 18 Growth plans out of 21 (approximately 90%) had better risk adjusted excess returns highlighting the fact that Growth plans are likely to reward the investors more for the extra risk they are assuming. Pearson's correlation coefficient between the returns of the two plans was found to be moderate (0.5290) and F-test (1-tailed test) indicated a low probability (0.3753) of the variances of the returns of the two plans. Further, Student's t-test (1-tailed test) led to the rejection of Null Hypothesis and acceptance of Alternate Hypothesis at confidence levels ranging from 0.40 to 0.0005 implying that Equity Growth funds provide higher returns than that of Equity Dividend funds and the differences were statistically significant.

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

Corrections for Type I Error in Social Science Research: A Disconnect between Theory and Practice

Type I errors are a common problem in factorial ANOVA and ANOVA based analyses. Despite decades of literature offering solutions to the Type I error problems associated with multiple significance tests, simple solutions such as Bonferroni corrections have been largely ignored by social scientists. To examine this discontinuity between theory and practice, a content analysis was performed on 5 flagship social science journals. Results indicate that corrections for Type I error are seldom utilized, even in designs so complicated as to almost guarantee erroneous rejection of null hypotheses.

Solving some statistical problems in analyses of experiments on choices of food and on associations with habitat

Statistical tests for non-random associations with components of habitat or different kinds of prey require information about the availability of sub-habitats or types of prey. The data are obtained from sampling (Stage 1 samples). Tests are then constructed using this information to predict what will be the occupancy of habitats or composition of diet under the null hypothesis of random association. Estimates of actual occupancy of habitats or composition of diet are then obtained from Stage 2 sampling and tests are done to compare the observed data from Stage 2 with what was predicted from Stage 1. Estimates from each stage of sampling are subject to sampling error, particularly where small samples are involved. The errors involved in Stage 1 sampling are often ignored, resulting in biases in tests and excessive rejection of null hypotheses (i.e. non-random patterns are claimed when they are not present). Here, accurate tests are developed which take into account both types of error. For animals in patchy habitats, with two or more types of patch, the data from Stages 1 and 2 are used to derive maximal likelihood estimators for the proportions of area occupied by the sub-habitats and the proportions of animals in each sub-habitat. These are then used in χ 2 tests. For composition of diets, data are more complex, because the consumption of food of each type (on its own) must be estimated in separate experiments or sampling. So, Stage 1 sampling is more difficult and the maximal likelihood estimators described here are more complex. The accurate tests described here give much more realistic answers in that they properly control rates of Type I error, particularly with small samples. The effects of errors in Stage 1 sampling are, however, shown to be important, even for quite large samples. The tests can and should be used in any analyses of non-random association or preference among sub-habitats or types of prey.

Progress and dilemma of contemporary clinical pharmacology

Owing to the great progress in clinical chemistry connected with utilization of applied mathematics, pharmacokinetics came into being. The unknown objective methods of research of drugs in human were discovered, among them controlled clinical trials (CCT). These new methodologies generated a new clinical discipline called clinical pharmacology (CPH) which has its roots in basic pharmacology but was applied in clinical specialties. This field is very young, recognized by World Health organization in 1970. Up to the 90s several enthusiasts developed quickly CPH. The scope and development of this discipline is presented in the first part of this article. At the end of the 20th century the science on drugs performed in humans was in the center of interest of the public as well as an object of great pressure of pharmaceutical industry, politicians, and the public. These phenomena started to influence CPH, practiced and taught in medical university faculties and patients care, unfavourably. Government, university authorities, non-profit organizations are not interested in supporting objective research in CPH on the highest academic level. The industry considers the mentioned studies as a threat for its profit. CCT was elaborated for objective comparison of effectiveness and efficacy of old (standard) drugs with the new approved substance. The main purpose of this type of study is a rejection of null hypothesis. Since 1990, these trials caused a strong movement toward evidence-based medicine. A few years ago trials were performed in independent academic centers. These studies were in experienced hands of the teams consistent of highly competent specialists of several fields of medicine. These centers contributed to the quality, intellectual rigor and impact of such clinical trials. But as economic pressure increases, this may belong to the past. Actually pharmaceutical companies curtailed the participation of academic centers in CCT to 40%. According to EU Parliament decision the pharmaceutical industry adopted the whole control of CCT. Politicians and society demand the instant application of new observations and discoveries into practice. Then new drugs approved in 2003 are mentioned. At the end, the general proposition to improve the Status of academic CPH and creditability of CCT is suggested: to develop essential studies on mechanisms of drugs on human being. The highest academic authorities, who understand the importance of CPH, have to discuss the necessity of funding of this type of research with university authorities, non-profit organizations and the Ministry of Health. To soften unavoidable conflict of interests, laborious discussions between academic scientists, pharmaceutic company authorities and governmental authorities are necessary. There is also an urgent necessity of new legislative acts. These proposals are very general and deficient. They were presented here to conclude this article on the present status of clinical pharmacology with the statement that the real threat for this discipline exists.

The Relationship between Returns and Trading Volume: Preliminary Evidence Concerning Taiwan Index Futures Contracts

This paper examines the causal relationship between returns and volume for four Taiwanrelated futures contracts and the co-movement between returns and volume. The findings were as follows: First, past returns could predict the volume for the SIMEX-TW contract; however, a significant lagged volume Granger-caused returns for TF contracts. Second, regarding trading period returns and volume, it was found that volume could be used to forecast returns for TE contracts. There exists a feedback relationship for TF contracts. Third, the study found evidence of significant transitory and permanent covariances except in the case of TX contracts when the close-to-close returns were considered. Fourth, results concerning the covariance between day-time returns and volume corresponded to rejection of the null hypotheses of a zero unconditional covariance (ZUC) and a zero conditional covariance (ZCC); but only in the case of the TE contracts did the author find evidence of ZUC.

Once‐weekly epoetin beta is highly effective in treating anaemic patients with lymphoproliferative malignancy and defective endogenous erythropoietin production

Once‐weekly epoetin beta is highly effective in treating anaemic patients with lymphoproliferative malignancy and defective endogenous erythropoietin production

A correlacional study between the stage of biological and somatotype maturation on children of the Olympic Village of Mare slum

To evaluate individuals in growth and development the expensive and invasive methods can make impracticable the applicability in many underprivileged populations. The identifi cation of the moment in which each individual's particularities manifest in relation to the maturation is determining for an ontogeny understanding, aiming at quality of life and the search for sporting talent. Purpose: To verify the correlation between the stages of biological maturation and somatotype in male young person population dwelling on Mare Slum. Materials and Methods: This study is an applied and descriptive research starting from the observation, analysis and description of results obtained from the analyses of the maturation effects. The population studied (n = 303) consisted of male young people, age group from 9 to 14, participants of the socially-oriented project of the Olympic Village of Mare Slum in Rio de Janeiro. For this, tests for the measurement of somatotype will be handed in (Heath and Carter in: Norton & Olds, 2000): and evaluation of the secondary sexual characteristics (Malina & Bouchard, 2002:228), which under the investigation and statistical analysis will allow that the hypotheses are tested. Aiming at verifying the dependence existent between the classifi cations according to discretional parameters: age, maturational phase and somatotopy, the non-parametric qui-square test was adopted, through which was verifi ed, according to level of signifi cance p < 0,05 for the rejection of null hypothesis. Results: For the signifi cance p=0.0331<0.05 is denoted that relation of dependence correlated between crossed age-group classifi cations exists with the respective maturational phases, for a signifi cance p=1.25E-05=0.0000125<0.05, still for the cros- sed age group classifi cations with the ones of somatotopy. It was not observed a relation of dependence between classifi cations of somatotopy and maturational phase. Conclusions: The age parameter is the interface between the parameters maturational and somatotopy phases, indicating that for the comprehension of these dimensions we have this parameter as the translating and combinatory link with the other two classifi catory processes.

Multiple—test Procedures and Smile Plots

multproc carries out multiple-test procedures, taking as input a list of p-values and an uncorrected critical p-value, and calculating a corrected overall critical p-value for rejection of null hypotheses. These procedures define a confidence region for a set-valued parameter, namely the set of null hypotheses that are true. They aim to control either the family-wise error rate (FWER) or the false discovery rate (FDR) at a level no greater than the uncorrected critical p-value. smileplot calls multproc and then creates a smile plot, with data points corresponding to estimated parameters, the p-values (on a reverse log scale) on the y-axis, and the parameter estimates (or another variable) on the x-axis. There are y-axis reference lines at the uncorrected and corrected overall critical p-values. The reference line for the corrected overall critical p-value, known as the parapet line, is an informal “upper confidence limit” for the set of null hypotheses that are true and defines a boundary between data mining and data dredging. A smile plot summarizes a set of multiple analyses just as a Cochrane forest plot summarizes a meta-analysis.

Pitfall of unit autoregressive root testing

This paper examines whether the usually tested unit autoregressive (AR) root null hypothesis can be informative about the presence of a unit AR root (integration). This is considered null in generic models when the underlying time series is mean or linear trend stationary. It is concluded that non rejection of the unit AR root null hypothesis is not sufficient for integration of a time series. For sufficiency, absence of a unit MA root from the MA representation of the first difference is required. Hence, the analysis here is in line with the general statistical argument that non rejection of a null should not be taken as acceptance of the null; a false practice which is widespread in the unit root and (especially) cointegration literature. An empirical example, involving real quarterly UK GDP, is also provided.

Unit root tests with a break in innovation variance

Abstract It is shown that an abrupt change in the innovation variance of an integrated process can generate spurious rejections of the unit root null hypothesis in routine applications of Dickey–Fuller tests. We develop and investigate modified test statistics, based on unit root tests of Perron for a time series with a changing level, or changing intercept and slope, which are applicable when there is a change in innovation variance of an unknown magnitude at an unknown location.

Application of the Dickey-Fuller test to the Nelson and Plosser (1982) Data

In this letter, Nelson and Plosser's (1982) (NP, hereafter) time series has been retested for unit roots using the Dickey and Fuller (1979) (DF, hereafter) test. There have been two potential misspecification sources identified that may have biased NP's inference towards non rejection of the unit root null hypothesis for all but one series in their data set. These are incorrect lag order choice and (conditional) heteroskedasticity. Furthermore, appropriate testing strategy has been undertaken to alleviate these problems and identify which NP time series have unit roots. In contrast to previous classical (non Bayesian) evidence, only a few time series of NP appear to have unit roots.

Testing for homogeneity of variance in time series: Long memory, wavelets, and the Nile River

We consider the problem of testing for homogeneity of variance in a time series with long memory structure. We demonstrate that a test whose null hypothesis is designed to be white noise can, in fact, be applied, on a scale by scale basis, to the discrete wavelet transform of long memory processes. In particular, we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process. The point at which the test statistic, using a nondecimated version of the discrete wavelet transform, achieves its maximum value can be used to estimate the time of the unknown variance change. We apply our proposed test statistic on five time series derived from the historical record of Nile River yearly minimum water levels covering 622–1922 A.D., each series exhibiting various degrees of serial correlation including long memory. In the longest subseries, spanning 622–1284 A.D., the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 A.D., which coincides closely with the construction of a new device around 715 A.D. for measuring the Nile River. The test also detects a change in variance for a record of only 36 years.

SURROGATE DATA PATHOLOGIES AND THE FALSE-POSITIVE REJECTION OF THE NULL HYPOTHESIS

It is shown that inappropriately constructed random phase surrogates can give false-positive rejections of the surrogate null hypothesis. Specifically, the procedure erroneously indicated the presence of deterministic, nonlinear structure in a time series that was constructed by linearly filtering normally distributed random numbers. It is shown that the erroneous identification was due to numerical errors in the estimation of the signal's Fourier transform. In the example examined here, the introduction of data windowing into the algorithm eliminated the false-positive rejection of the null hypothesis. Additional guidelines for the use of surrogates are considered, and the results of a comparison test of random phase surrogates, Gaussian scaled surrogates and iterative surrogates are presented.

Spurious Rejections by Perron Tests in the Presence of a Break

In this paper, we concentrate on the case of an exogeneously chosen break date, but entertain the possibility that an incorrect choice is made. In fact, the Perron test statistics considered are invariant to any break in the generating process at the assumed break date. Our results therefore apply equally to the case of a generating process with two breaks, only one of which is specifically accounted for in the analysis. As in Leybourne et al. (1998), we find that a neglected relatively early break can lead to spurious rejections of the unit root null hypothesis. Moreover, for all but one of the tests analyzed, spurious rejections now also arise if a true break occurs relatively soon after the assumed break date.

Are the consumption/output and investment/output ratios stationary? An international analysis

This paper analyses the integration order of the consumption/output and investment/output ratios for a group of the most important OECD countries. Results show that these ratios can exhibit some structural breaks. Thus, the use of those statistics which do not take into account the presence of breaks leads to the acceptance of the unit root null hypothesis. A clear increase in the number of rejections of the unit root null hypothesis is found when these structural breaks are included in the model specification.

Term structure and interest differentials as predictors of future inflation changes and inflation differentials

The paper tests the unbiasedness of interest differentials and term structure as predictors of inflation differentials and inflation changes, respectively, using three-, six- and twelve-month maturities in eight major industrial countries over the period 1981–1992. The first hypothesis requires rational expectations (RE) and equality of ex-ante real interest rates, which in turn holds only in the presence of uncovered interest parity (UIP) and ex-ante purchasing power parity (PPP). The second is correct if, in addition to RE, the Fisher hypothesis and constancy of ex-ante real rates are satisfied. The empirical results lead to the rejection of both null hypotheses, although interest differentials and term structure do appear to be relatively useful for forecasting purposes. In particular, the interest differential model performs better than simple ARMA models at the shortest end of the maturity spectrum in out-of-sample forecasting.

Spurious rejections by Dickey–Fuller tests in the presence of a break under the null

It is well known that if a series is generated by a process that is stationary around a broken trend, conventional Dickey–Fuller tests can have very low power. In this paper, the converse phenomenon is studied and illustrated. Suppose that the true generating process is integrated of order one, but with a break. Then it is shown that, if the break occurs early in the series, routine application of standard Dickey–Fuller tests can lead to a very serious problem of spurious rejection of the unit root null hypothesis.

Comment: Recruitment paradigms for fish stocks

Over the last 20 years, there has been a substantial shift in the importance most fisheries scientists ascribe to recruitment overfishing; it was widely assumed (Gulland 1983) that most marine fishes could not be recruitment overfished, and the greatest emphasis in fisheries management was on yield per recruit. However, a large number of fish stock collapses that showed reduced recruitment at low spawning stocks led to a general reappraisal, so that Hilborn and Walters (1992) stated that ithe most important and generally most difficult problem in biological assessment of fisheries is the relationship between stock and recruitment.i Myers et al. (1994) used a large data base on many marine fishes to confirm that most stocks showed reduced recruitment at low spawning stock. Gilbert (1997) offers a revisionist interpretation of the Myers et al. (1994) data and appears to threaten to turn back the clock to a time when fishery managers believed they did not have to worry about maintaining spawning stock biomass. Is this truly a backwards step? I have to answer no; Gilbertis paper is a positive step in our ongoing scientific investigation of stock and recruitment because Gilbert highlights the chicken-or-the-egg dilemma in most spawner recruit analysis. Did low spawning stock lead to low recruitment, or did low recruitment lead to low spawning stock? The growing recognition of the importance of environmental changes in fish recruitment (Francis and Hare 1994) emphasizes the difficulty in interpreting the causes of declines in recruitment, and we are essentially revisiting the ThompsonnBurkenroad debate of 50 years ago (Thompson 1950; Burkenroad 1948; Skud 1975) with more data in hand. Gilbertis paper challenges those of us who have advocated maintaining spawning stock biomass as a prudent form of management to tighten up our arguments. We need to develop statistical analyses that determine the relative probability of competing hypotheses about the cause of recruitment declines. The analysis of Myers et al. (1994) did not consider an environmental change hypothesis; Gilbertis analysis is of limited utility because it relies on acceptance and rejection of null hypotheses, a statistical format that is of no utility for decision making. While Gilbert makes us face the alternative hypothesis that recruitment declined because of environmental conditions, he stops short of the next step and asking what is the prudent management action given the uncertainty regarding the cause of the recruitment decline. If we accept that both a recruitment overfishing hypothesis and an environmental change hypothesis are consistent with an individual stockis history, then what should a manager do if faced with a stock showing both reduced recruitment and reduced spawning stock: continue fishing on the assumption that the environment changed, or reduce fishing in an effort to rebuild spawning stock size? This is a problem in statistical decision theory that requires understanding the probabilities of competing hypotheses and a manageris analysis of risk. Clearly, the costs of not reducing fishing pressure at low abundance, if the true cause is recruitment overfishing, are grave: the stock will simply fail to recover until fishing pressure is reduced. The cost of reducing fishing pressure if the cause of the decline is environmental is simply short-term lost catch. These options are summarized in Table 1: the prudent form of management would seem to be to act as if recruitment overfishing were the cause. However, the choice of management option depends upon the probabilities assigned to the alternative hypotheses and the risk preference of the decision maker. The challenge to fisheries science is now to develop methods to determine the probabilities of alternative hypotheses and perform the risk analysis.

Sex and Gender Comparisons: Does Null Hypothesis Testing Create a False Dichotomy?

In an ongoing debate about the value of doing tests for sex differences, those in favour claim that if sex differences exist, it is important to know about them. However, the null hypothesis (NH) tests that are used for inferring group differences can detect only mean differences and provide no information about how the differences are distributed across groups. Theoretical and empirical examples show how NH rejection can occur when only a small proportion of individuals differ from all others, demonstrating that these tests are incapable of supporting inferences to general group differences. This forces a reevaluation of sex difference research which has been interpreted as distinguishing males from females in general, particularly where inferences have been to general biological factors. However, even knowing the limitations of these tests may not lead to more judicious interpretations in the context of an androcentric culture which dichotomizes the sexes.