Statnote 7: chi-square contingency tables

When the data are counts or the frequencies of particular events and can be expressed as a contingency table, then they can be analysed using the chi-square distribution. When applied to a 2 x 2 table, the test is approximate and care needs to be taken in analysing tables when the expected frequencies are small either by applying Yate’s correction or by using Fisher’s exact test. Larger contingency tables can also be analysed using this method. Note that it is a serious statistical error to use any of these tests on measurement data!

The impact of visual-verbal relationships on native-nonnative english speakers' reading processes and comprehension

The aim of this study was to comparatively investigate the impact of visual-verbal relationships that exist in expository texts on the reading process and comprehension of readers from different language background: native speakers of English (LI) and speakers of English as a foreign language (EFL). The study focussed, in this respect, on the visual elements (VEs) mainly graphs and tables that accompanied the selected texts. Two major experiments were undertaken. The first, was for the reading process using the post-reading questionnaire technique. Participants were 163 adult readers representing three groups: 77 (LI), 56 (EFL postgraduates); and 30 (EFL undergraduates). The second experiment was for the reading comprehension using cloze procedure. Participants were 123 representing the same above gorups: 50, 33 and 40 respectively. It was hypothesised that the LI readers would make use of VEs in the reading process in ways different from both EFL groups and that use would enhance each group's comprehension in different aspects and to different levels. In the analysis of the data of both experiments two statistical measurements were used. The chi-square was used to measure the differences between frequencies and the t-test was used to measure the differences between means. The results indicated a significant relationship between readers' language background and the impact of visual-verbal relationships on their reading processes and comprehension of such type of texts. The results also revealed considerable similarities between the two EFL groups in the reading process of texts accompanied by VEs. In the reading comprehension, however, the EFL undergraduates seemed to benefit from the visual-verbal relationships in their comprehension more than the postgraduates, suggesting a weak relationship of this impact for older EFL readers. Furthermore, the results showed considerable similarities between the reading process of texts accompanied by VEs and of whole prose texts. Finally an evaluation of this study was undertaken as well as practical implications for EFL readers and suggestions for future research.

Measuring the degree of spatial correlation between pathological lesions in Alzheimer's disease

The pathological lesions characteristic of Alzheimer's disease (AD), viz., senile plaques (SP) and neurofibrillary tangles (NFT) may not be randomly distributed with reference to each other but exhibit a degree of sptial association or correlation, information on the degree of association between SP and NFT or between the lesions and normal histological features, such as neuronal perikarya and blood vessels, may be valuable in elucidating the pathogenesis of AD. This article reviews the statistical methods available for studying the degree of spatial association in histological sections of AD tissue. These include tests of interspecific association between two or more histological features using chi-square contingency tables, measurement of 'complete' and 'absolute' association, and more complex methods that use grids of contiguous samples. In addition, analyses of association using correlation matrices and stepwise multiple regression methods are described. The advantages and limitations of each method are reviewed and possible future developments discussed.

The spatial pattern of beta-amyloid (Abeta) deposits in Alzheimer’s disease patients is related to apolipoprotein genotype

The spatial patterns of the diffuse, primitive, and classic beta-amyloid (Abeta) deposits was studied in the frontal and temporal cortex in cases of Alzheimer’s disease (AD) expressing different apolipoprotein (Apo E) genotypes. No significant differences in the density of the three Abeta deposit subtypes were observed in individuals expressing genotypes e2/3 and e3/3 compared with those expressing e3/4 and e4/4. In all patients, Abeta deposit subtypes occurred in the tissue in clusters. Chi-square contingency analyses of the data suggested that the cluster size of the diffuse and classic Abeta deposits was unrelated to Apo E genotype. However, the primitive (‘neuritic’) type Abeta deposits occurred more frequently in smaller, denser clusters in individuals expressing genotypes e3/4 and e4/4 compared with those expressing e2/3 and e3/3. Hence, the presence of the e4 allele may be associated with a more specific pattern of neuronal degeneration in the frontal and temporal cortex in AD.

Statnote 1: is the data normal?

Testing whether an observed distribution of observations deviates from normality is a common type of statistical test available in statistics software. Most software offer two ways of judging whether there are significant deviations of the observed from the expected distributions, viz., chi-square and the KS test. These tests have different sensitivities and problems and often give conflicting results. The results of these tests together with observations of the shape of the observed distribution should be used to judge normality.

Statnote 34 : the Kolmogorov-Smirnov (KS) test

The Kolmogorov-Smirnov (KS) test is a non-parametric test which can be used in two different circumstances. First, it can be used as an alternative to chi-square (?2) as a ‘goodness-of-fit’ test to compare whether a given ‘observed’ sample of observations conforms to an ‘expected’ distribution of results (KS, one-sample test). An example of the use of the one-sample test to determine whether a sample of observations was normally distributed was described previously. Second, it can be used as an alternative to the Mann-Whitney test to compare two independent samples of observations (KS, two-sample test). Hence, this statnote describes the use of the KS test with reference to two scenarios: (1) to compare the observed frequency (Fo) of soil samples containing cysts of the protozoan Naegleria collected each month for a year with an expected equal frequency (Fe) across months (one-sample test), and (2) to compare the abundance of bacteria on cloths and sponges sampled in a domestic kitchen environment (two-sample test).

Gender comparisons of fat talk in the United Kingdom and the United States

This study compared different forms of body talk, including "fat talk," among 231 university men and women in central England (UK; n = 93) and the southeastern United States (US; n = 138). A 2 (gender) by 2 (country) repeated measures ANOVA across types of body talk (negative, self-accepting, positive) and additional Chi-square analyses revealed that there were differences across gender and between the UK and US cultures. Specifically, UK and US women were more likely to report frequently hearing or perceiving pressure to engage in fat talk than men. US women and men were also more likely to report pressure to join in self-accepting body talk than UK women and men. © 2010 Springer Science+Business Media, LLC.

Cross-cultural confirmatory factor analysis of the CES-D in Spanish and Mexican dementia caregivers

The Center for Epidemiologic Studies-Depression Scale (CES-D) is the most frequently used scale for measuring depressive symptomatology in caregiving research. The aim of this study is to test its construct structure and measurement equivalence between caregivers from two Spanish-speaking countries. Face-to-face interviews were carried out with 595 female dementia caregivers from Madrid, Spain, and from Coahuila, Mexico. The structure of the CES-D was analyzed using exploratory and confirmatory factor analysis (EFA and CFA, respectively). Measurement invariance across samples was analyzed comparing a baseline model with a more restrictive model. Significant differences between means were found for 7 items. The results of the EFA clearly supported a four-factor solution. The CFA for the whole sample with the four factors revealed high and statistically significant loading coefficients for all items (except item number 4). When equality constraints were imposed to test for the invariance between countries, the change in chi-square was significant, indicating that complete invariance could not be assumed. Significant between-countries differences were found for three of the four latent factor mean scores. Although the results provide general support for the original four-factor structure, caution should be exercised on reporting comparisons of depression scores between Spanish-speaking countries.

The complements towards developing a new risk management framework and Its applicability to the Nigerian power sector

The availability of regular supply has been identified as one of the major stimulants for the growth and development of any nation and is thus important for the economic well-being of a nation. The problems of the Nigerian power sector stems from a lot of factors culminating in her slow developmental growth and inability to meet the power demands of her citizens regardless of the abundance of human and natural resources prevalent in the nation. The research therefore had the main aim of investigating the importance and contributions of risk management to the success of projects specific to the power sector. To achieve this aim it was pertinent to examine the efficacy of risk management process in practice and elucidate the various risks typically associated with projects (Construction, Contractual, Political, Financial, Design, Human resource and Environmental risk factors) in the power sector as well as determine the current situation of risk management practice in Nigeria. To address this factors inhibiting the proficiency of the overarching and prevailing issue which have only been subject to limited in-depth academic research, a rigorous mixed research method was adopted (quantitative and qualitative data analysis). A review of the Nigeria power sector was also carried out as a precursor to the data collection stage. Using purposive sampling technique, respondents were identified and a questionnaire survey was administered. The research hypotheses were tested using inferential statistics (Pearson correlation, Chi-square test, t-test and ANOVA technique) and the findings revealed the need for the development of a new risk management implementation Framework. The proposed Framework was tested within a company project, for interpreting the dynamism and essential benefits of risk management with the aim of improving the project performances (time), reducing the level of fragmentation (quality) and improving profitability (cost) within the Nigerian power sector in order to bridge a gap between theory and practice. It was concluded that Nigeria’s poor risk management practices have prevented it from experiencing strong growth and development. The study however, concludes that the successful implementation of the developed risk management framework may help it to attain this status by enabling it to become more prepared and flexible, to face challenges that previously led to project failures, and thus contributing to its prosperity. The research study provides an original contribution theoretically, methodologically and practically which adds to the project risk management body of knowledge and to the Nigerian power sector.