Inequality Of Variances Research Articles

Analisis Komparatif Penerbangan Boeing B-737 dan Airbus A-320 Rute Palembang – Cengkareng Pasca Pandemi Covid-19

Aviation activities experienced a strong disruption during the Covid-19 pandemic with restrictions on passenger movement. This article describes a statistical analysis related to flight activity on two types of aircraft, the Boeing B-737 and Airbus A-320, during the end of the pandemic. This research uses the case study method using daily data on the number of passengers, baggage weight, cargo weight, and total fuel needed during the 2021-2022 period. The data is analyzed using descriptive statistics and inferential analysis, namely one-way t-test with the assumption of inequality of variance. The results of the descriptive analysis show that in 2021-2022 there were fluctuations in number of passengers and cargo. Flight activity of the Airbus A-320 is more frequent than that of the Boeing B-737. These results also prove that flight activity on weekends is busier than on weekdays. In addition, the results of the t-test analysis show that there is a significant difference at 95% confidence level between the flight activities of the Airbus A-320 and the Boeing B-737 on the Palembang-Cengkareng departure route at Sultan Mahmud Badaruddin II Airport. This article is also expected to provide an overview regarding the use of statistics to test differences between two variables.

Level of physical activity of students from the police force academy in Bratislava

Background and Study Aim. A healthy and active lifestyle is becoming one of the most talked topics amongst people from all over the world. Being more physically active has never been more important than today as both jobs and leisure activities are becoming increasingly sedentary. Humans have moved from being very physically active to being less and less active each year. The aim of our study was to find out the degree of satisfaction and the frequency of performing leisure activities among students of the Police Academy in Bratislava, Slovakia. Material and Methods. For the purpose of our study, we have used a short version of International Physical Activity Questionnaire (IPAQ) that consisted of 7 questions. The survey was attended by 439 students of the Police Academy located in Bratislava, capital of Slovakia. Our study group was divided into two groups according to their gender, the first group consisted of 249 female students and the second o 190 male students. The overall average age of our students of 21.55 years. Our survey was carried out at the end of the summer semester in June 2022. Questionnaire was carried out online and created through Google forms. The results of the questionnaire were later compared based on the participants gender and analysed using homogeneity test of two independent samples, two-sample t-test with equality and inequality of variances and the chi-square test at the level of significance p < 0.01 or p < 0.05. Results. When compared, male students in general were more active than female students - median of 30 minutes a week. Male students engaged in vigorous intensity physical activity on average more than 15 minutes a week compared to female students. Moderate intensity physical activity difference was even bigger (23,09 minutes a week) in favour of male students, these results have proven to be also statistically significant at the level of significance p < 0.01. Female participants of our study were slightly more active in walking physical activity, 2.92 minutes a week on average, but the difference between our two studied groups have not proven to be statistically significant at the level of significance p < 0.05. Conclusions. Here in our study, we’ve looked at physical activity, physical activity levels and how much students attending Academy of the Police Force in Bratislava engage in them. By comparing our survey participants to adults from other countries we can conclude that both our male and female participants have shown higher physical activity levels.

A Simulation Study Using a Mixed Model Framework to Analyze the Impact of Sample Size and Variability on Type I Error

Aims: This simulation study was conducted to check the validity of a MIXED model’s statistical inference when violating the underlying assumptions – normality of random errors when there are unbalanced group sizes and inequality of variance of errors [Scheffe, 1959].
 Study Design: Monte Carlo Simulation Study.
 Place and Duration of Study: North Dakota State University 2020-2021.
 Methodology: Repeated measures designs (or longitudinal studies) are commonly seen in many research fields, especially in pharmaceutical clinical trials, agricultural research, and psychology. PROC MIXED (SAS Inc.) is a well-known standard tool for analyzing repeated measures data nowadays. The MIXED procedure is based on the standard linear MIXED model, which estimates parameters by maximizing the restricted likelihood. The usual assumption for a standard linear MIXED model is normality. However, the character of data in the real world may be non- smoothed, or non-symmetric, or having heavy tails. We estimate the Type I error rates in different combinations of settings and compare them with the stated Type I error.
 Conclusion: The main results in this study show us that the MIXED model is reasonably robust to modest violations of the normal distribution. However, when a small sample size associated with a treatment was combined with the effects of that treatment having a large variance, a severe inflation problem on Type I error rates could occur when using the MIXED model procedure. When the Type I errors were found to be inflated, the Group= option was found to often help with this problem. A Sub-Sampling procedure was also found to help with this problem.

ЕКОНОМІЧНИЙ РОЗВИТОК РЕГОНІВ УКРАЇНИ: МОДЕЛЮВАННЯ НА ПАНЕЛЬНИХ ДАНИХ

At the current stage, the development of the economy of Ukraine is impossible without considering territorial features, in particular, the strengths and weaknesses of the functioning of regional economic systems, favorable and negative trends in their development. The purpose of the investigation is analyzing and modelling the specifics of economic growth, the factors that influence it, in terms of individual regions of Ukraine at a certain point in time, to develop such a model that would be suitable for further forecasting. A vector autoregression model based on longitudinal data of economic development across regions of Ukraine is used for achieving the purpose. The investigation implemented a model of economic development of the regions of Ukraine based on longitudinal or panel data. As factor variables for the model, the retail trade turnover, the volume of sold industrial products, capital investments, the volume of manufactured construction products, the volume of exports, and the number of the employed population were used. The resulting variable is gross regional product. Input information on factor variables and gross regional product was collected across the regions of Ukraine for the period 2000–2020. After conducting a number of tests (causality test and series stationarity test, Durbin-View-Hausman test, and Wald test), the model was specified as a panel autoregressive model with cross-sectional fixed effects. For such a model, it was necessary to apply the estimated generalized least squares method (panel EGLS), which is based on the assumed inequality of variance and therefore provides the opportunity to obtain the best linear estimates. In general, the quality assessment of the built model gives good results, the determination ratio is close to unity. In the regions of Ukraine, 99.69% of changes in the gross regional product are explained by changes in the values of the gross product itself, the volumes of capital investments, realized industrial products and exports, as well as the turnover of retail trade, with a corresponding lag, according to the r squared value. The proposed model of economic development of regions is adequate to reality and can be used for forecasting. Of course, russian war against Ukraine will make adjustments to the development of the economy of the country and its regions in the future. Therefore, the model characterizes the pre-war situation and may inadequately describe the development of economic processes after Ukraine's victory in the war.

ПАНЕЛЬНЕ МОДЕЛЮВАННЯ ІНФЛЯЦІЙНИХ ПРОЦЕСІВ УКРАЇНИ

Inflation is a well-known and at the same time still insufficiently explained phenomenon of the socio-economic life of any country. This fact is related to the complexity and uncertain of the problem of inflation processes, as well as the fact that the essence of inflation evolves in time and changes in space, depending on the specific economic and political conditions in which the state finds itself. The investigation implemented a model of inflationary processes of Ukraine based on longitudinal data. Average wage index, industrial production index, regional volumes of foreign trade in goods and unemployment rate were used as factor variables for the model. Input information on the factor variables and the consumer price index as the resulting variable was collected across the regions of Ukraine for the period 2000–2020. After conducting a series of tests (Durbin-Wu-Hausman test and Wald test), the model was specified as a longitudinal data model with cross-sectional fixed effects. For such a model, it was necessary to apply the panel estimated generalized least squares method (panel EGLS), which is based on the assumed inequality of variance and therefore provides the opportunity to obtain the best linear estimates. After evaluating the unknown parameters of the model, namely the scalar coefficients, industrial production index, unemployment rate, average wage index, regional volumes of foreign trade in goods, we obtained the following values, respectively: 113.1856, 0.017839, -0.083791, -0.017515, -0.007895. In general, the quality assessment of the model gives good results. We can definitely state that the relationship between the consumer price index is close to, because the determination ratio is close to 1. Based on this, it is obvious that on average in the regions of Ukraine, 99.39% of changes in the consumer price index are explained by changes in the values of the average wage index wages, the index of industrial production, the size of regional volumes of foreign trade in goods and the level of unemployment. And the calculated value of the F-statistic exceeds the empirical value so the model adequately describes such a dependence. In general, the proposed panel model of inflationary processes of Ukraine has good quality indicators and is suitable and can be used for forecasting inflation at the regional level.

Employee motivation and job satisfaction in family-owned businesses

This study aimed to investigate the differences in motivational focus and sources of satisfaction between family and non-family employees in family businesses. Data from a questionnaire survey conducted between May and September 2021 were used to examine the relationship of work motivation between family and non-family employees. Data were collected via a questionnaire and interviews with 56 non-family employees and 148 family employees from family businesses of eight Slovak regions. To meet the stated aim, relevant quantitative methods such as the two-sample Fisher’s F-test, two-sample Student’s t-test with inequality of variances, and the Pearson correlation method were applied. Based on the established results, it can be assumed that it is possible to adapt the dealings with the employees of family companies more closely to their individual needs, and thus contribute to their performance. Non-family employees are more oriented towards economic benefits. Family employees show a more balanced orientation between economic benefits and moral satisfaction. This confirms that financial considerations are still an important factor of motivation for non-family employees. According to the results of the study, non-family employees tend to focus on content and activity, while family employees rather focus on success. A possible explanation could be that family members perceive the success of a company more than their own and feel more confident in the choice of activities they would like to carry out, so they take this fact more than for granted. AcknowledgmentThis paper has been supported by funds of the project VEGA No. 1/0240/20. This study was supported by the project GAAA 5-5/2020 “Development of family businesses in Slovak regions”, which has received funding from Grant Agency Academia Aurea and by project VEGA 1/0813/19 “Managing the development of innovative and start-up forms of businesses in international environment and verification of INMARK concept”, which has received funding from the Ministry of Education, Science, Research and Sport of the Slovak Republic.

Effectiveness of creative arts-based parent training for parents with children with Autism Spectrum Disorder

The mixed-method study evaluated the effectiveness of the 6-week long Creative Arts-based Parent Training program for parents with children with Autism Spectrum Disorder (ASD). Korean Parenting Stress Index-Short Form and Korean Parenting Efficacy Test were used to examine parental stress and sense of competence. Qualitative data were collected for the experimental group (EG) (n = 17) using a 30 min focus group interview, art journaling, and questionnaires. There was no difference in age (t(25) = 1.38, p = .19) and gender (p = .86) between the experimental and control groups (n = 15). The program was a positive experience. Qualitative data on parental experience and quantitative data on parental stress showed significant change, favoring the EG, t(17)=−2.72, p = .014 after controlling for inequality of variances. The EG highlighted the program as: (a) a social connection; (b) new opportunities to be child-focused, and (c) the learning of importance of emotion for child development. More, implementation promoted changes in both parents and children as the fundamental parenting style and the view on the child and disability changed. Therefore, although the study had some limitations, the program showed the promise of group-based supplementary parent training in parent-mediated, creative arts–based intervention as an early intervention treatment for children with ASD.

The delayed Cucker-Smale model with short range communication weights

<p style='text-indent:20px;'>Various flocking results have been established for the delayed Cucker-Smale model, especially in the long range communication case. However, the short range communication case is more realistic due to the limited communication ability. In this case, the non-flocking behavior can be frequently observed in numerical simulations. Furthermore, it has potential applications in many practical situations, such as the opinion disagreement in society, fish flock breaking and so on. Therefore, we firstly consider the non-flocking behavior of the delayed Cucker<inline-formula><tex-math id="M2">\begin{document}$ - $\end{document}</tex-math></inline-formula>Smale model. Based on a key inequality of position variance, a simple sufficient condition of the initial data to the non-flocking behavior is established. Then, for general communication weights we obtain a flocking result, which also depends upon the initial data in the short range communication case. Finally, with no restriction on the initial data we further establish other large time behavior of classical solutions.</p>

Quality assessment of a satellite altimetry data product DT18 in the Norwegian Sea: A comparison to tide gauge records and drifters data

• The altimetric product DT18 reproduces the sea level variability in the Norwegian Sea with an average error 3–4 cm. • Statistical tests conducted for the DT18 reveal some problems. • Errors of the DT18 have a shape of “diamonds” in the open sea. • Ageostrophic factors influence strongly the real current velocities in the Norwegian Sea. The objective of this paper is to assess the quality of the gridded altimetric sea level product DT18 as well as altimetry data from the Sea Level Climate Change Initiative in the Norwegian Sea. We compare the satellite altimetry data with two types of instrumental data. We use tide gauge records to assess the quality in the coastal zone and data from surface drifting buoys to assess the quality in the open ocean. Thus, we aim to complement previous studies by providing the objective assessment of the quality and performance of satellite altimetry in this important region. We demonstrate that the product DT18 reproduces the sea level variability in the coastal zone at an acceptable level (an average error is 3–4 cm), and it reproduces the structure of the time series quite well (almost with a 96% correlation). We found out that altimetry substantially smoothes the pattern of the sea level. This pattern is revealed in the coastal zone as well as in the open sea, where, in addition, it also manifests errors in a shape of “diamonds”, which can be due to data interpolation from satellite tracks. We detected the influence of ageostrophic factors on the current velocities using altimetry in the open sea, and this is also true for the coastal zone. Statistical tests also showed some discrepancies between altimetry data and field (buoys and drifters) data in the open sea. This is manifested in the statistical inequality of variances and in differences of empirical distribution functions. Summing up, we assert that some errors or discrepancies in altimetric data are still observed in high latitudes, both in the coastal zone and in the open part of the Norwegian Sea.

THE BURDEN OF ROTAVIRUS GASTROENTERITIS, AS THE RATIONALE FOR ROUTINE VACCINATION

Rotavirus infection is the second after pneumococcal cause in the incidence of diseases and mortality in children under 5 years. That has defined the who’s recommendation for the introduction of vaccination against rotavirus infection in the vaccination schedules of all countries of the world. In our country that vaccination recommended for epidemic indications for introduction into the regional program. However, vaccination is carried out only in certain regions. One of the reasons for low uptake of this vaccine is the underestimation of the burden of disease.The aim the study.To assess the significance of rotavirus gastroenteritis in the structure of acute gastroenteritis in children under 5 years receiving treatment in outpatient clinics, to study the genetic diversity of rotaviruses, to compare the costs associated with the treatment of acute rotavirus and non-rotavirus gastroenteritis.Methods.Prospective, observational, epidemiological study. The inclusion of participants under the age of 5 years with the symptoms of acute gastroenteritis who meet the criteria of inclusion/exclusion. Examination, medical history, samples of faeces were carried out in the first day of treatment (day of inclusion in the study). Parents were given a questionnaire for 14 days. The severity of the disease was determined according to the scale of Vesicare, the disease dynamics was assessed by the answers of the questionnaire. Examination of feces samples was carried out centrally by PCR. Rotavirus positive samples were genotypically PCR and in case of detection of rare genotypes have been sequenced genomic RNA.Results.The study included 501 baby — boys — 286 (57,1%), girls — 215 (42,9%). The average age was 22.6 ± 15.2 months. 50 children (10.0 per cent) mentioned various background pathology, the others were deemed healthy. Rotavirus was diagnosed in 151 patients 31.4% (95% CI: 26.9 percent - 35.3 percent), which accounted 66,52% (151 of 227) among all cases with confirmed etiology. Genotyping was prevalent G1P [8] to 34.5%, and G4P[8] — 39,2%. Clinical manifestations in rotavirus gastroenteritis was more severe, severe course observed in 65.5% of cases in the comparison group -at 30.4%. Significantly more often than in the comparison group (Р χ2 < 0,001) was observed vomiting (140cases из151 — 93,3%, compared to 239 of 336 -71,1%) and elevated temperature (146 of 151 — 97,3% compared with 254 of 336 — 75,6%). The average temperature was 38,5 ± 0,6 OS in the comparison group — 38,0 ± 2,2 OS, remained 3,1 ± 1,4 and 2.5 ± 1.2 day, respectively. The frequency of episodes of diarrhoea in the first day of illness was 6.4 ± 2.7 times, in comparison with 5.2 ± 2.8, duration of diarrhea was 6.3 ± 3.2 days and 4.5 ± 2.6 days. The costs for parents of patients with acute rotavirus gastroenteritis was (M ± SD) 2873.4 ± 2276.4 rubles, against 2007.4 ± 2150.4 rubles in the comparison group (t = 3.965; p= < 0,001, as amended by Starlite for inequality of variances).Conclusion.The introduction of routine vaccination of children in the first year of life will reduce by more than a third of the number of appeals to medical institutions about intestinal infections and partially prevent the costs associated with the treatment of this pathology.

Clarifying Discrepancies in Responsiveness Between Reliable Change Indices.

Several reliable change indices (RCIs) exist to evaluate statistically significant individual change with repeated neuropsychological assessment. Yet there is little guidance on model selection and subsequent implications. Using existing test-retest norms, key parameters were systematically evaluated for influence on different RCI models. Normative test-retest data for selected Wechsler Memory Scale-IV subtests were chosen based on the direction and magnitude of differential practice (inequality of test and retest variance). The influence of individual relative position compared to the normative mean was systematically manipulated to evaluate for predictable differences in responsiveness for three RCI models. With respect to negative change, RCI McSweeny was most responsive when individual baseline scores were below the normative mean, irrespective of differential practice. When an individual score was greater than the normative mean, RCI Chelune was most responsive with lower retest variance, and RCI Maassen most responsive with greater retest variance. This pattern of results can change when test-retest reliability is excellent and there is greater retest variability. Order of responsiveness is reversed if positive change is of interest. RCI models tend to agree when the individual approximates the normative mean at baseline and test-retest variability is equal. However, no RCI model will be universally more or less responsive across all conditions, and model selection may influence subsequent interpretation of change. Given the systematic and predictable differences between models, a more rationale choice can now be made. While a consensus on RCI model preference does not exist, we prefer the regression-based model for several reasons outlined.

Two-Stage Change Detection for Synthetic Aperture Radar

Coherent change detection using paired synthetic aperture radar (SAR) images is often performed using a classical coherence estimator that is invariant to the true variances of the populations underlying each paired sample. While attractive, this estimator is biased and requires a significant number of samples to yield good performance. Increasing sample size often results in decreased image resolution. Thus, we propose the use of Berger's coherence estimate because, with the same number of pixels, the estimator effectively doubles the sample support without sacrificing resolution when the underlying population variances are equal or near equal. A potential drawback of this approach is that it is not invariant since its distribution depends on the pixel pair population variances. While Berger's estimator is inherently sensitive to the inequality of population variances, we propose a method of insulating the detector from this acuity. A two-stage change statistic is introduced to combine a noncoherent intensity change statistic given by the sample variance ratio, followed by the alternative Berger estimator, which assumes equal population variances. The first-stage detector identifies pixel pairs that have nonequal variances as changes caused by the displacement of sizeable object. The pixel pairs that are identified to have equal or near-equal variances in the first stage are used as an input to the second stage. The second-stage test uses the alternative Berger coherence estimator to detect subtle changes such as tire tracks and footprints. We show experimentally that the proposed method yields higher contrast SAR change detection images than the classical coherent change detector (state of the art), the alternative coherent change detector, and the intensity change detector. Experimental results are presented to show the effectiveness and robustness of the proposed algorithm for SAR change detection.

Analysis of high-dimensional repeated measures designs: The one sample case

A one sample statistic is derived for the analysis of repeated measures design when the data are multivariate normal and the dimension, d , can be large compared to the sample size, n , i.e. d > n . Quadratic and bilinear forms are used to define the statistic based on Box’s approximation [Box, G.E.P., 1954. Some theorems on quadratic forms applied in the study of analysis of variance problems I: Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics 25 (2), 290–302]. The statistic has an approximate χ f 2 distribution, even for moderately large n . One of the main advantages of the statistic is that it can be used both for unstructured and factorially structured repeated measures designs. In the asymptotic derivations, it is assumed that n → ∞ while d remains finite and fixed. However, it is demonstrated through simulations that for n as small as 10, the new statistic very closely approximates the target distribution, unaffected by even large values of d ( d > n ) . The application is illustrated using a sleep lab example with n = 10 , d = 18 .

Improving Rubber Mixing Performance of Hot Water Bag Compound

ABSTRACT A rubber factory in India encountered extensive amount of rework at the rubber mixing stage for one of its medicare products, the hot water bag. The scorch time and the optimum cure time of the rubber-mixing compound were the potential product parameters for which this rework took place. Regression analysis shows that the process parameters, the temperature of the dispersion kneader and the temperature of the open mill, with adjusted R 2 values of 79.9 and 89.5%, respectively can predict both the scorch time and the optimum cure time. Subsequently analyzing the multiple linear regression equation for optimum cure time, which is the key process output variable, with the help of linear programming has arrived at the optimum levels of these temperatures. Besides this, analysis of variance for scorch time has shown that the mixing technique of the workers is not identical. Duncan's multiple range tests has revealed operator group 3 as the best performer for scorch time. Bartlett's test has revealed inequality of variances of four operator groups for optimum cure time. This substantiated the training need of the concerned operators. The study has resulted in reduction of the extent of rework from 80762 to 17865 PPM. Naturally this substantial reduction in rework will reduce the process cycle time and cost of production immensely.

The logistic transform for bounded outcome scores

The logistic transformation, originally suggested by Johnson (1949), is applied to analyze responses that are restricted to a finite interval (e.g. (0,1)), so-called bounded outcome scores. Bounded outcome scores often have a non-standard distribution, e.g. J- or U-shaped, precluding classical parametric statistical approaches for analysis. Applying the logistic transformation on a normally distributed random variable, gives rise to a logit-normal (LN) distribution. This distribution can take a variety of shapes on (0,1). Further, the model can be extended to correct for (baseline) covariates. Therefore, the method could be useful for comparative clinical trials. Bounded outcomes can be found in many research areas, e.g. drug compliance research, quality-of-life studies, and pain (and pain relief) studies using visual analog scores, but all these scores can attain the boundary values 0 or 1. A natural extension of the above approach is therefore to assume a latent score on 0,1) having a LN distribution. Two cases are considered: (a) the bounded outcome score is a proportion where the true probabilities have a LN distribution on (0,1) and (b) the bounded outcome score on [0,1] is a coarsened version of a latent score with a LN distribution on (0,1). We also allow the variance (on the transformed scale) to depend on treatment. The usefulness of our approach for comparative clinical trials will be assessed in this paper. It turns out to be important to distinguish the case of equal and unequal variances. For a bounded outcome score of the second type and with equal variances, our approach comes close to ordinal probit (OP) regression. However, ignoring the inequality of variances can lead to highly biased parameter estimates. A simulation study compares the performance of our approach with the two-sample Wilcoxon test and with OP regression. Finally, the different methods are illustrated on two data sets.

Stepwise procedures for the identification of minimum effective dose with unknown variances

Hsu and Berger (J. Amer. Statist. Assoc. 50 (1999) 468) proposed a stepwise confidence interval procedure for identifying the minimum effective dose in dose-response studies under homoscedasticity. In practice, homogeneity of variance is often in doubt. In this paper, we extend Hsu and Berger's stepwise confidence interval procedure to the case of heteroscedasticity (i.e., inequality of variances across dosages). In addition, we show that the new procedure can properly control the family-wise error rate. We illustrate our procedure with a real example. Finally, we investigate the performance of our procedure and a step-down test procedure based on Welch's approximate t-test via a simulation study. Our procedure is shown, empirically, to perform similar to Welch's procedure.

A powerful transformation trimmed mean method for one‐way fixed effects ANOVA model under non‐normality and inequality of variances

The present study proposes a transformation trimmed mean method for the one‐way fixed effects ANOVA model to deal with non‐normality and inequality of variances. First, the data are trimmed on both sides. Then the test statistic is transformed by Johnson's method for each group to deal with non‐normality. Finally, an approximate test such as the Alexander‐Govern test, the James second‐order test or the Welch test is applied to test the equality of population trimmed means. Monte Carlo simulation results show that, under non‐normal cases, the proposed method can control Type I error rates, and has greater power than other competitors, such as the original Alexander‐Govern method, the Alexander‐Govern trimmed mean method, the James second‐order trimmed mean method, the Welch trimmed mean method, as well as the corresponding bootstrapping methods. The Johnson's transformation trimmed mean method can be programmed easily and is highly recommended as an alternative for the one‐way fixed effects ANOVA model if normality or equality of variances cannot be assumed.

Effects of model misspecification in the estimation of variance components and intraclass correlation for paired data

Paired data occur in many experimental situations. When one views the subjects as a random sample from some large population, it may seem reasonable to model the data according to the typical one-way random effects analysis of variance (ANOVA). It is then usually of interest to estimate variance components and intraclass correlation. These estimators can be biased if key assumptions are violated, leading to erroneous interpretations and conclusions. We focus upon assumptions about the equality or inequality of means and/or variances of the two measures on each subject. In the framework of the one-way random effects ANOVA model, and three generalizations of it, we document estimators obtained as solutions to the likelihood equations. We consider the potentially serious effects of mistaken assumptions. Our findings suggest that the most general model considered is most desirable if consistent and efficient estimation of the between-subject variance component and intraclass correlation is the main goal. We also briefly connect our exposition to the study of reliability or agreement.

ISSUES IN BIOMEDICAL STATISTICS: COMPARING MEANS UNDER NORMAL DISTRIBUTION THEORY

The test used most commonly in biomedical research to compare means when measurements have been made on a continuous scale is Student's t-test, followed closely by various forms of analysis of variance. These tests require that defined populations have been randomly sampled, but there are other assumptions about populations and samples that must be satisfied. These include: (i) normality of the population distributions; (ii) equal variance in those normal populations; and (iii) statistical independence of the samples. This review offers advice to investigators on how to recognize breaches of the assumptions of normality and equality of variance, and how to deal with them by modifying the usual t-test or by transforming the experimental data. The sample-size also has an important bearing on statistical inferences: (i) if it is too small, the risk of Type II error is inflated; and (ii) inequality of sample size exaggerates the effects of inequality of variance. The assumption of independence is breached if repeated measurements are made serially rather than in random order, but adjustments to analysis of variance can be made to correct for the inflated risk of Type I error. The review also considers the problem of making multiple comparisons of means, and recommends solutions.

Ovarian synchronization following ultrasound-guided transvaginal follicle ablation in heifers

In Experiments 1 and 2, ultrasound-guided transvaginal follicle aspiration was used as a method of follicle ablation to induce and synchronize subsequent follicular wave emergence and enhance ovulation synchrony following PGF 2α administration. Heifers were at unknown stages of the estrous cycle at the start of both experiments in which all follicles ≥5 mm in diameter were ablated; luteolysis was induced 4 d later with cloprostenol (500 ug/dose, im). In Experiment 1, heifers were randomly assigned to either an ablation (n=17) or a procedural control (no follicle ablation, n=17) group. Ablation-induced wave emergence was indicated by a significant increase in the total number of follicles ≥5 mm within 2 d of ablation (mean, 1.5 d), which was preceded by a significant surge in circulating FSH. Although the mean (±SEM) interval from PGF 2α administration to ovulation did not differ between follicle-ablated heifers (5.1±0.5 d range, 3 to 9 d) and control heifers (5.1±1.0 d; range, 1 to 5 d), the variability of the interval was different (P<0.05). Inequality of variance between the 2 groups was attributed to a greater (P<0.08) degree of ovulation synchrony in the ablation group than in the control group; 13 16 (81%) versus 9 17 (53%), respectively, ovulated within 5 d of cloprostenol administration. Relative asynchrony of ovulations in control heifers was associated with the status of the follicular wave at the time of PGF 2α administration and, in part, to incomplete luteolysis following a single dose of PGF 2α. Experiment 2 was designed to examine the efficacy of 2 doses of cloprostenol 12 h apart (n=7) versus a single dose (n=8) to induce complete luteolysis subsequent to follicle ablation-induced wave emergence. Two doses of cloprostenol potentiated ovulation synchrony; more (P<0.05) 2-dose heifers ( 7 7 , 100%) than single-dose heifers ( 4 8 , 50%) ovulated within 5 d after PGF 2α administration. In summary, ultrasound-guided transvaginal follicle ablation, done at random during the estrous cycle, induced and synchronized subsequent follicular wave emergence, and resulted in a high degree of ovulation synchrony among heifers after PGF 2α induced luteolysis, especially when 2 doses of PGF 2α were administered 12 h apart.