Satisfaction of customers is extremely critical for any industry especially the highly competitive Telecom industry in India. This research examines statistical association of various demographic ...factors like age, gender, marital status, income, qualification, profession and locality with customer satisfaction of the mobile users of Gujarat, the 5th largest state of India in terms of area. In this research, responses of 800 mobile users with various demographic factors and from 4 different zones of Gujarat were gathered using various close ended questionnaires and simple random sampling. To capture the information and attributes related to satisfaction from mobile services a 5 point Likert Scale was used. The results were analyzed using ANOVA (Welch test, Brown-Forsythe and F test as applicable) and independent samples T test to reach to the desired objectives. Further post hoc tests (Games Howell and Tukey tests) as applicable were also carried out to pin point the group with significant difference in their mean values. These findings will be useful from telecom operator’s perspective for enhancing the customer retention and accusation of new customer base.
Studies evaluating calving sensors provided evidence that attaching the sensor to the tail may lead to changes in the cows’ behavior. Two different calving sensors were attached to 18 cows, all of ...which were equipped with a rumen bolus to record their activity. Two methodological approaches were applied to detect potential behavioral changes: analysis of homogeneity of variance in cow activity (5 days pre-sensor and 24 h post-sensor) and analysis of video-recorded behavior (12 h pre- and post-sensor, respectively) in a subgroup. The average results across the sample showed no significant changes in the variability of activity and no statistically significant mean differences in most visually analyzed behaviors, namely walking, eating, drinking, social interaction, tail raising, rubbing the tail, and the number of standing and lying bouts after calving sensor attachment. In addition to considering mean values across all cows, individual cow investigations revealed an increased number of time slots showing a significant increase in the variability of activity and an increased frequency of tail raising and rubbing the tail on objects after calving sensor attachment in some cows, which should be investigated in more detail on a larger scale.
An important step in the full definition of an analytical method is the characterization of the within and between laboratory variability. This is typically done through collaborative studies ...involving multiple laboratories. The statistical analysis of the results of collaborative studies is generally carried out using standardized protocols such as those given in ISO 5725-2 or ASTM E691-14.
One aspect of the evaluation of collaborative studies is the identification of outlying laboratories which are then excluded from the variance calculation associated with the analytical method. Whether particular laboratories are identified as outliers can have a dramatic effect on the calculated variances.
The generally recommended approach to identify laboratories with excessive within-laboratory variation is Cochran’s Test or something similar. However, Cochran’s Test is very sensitive to non-normality of the underlying statistical distribution. When the assumption of normality is violated, Cochran’s Test can wrongly identify laboratories as outliers at much greater than the nominally stated error rate, even for deviations from normality that are very difficult to detect analytically.
In this paper, an alternative to Cochran’s Test, adapted from Levene’s Test, is proposed and shown to approximately maintain the stated error rate when the underlying distribution is not normal. This newly adapted test is recommended for future collaborative study analysis in place of Cochran’s Test.
Likert-type data are often assumed to be equidistant by applied researchers so that they can use parametric methods. Since this rarely is tested, the validity of parametric analyses of Likert-type ...data is often unclear. This paper consists of two parts where the authors deal with this validity problem in two different respects. In the first part, the authors use an experimental design to show that the perceived distance between scale points on a regular five-point Likert-type scale depends on how the verbal anchors are used. In the second part of the paper, the authors use Monte Carlo simulations to explore how parametric methods commonly used to compare means between several groups perform in terms of actual significance and power when data are assumed to be equidistant even though they are not. The results show that the preferred statistical method to analyse Likert-type data depends on the nature of their nonequidistance as well as their skewness.
Two adjustments to the F test for variances are introduced that ameliorate the poor robustness properties of the test. A comparison of these adjustments to the classical F test, ...Levene/Brown-Forsythe's test, and squared ranks test demonstrates a substantial improvement for various sample sizes and distributions. One of the adjustments is extended to testing homogeneous variances in multiple samples and comparisons are made to Levene's, squared ranks, and Bartlett's tests for equal variability.
Oral squamous cell carcinoma (OSCC) represents more than 90% of all oral cancers. The etiology of the disease has been linked to genetics. To determine OSCC-associated genes, researchers usually test ...if the mean expression level of a gene among OSCC patients is different from that among non-OSCC patients. Recently, researchers found that genes having different variances between two biological states are also relevant to the disease of interest. To the best of our knowledge, no differential variability analysis has been conducted to investigate the genetic risk factors of OSCC yet. In this article, we identified genes differentially variable between the OSCC cases and controls by using the Brown-Forsythe test (BF test) based on two public available gene expression data sets (GSE30784 and GSE6791) from the Gene Expression Omnibus. By using the discovery set, we identified 2,904 DV gene probes, among which 456 DV probes were replicated by the validation set. Our results showed that differential variable genes could provide additional information about the mechanisms of OSCC.
Tsui and Weerahandi (1989) introduced the notion of generalized p-values and since then this idea is used to solve many statistical testing problems. Heteroskedasticity is one of the major practical ...problems encountered in ANOVA problems. To compare the means of several groups under heteroskedasticity approximate tests are used in the literature. Weerahandi (1995a) introduced a test using the notion of generalized p-values for comparing the means of several populations when the variances are not equal. This test is referred to as a generalized F-test.
In this paper we compare the size performance of the Generalized F-test and four other widely used procedures: the Classical F-test for ANOVA, the F-test obtained by the weighted least-squares to adjust for heteroskedasticity, the Brown-Forsythe-test, and the Welch-test. The comparison is based on a simulation study of size performance of tests applied to the balanced one-way model. The intended level of the tests is set at 0.05. While the Generalized F-test was found to have size not exceeding the intended level, as heteroskedasticity becomes severe the other tests were found to have poor size performance. With mild heteroskedasticity the Welch-test and the classical ANOVA F-test have the intended levels, and the Welch-test was found to perform better than the latter. Widely used (due to computational convenience) weighted F-test was found to have very serious size problems. The size advantage of the generalized F-test was also found to be robust even under severe deviations from the assumption of normality.
The classical normal‐theory tests for testing the null hypothesis of common variance and the classical estimates of scale have long been known to be quite nonrobust to even mild deviations from ...normality assumptions for moderate sample sizes. Levene (1960) suggested a one‐way ANOVA type statistic as a robust test. Brown and Forsythe (1974) considered a modified version of Levene's test by replacing the sample means with sample medians as estimates of population locations, and their test is computationally the simplest among the three tests recommended by Conover, Johnson, and Johnson (1981) in terms of robustness and power. In this paper a new robust and powerful test for homogeneity of variances is proposed based on a modification of Levene's test using the weighted likelihood estimates (Markatou, Basu, and Lindsay, 1996) of the population means. For two and three populations the proposed test using the Hellinger distance based weighted likelihood estimates is observed to achieve better empirical level and power than Brown‐Forsythe's test in symmetric distributions having a thicker tail than the normal, and higher empirical power in skew distributions under the use of F distribution critical values.
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