t-Tests for Single Means of Autocorrelated Data — A Simulation Study —

A simulation study is reported in which the effect of positive and negative autocorrelation on the quantiles of Student's t-test variable is investigated. It is shown that negative autocorrelations lead to smaller quantiles. Positive autocorrelations lead to larger quantiles.     

An Approximate Solution to the Behrens-Fisher Problem

An approximate and practical solution is proposed for the Behrens-Fisher problem. This solution is compared to the solutions considered by Mehta and Srinivasan (1970) and Welch's (1937) approximate t-test in terms of the stability of the size and magnitude of the power. It is shown that the stability of the size of the new test is better than that of Welch's t when at least one of the sample sizes is small. When the sample sizes are moderately large or large the sizes and powers of all the recommended tests are almost the same.     

The Matched Pairs Problem with Exponential Variates

Two classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times (t_1j, t_2j), the classes of tests are those based on t_1j-t_2j and those based on log t_1j–log t_2j. For each class the sign, signed ranks, t and likelihood ratio tests are compared via Pitman's criterion of asymptotic relative efficiency (ARE). For tests based on t_1j — t_2j, it is found that: (1) the efficacy of the paired t depends on the coefficient of variation (CV) of the pair means, (2) the signed rank test has the same ARE to the sign test as for the usual location problem. For tests based on log t_1j — log t_2j, the ARE comparisons reduce to the well-known results for the one-sample location problem for samples from a logistic density. Hence, the signed rank test is asymptotically efficient. Furthermore, analyses based on log t_1j — log t_2j are not complicated by the underlying pairing mechanism.     

Comparison of t-tests for differences in sexual dimorphism between populations

A t-test that can be used for evaluating the significance of differences in metric sexual dimorphism between populations is derived directly from mathematical considerations of the differences between distributions. It is compared with the t-test derived by Relethford and Hodges (1985), which was based upon linear regression with sex as a dummy variable. Both are determined to be mathematically equivalent, though the one derived here is more similar in form to traditional t-tests of differences and therefore may be simpler to employ. Both tests require only summary statistics for comparisons between populations and comparisons between generations within populations.     

Sample Sizes for Comparisons of k Treatments with a Control Based on Different Definitions of the Power

The determination of sample sizes for the comparison of k treatments against a control by means of the test of Dunnett (1955, 1964) as well as by means of the multiple t-test will be considered. The power in multiple comparisons can be defined in different ways, see Hochberg and Tamhane (1987). We will derive formulas for the per-pair power, the any-pair power and the all-pairs power for both one- and two-sided comparisons. Tables will be provided that allow sample sizes to be determined for preassigned values of the power.     

Inter- and intra-specific differences in filtering activities between two unionids, Anodonta woodiana and Unio douglasiae, in ambient eutrophic lake waters

Inter-specific and intra-specific differences in the filtering activities of two unionid bivalves, Unio douglasiae and Anodonta woodiana, which thrive in small agricultural canals, were compared using a flow-through chamber system of ambient eutrophic lake water. The mean filtration rates (FRs) of these two species, size-matched for similar shell length, were not significantly different (t-test, t = 0.024, P = 0.981), whereas there were significant differences in the FRs between mussels of different ages (t-test, t = 5.137, P = 0.001), different densities (t-test, t = 8.297, P < 0.0001), and different currents (t-test, t = 3.898, P = 0.005). The FRs of A. woodiana increased significantly more with higher temperatures in younger mussels (P < 0.01, maximum FR = 0.352 ± 0.157 L/h at 13.5–20.4 °C) than in adults. However, the mortality of the mussels was comparatively higher in younger mussels due to a low tolerance to ammonia. Correlation coefficients and PCA results collectively indicate that the two dominant unionid mussels in the canal had a strong relationship with the seston level in the lake (turbidity, suspended solids and chlorophyll-a), resulting in a higher FR, pseudo-faeces production, and ammonia tolerance and a lower mortality. In addition, the validation of the biomanipulation used in the mussel-controlled system is discussed in an effort to improve the water quality of eutrophic lakes and streams and the conservation of the benthic mussel community.     

Testing for differentially expressed genes with microarray data

This paper compares the type I error and power of the one- and two-sample t-tests, and the one- and two-sample permutation tests for detecting differences in gene expression between two microarray samples with replicates using Monte Carlo simulations. When data are generated from a normal distribution, type I errors and powers of the one-sample parametric t-test and one-sample permutation test are very close, as are the two-sample t-test and two-sample permutation test, provided that the number of replicates is adequate. When data are generated from a t-distribution, the permutation tests outperform the corresponding parametric tests if the number of replicates is at least five. For data from a two-color dye swap experiment, the one-sample test appears to perform better than the two-sample test since expression measurements for control and treatment samples from the same spot are correlated. For data from independent samples, such as the one-channel array or two-channel array experiment using reference design, the two-sample t-tests appear more powerful than the one-sample t-tests.     

Spline and General Regression of Polytomous Data

The paper shows a formulation for a general linear regression as well as a spline regression of multinomial responses on a quantitative input variables. Application of least squares and asymptotic theory yields the F-test for significance of coefficients and a t-test for structural discontinuity.     

How to Use the Two Sample t-Test

This work discusses how two sample t-tests behave when applied to data that may violate the classical statistical assumptions of independence, heteroscedasticity and Gaussianity. The usual two sample t-statistic based on a pooled variance estimate and the Welch-Aspin statistic are treated in detail. Practical “rules-of-thumb” are given along with their applications to various examples so that readers will easily be able to use such tests on their own data sets.     

Improving identification of differentially expressed genes in microarray studies using information from public databases

We demonstrate that the process of identifying differentially expressed genes in microarray studies with small sample sizes can be substantially improved by extracting information from a large number of datasets accumulated in public databases. The improvement comes from more reliable estimates of gene-specific variances based on other datasets. For a two-group comparison with two arrays in each group, for example, the result of our method was comparable to that of a t-test analysis with five samples in each group or to that of a regularized t-test analysis with three samples in each group. Our results are further improved by weighting the results of our approach with the regularized t-test results in a hybrid method.     

Permutation – based statistical tests for multiple hypotheses

Background  

Genomics and proteomics analyses regularly involve the simultaneous test of hundreds of hypotheses, either on numerical or categorical data. To correct for the occurrence of false positives, validation tests based on multiple testing correction, such as Bonferroni and Benjamini and Hochberg, and re-sampling, such as permutation tests, are frequently used. Despite the known power of permutation-based tests, most available tools offer such tests for either t-test or ANOVA only. Less attention has been given to tests for categorical data, such as the Chi-square. This project takes a first step by developing an open-source software tool, Ptest, that addresses the need to offer public software tools incorporating these and other statistical tests with options for correcting for multiple hypotheses.     

Energy exploitation in Chirocephalus croaticus (Steuer, 1899) (Crustacea: Anostraca): survival strategy in an intermittent lake

Electron transport system (ETS) activity was measured in Chirocephalus croaticus from the intermittent lake, Petelinjsko Jezero. The ETS activities were measured at 5, 10, 15, 20, and 25 °C, and were studied separately in juveniles, females and males. Juveniles had significantly higher activity than adults at a standard temperature of 20 °C. The mass-specific ETS activity decreased with increasing size of the animals; the value b was 0.787. Respiration rates (R) were determined at 20 °C and the ratio ETS/R (±standard deviation) for C. croaticus was 1.43±0.46 (n=38). ETS activity increased with temperature. Females had higher Q₁₀ than males in higher temperature range (t-test; t=2.50; d.f.=8; p<0.05). Activation energy E_a was higher for females than males (t-test; t=2.35; d.f.=8; p<0.05). Females exhibited lower ETS activity than males over the lower temperature range, but their ETS could function more efficient at higher temperature.     

On Testing Equality of Means of Correlated Variates with Incomplete Data

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

Effect of exercise-induced hyperventilation on airway resistance and cycling endurance

The purpose of the present study was to investigate the effect of exercise induced hyperventilation and hypocapnia on airway resistance (R _aw), and to try to answer the question whether a reduction of R _aw is a mechanism contributing to the increase of endurance time associated with a reduction of exercise induced hyperventilation as for example has been observed after respiratory training. Eight healthy volunteers of both sexes participated in the study. Cycling endurance tests (CET) at 223 (SD 47) W, i.e. at 74 (SD 5)% of the subject's peak exercise intensity, breathing endurance tests and body plethysmograph measurements of pre- and postexercise R _aw were carried out before and after a 4-week period of respiratory training. In one of the two CET before the respiratory training CO₂ was added to the inspired air to keep its end-tidal concentration at 5.4% to avoid hyperventilatory hypocapnia (CO₂-test); the other test was the control. The pre-exercise values of specific expiratory R _aw were 8.1 (SD 2.8), 6.8 (SD 2.6) and 8.0 (SD 2.1) cm H₂O · s and the postexercise values were 8.5 (SD 2.6), 7.4 (SD 1.9) and 8.0 (SD 2.7) cm H₂O · s for control CET, CO₂-CET and CET after respiratory training, respectively, all differences between these tests being nonsignificant. The respiratory training significantly increased the respiratory endurance time during breathing of 70% of maximal voluntary ventilation from 5.8 (SD 2.9) min to 26.7 (SD 12.5) min. Mean values of the cycling endurance time (t _cend) were 22.7 (SD 6.5) min in the control, 19.4 (SD 5.4) min in the CO₂-test and 18.4 (SD 6.0) min after respiratory training. Mean values of ventilation ( _E) during the last 3␣min of CET were 123 (SD 35.8) l · min⁻¹ in the control, 133.5 (SD 35.1) l · min⁻¹ in the CO₂-test and 130.9 (SD 29.1) l · min⁻¹ after respiratory training. In fact, six subjects ventilated more and cycled for a shorter time, whereas two subjects ventilated less and cycled for a longer time after the respiratory training than in the control CET. In general, the subjects cycled longer the lower the _E, if all three CET are compared. It is concluded that R _aw measured immediately after exercise is independent of exercise-induced hyperventilation and hypocapnia and is probably not involved in limiting t _cend, and that t _cend at a given exercise intensity is shorter when _E is higher, no matter whether the higher _E occurs before or after respiratory training or after CO₂ inhalation. Accepted: 11 September 1996     

EXISTENCE OF TWO STOMATAL SHAPES IN THE GENUS DENDROBIUM (ORCHIDACEAE) AND ITS SYSTEMATIC SIGNIFICANCE

On the basis of the shape and size of the outer stomatal ledge, 153 species of the genus Dendrobium (Orchidaceae) were divided into three groups, i.e., species group I, species group II, and section Grastidium. Student's t-test and principal components analysis using seven stomatal characters suggest that the first two groups are quite distinct from each other. The values for section Grastidium, however, are scattered and indicative of heterogeneity. Our data suggest a high probability that species groups I and II are monophyletic sister groups. However, section Grastidium, in which stomatal diversification has occurred, may be para- or polyphyletic relative to the genus Dendrobium.     

An Improvement of the Westlake Symmetric Confidence Interval

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST -LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one-sided t-tests. An (1-α)-confidence interval consistent with the two one-sided t-tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)-confidence interval of the t-test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one-sided confidence intervals.     

Effect of Permanent Shading on Adult Size and Biomass of the Caddisfly <Emphasis Type="Italic">Lype phaeopa</Emphasis> (Stephens, 1836) (Psychomyiidae)

To investigate the effect of shading on the development of aquatic insect larvae, estimated by the size and biomass of freshly emerged adults, a laboratory experiment was conducted in which larvae of the psychomyiid caddisfly Lype phaeopa were reared in glass aquaria covered by gauze pervious to light and compared to aquaria which were covered by a black textile distinctly reducing the light irradiation. Seven submerged branches colonized by larvae of L. phaeopa were collected from a small lowland stream, cut in two equally sized halves and one of the halves was reared under natural light and the other one under shaded condition. The hypothesis of the study was that larvae reared under natural light conditions can develop faster resulting in earlier emergence and larger adults compared to larvae reared under a shaded conditions. Females were always significantly larger and heavier than simultaneously emergent males (paired t-test, p < 0.001) independent of the treatment. The experiment revealed no effects of the shading on the adult size and biomass of emergent adults, neither for males (t-test, p = 0.197) nor for females (p = 0.303). Adult biomass was influenced by seasonal temperature (smaller adults during the warm summer months). Females’ biomass was also different between the branches independent from the treatment (one way ANOVA, p = 0.002) whereas males showed only a trend (p = 0.055). The shading displayed a significant effect on the emergence date of males with earlier emergence in the light treatment compared to the dark treatment (t-test, p = 0.046), but this could be not ascertained for females (p = 0.828). The experiment indicated that shading has no significant effect on the adult biomass of L.␣phaeopa, but it could delay the time of emergence in males. Main driving factors of larval development and subsequent adult biomass in L. phaeopa were temperature and habitat quality.     

Pulse transit time reveals drug kinetics on vascular changes affected by propofol

Pulse transit time (PTT) is the duration in which a pulse wave travels between two arterial sites within the same cardiac cycle. The aim of our study is to use PTT to examine propofol's effects on the vascular system. Methods. We collected data from 50 healthy women, between 28 and 51 years old, who underwent gynaecological surgery under general anaesthesia. The general anaesthesia was induced with propofol injection (2 mg/kg). PTT measurements were obtained from the R-wave of electrocardiogram and the pulse wave of photoplethysmograph. Two PTT values were obtained; one before (the control) and the other after propofol injection. The results were analysed by Student's t-test. Results. After propofol injection, the PTT was prolonged. The change in the PTT value from that of baseline was significant statistically (P < 0.05, by Student's t-test). The PTT change over time correlated with the degree of vasodilatation over time. Monitoring of PTT not only revealed the magnitude of vascular changes but also demonstrated the onset of vascular dilation, its peak and duration. We conclude that PTT is a useful guide in monitoring the drug kinetics of propofol.     

Stein's Two-Stage Test in Linear Models

After a brief presentation of Stein's two-sample test there is shown an improved procedure for general linear hypotheses analogous to the improvement of the two-sample-t-test described by Stein. The example of an analysis of variance in an one-way layout demonstrates the execution of the procedure as well as the problems that occur with the determination of the test parameters n₀ and z. For these problems there is finally suggested a practicable way of solution.     

Involvement of the specific nucleolar protein SURF6 in regulation of proliferation and ribosome biogenesis in mouse NIH/3T3 fibroblasts

The nucleolar proteins which link cell proliferation to ribosome biogenesis are regarded to be potentially oncogenic. Here, in order to examine the involvement of an evolutionary conserved nucleolar protein SURF6/Rrp14 in proliferation and ribosome biogenesis in mammalian cells, we established stably transfected mouse NIH/3T3 fibroblasts capable of conditional overexpression of the protein. Cell proliferation was monitored in real-time, and various cell cycle parameters were quantified based on flow cytometry, Br-dU-labeling and conventional microscopy data. We show that overexpression of SURF6 accelerates cell proliferation and promotes transition through all cell cycle phases. The most prominent SURF6 pro-proliferative effects include a significant reduction of the population doubling time, from 19.8 ± 0.7 to 16.2 ± 0.5 hours (t-test, p < 0.001), and of the length of cell division cycle, from 17.6 ± 0.6 to 14.0 ± 0.4 hours (t-test, p < 0.001). The later was due to the shortening of all cell cycle phases but the length of G1 period was reduced most, from 5.7 ± 0.4 to 3.8 ± 0.3 hours, or by ～30%, (t-test, p < 0.05). By Northern blots and qRT-PCR, we further showed that the acceleration of cell proliferation was concomitant with an accumulation of rRNA species along both ribosomal subunit maturation pathways. It is evident, therefore, that like the yeast homologue Rrp14, mammalian SURF6 is involved in various steps of rRNA processing during ribosome biogenesis. We concluded that SURF6 is a novel positive regulator of proliferation and G1/S transition in mammals, implicating that SURF6 is a potential oncogenic protein, which can be further studied as a putative target in anti-cancer therapy.