Analysis of Normality and Homogeneity of Variance

2021 ◽  
Vol 13 (14) ◽  
pp. 8066
Author(s):  
Thowayeb H. Hassan ◽  
Abu Elnasr E. Sobaih ◽  
Amany E. Salem

The cost of fuel and its availability are among the most major concerns for aircrafts and the aviation industry overall. Environmental difficulties with chemical pollutant emissions emitted by aviation machines are also connected to fuel consumption. As a result, it is crucial to examine factors that affect the overall fuel usage and consumption in the airport-based aviation industry. Several variables were investigated related to the total fuel consumed, such as dry operating weight (DOW) (KG), zero-fuel weight (ZFW), take-off weight (TOW), air distance (AIR DIST) (KM), and ground distance (GDN DIST). Analysis of the correlation between total fuel consumed as well as the extra fuel and selected variables was conducted. The results showed that the most positively associated factors with the total used fuel were the air distance (r2 = 0.86, p < 0.01), ground distance (r2 = 0.78, p < 0.01), TOW (r2 = 0.68, p < 0.01), and flight time (r2 = 0.68, p < 0.01). There was also a strong positive association between the average fuel flow (FF) and actual TOW (r2 = 0.74, p < 0.01) as well as ZFW (r2 = 0.61, p < 0.01). The generalized linear model (GLM) was utilized to assess the predictions of total energy usage after evaluating important outliers, stability of the homogeneity of variance, and the normalization of the parameter estimation. The results of multiple linear regression revealed that the most significant predictors of the total consumed fuel were the actual ZFW (p < 0.01), actual TOW (p < 0.01), and actual average FF (p < 0.05). The results interestingly confirmed that wind speed has some consequences and effects on arrival fuel usage. The result reflects that thermal and hydrodynamic economies impact on the flying fuel economy. The research has various implications for both scholars and practitioners of aviation industry.


1977 ◽  
Vol 2 (3) ◽  
pp. 187-206 ◽  
Author(s):  
Charles G. Martin ◽  
Paul A. Games

This paper presents an exposition and an empirical comparison of two potentially useful tests for homogeneity of variance. Control of Type I error rate, P(EI), and power are investigated for three forms of the Box test and for two forms of the jackknife test with equal and unequal n's under conditions of normality and nonnormality. The Box test is shown to be robust to violations of the assumption of normality. The jackknife test is shown not to be robust. When n's are unequal, the problem of heterogeneous within-cell variances of the transformed values and unequal n's affects the jackknife and Box tests. Previously reported suggestions for selecting subsample sizes for the Box test are shown to be inappropriate, producing an inflated P(EI). Two procedures which alleviate this problem are presented for the Box test. Use of the jack-knife test with a reduced alpha is shown to provide power and control of P(EI) at approximately the same level as the Box test. Recommendations for the use of these techniques and computational examples of each are provided.


2021 ◽  
Vol 1 (11) ◽  
pp. 735-748
Author(s):  
Hermansyah Hermansyah ◽  
Nurhendi Nurhendi

The purpose of this research is to see how flash cards influence the students' English vocabulary mastery. The researchers of this research used quantitative research methods with posttest only control design of true experimental design. The random sampling method was employed in this research's sampling. The data collected in this research was put to the test (multiple choice test). The researchers of this research gave different treatments for the experimental and control groups. The treatment for the experimental group was learning English with flash card media and the treatment for the control group was learning English conventionally. After the two sample groups were given different treatment, the two sample groups were each given a posttest with an instrument consisting of 20 multiple-choice questions with 4 alternative answer choices that had been tested beforehand and validated empirically. Analysis of research data is descriptive and inferential, which inferentially uses the t test, by first testing the assumptions of data normality and homogeneity of variance. The results showed that flash cards had an influence on students' English vocabulary mastery. Therefore, it can be said that this research has proved that there was a significant result of using Flash Cards towards children's English vocabulary mastery.


Author(s):  
Iwa Sungkawa

This paper discusses the application of khi-square distribution in homogeneity of variance test on the control of a system used in a process considered normally spread with a mean of and a variance (degree of homogeneity) of . It is necessary to test the hypothesis statistically Ho: with the average μo value is unknown, and the statistic used is Khi-square distribution. On this occasion, an evaluation is executed upon a "Matsuyama" stabilizer (standard volt single phase (L)) to be used in Srengseng, Lenteng Agung, South Jakarta. Based on the test results of upon the variance with average standard voltage 220 volt, the electricity consumers in Srengseng are encouraged to use the stabilizer for household appliances that require voltage stability. By examining the voltage fluctuations at the location and stabilizer conditions (input range), the test result carried out through variance similarity test states that “Matsuyama” stabilizer is eligible and applicable in the area. 


Author(s):  
Bosson-Amedenu Senyefia ◽  
Eyiah-Bediako Francis ◽  
Kusi Prince

Understanding the dynamics, patterns, and probabilities associated with the correlates of crime is a promising way to managing crime. In this study, a multinomial logistic regression was used to predict the propensity of individuals for committing particular crimes. The secondary data of 6702 prisoners was collated from Ghana Prisons Service for the purpose of the study. ANOVA and Brown-Forsythe robust tests of equality of means were employed, where the assumptions for homogeneity of variance were sustained and violated respectively. Pearson’s correlation matrix was also used in the analysis. Our findings showed that religious affiliation and educational level of convicts significantly affected the odds that they would commit a particular crime. Multinomial logistic regression analysis indicated that illiteracy significantly affected the odds that one would commit the crimes of manslaughter, rape, theft, causing harm, and issuing death threats. On the other hand, religious affiliation of an offender significantly affected the odds to commit the crime of murder. Educational level (r= -0.25; p< 0.05) and religious affiliation (r= -0.26; p<0.05) correlated negatively with crime. There were no significant differences in the mean score of crime across educational and religious levels. However, there were significant differences in the mean score of crime across age and gender. The mean difference from the post-hoc analysis showed a pattern of an initial rise in crime among the younger age group (8-25 years), a subsequent decline in the age group of 26-35, and a final surge in individuals beyond 35 years that did not surpass the initial peak. Females (M: 6.89, SD: 1.253) were found to have lower crime incidence than males (M: 7.43, SD: 3.008) for all crimes considered in this study. We recommend that Ghana’s Prison Service consider incorporating further demographic information of inmates in order to support research; which could help identify avenues for the amelioration of crime locally.


1972 ◽  
Vol 32 (4) ◽  
pp. 887-909 ◽  
Author(s):  
Paul A. Games ◽  
Henry B. Winkler ◽  
David A. Probert

2019 ◽  
Vol 57 (9) ◽  
pp. 2239-2260 ◽  
Author(s):  
Guotai Chi ◽  
Bin Meng

Purpose The purpose of this paper is to propose a debt rating index system for small industrial enterprises that significantly distinguishes the default state. This debt rating system is constructed using the F-test and correlation analysis method, with the small industrial enterprise loans of a Chinese commercial bank as the data sample. This study establishes the weighting principle for the debt scoring model: “the more significant the default state, the larger is the weight.” The debt rating system for small industrial enterprises is constructed based on the standard “the higher the debt rating, the lower is the loss given default.” Design/methodology/approach In this study, the authors selected indexes that pass the homogeneity of variance test based on the principle that a greater deviation of the default sample’s mean from the whole sample’s mean leads to greater significance in distinguishing the default samples from the non-default samples. The authors removed correlated indexes based on the results of the correlation analysis and constructed a debt rating index system for small industrial enterprises that included 23 indexes. Findings Among the 23 indexes, the weights of 12 quantitative indexes add up to 0.547, while the weights of the remaining 11 qualitative indexes add up to 0.453. That is, in the debt rating of the small industry enterprises, the financial indexes are not capable of reflecting all the debt situations, and the qualitative indexes play a more important role in debt rating. The weights of indexes “X17 Outstanding loans to all assets ratio” and “X59 Date of the enterprise establishment” are 0.146 and 0.133, respectively; both these are greater than 0.1, and the indexes are ranked first and second, respectively. The weights of indexes “X6 EBIT-to- current liabilities ratio,” “X13 Ratio of capital to fixed” and “X78 Legal dispute number” are between 0.07 and 0.09, these indexes are ranked third to fifth. The weights of indexes “X3 Quick ratio” and “X50 Per capital year-end savings balance of Urban and rural residents” are both 0.013, and these are the lowest ranked indexes. Originality/value The data of index i are divided into two categories: default and non-default. A greater deviation in the mean of the default sample from that of the whole sample leads to greater deviation from the non-default sample’s mean as well; thus, the index can easily distinguish the default and the non-default samples. Following this line of thought, the authors select indexes that pass the F-test for the debt rating system that identifies whether or not the sample is default. This avoids the disadvantages of the existing research in which the standard for selecting the index has nothing to do with the default state; further, this presents a new way of debt rating. When the correlation coefficient of two indexes is greater than 0.8, the index with the smaller F-value is removed because of its weaker prediction capacity. This avoids the mistake of eliminating an index that has strong ability to distinguish default and non-default samples. The greater the deviation of the default sample’s mean from the whole sample’s mean, the greater is the capability of the index to distinguish the default state. According to this rule, the authors assign a larger weight to the index that exhibits the ability to identify the default state. This is different from the existing index system, which does not take into account the ability to identify the default state.


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