This study compared the results of his chi square text of independence and the corrected chi square statistic against Fisher's exact probability test (the hypergeometric distribution) in contection with sampling from a finite population. Data were collected by advancing the minimum call size from zero to a maximum which resulted in a tail area probability of 20 percent for sample sizes from 10 to 100 by varying increments. Analysis of the data supported the rejection of the null hypotheses regarding the general rule-of-thumb guidelines concerning sample size, minimum cell expected frequency and the continuity correction factor. it was discovered that the computation using Yates' correction factor resulted in values which were so overly conservative (i.e. tail area porobabilities that were 20 to 50 percent higher than Fisher's exact test) that conclusions drawn from this calculation might prove to be inaccurate. Accordingly, a new correction factor was proposed which eliminated much of this discrepancy. Its performance was equally consistent with that of the uncorrected chi square statistic and at times, even better.

An analysis of the presence or absence of black melanin in broiler chickens as affected by the presence of different traits is studied in the following project. The purpose of this analysis is to show that the simple partitioning of chi-square method is as good as any method. This project also shows the equivalence of different statistical methods. / Thesis / Master of Science (MSc)

Master of Science / Department of Statistics / Paul I. Nelson / The standard Chi-square test for the equality of proportions of positive responses to c specified binary questions is valid when the observed responses arise from independent random samples of units. When the responses to all c questions are recorded on the same unit, a situation called correlated proportions, the assumptions under which this test is derived are no longer valid. Under the additional assumption of compound symmetry, the Cochran-Q test is a valid test for the equality of proportions of positive responses. The purpose of this report is to use simulation to examine and compare the performance of the Cochran-Q test and the standard Chisquare test when testing for the equality of correlated proportions. It is found that the Cochran-Q test is superior to the Chi-square test in terms of size and power, especially when the common correlation among the binary responses is large.

Published Article / Pricing management, as part of the marketing strategy of an organisation, is a difficult and highly complex - but also critically important - management activity, as it affects the revenue and therefore the profits of an organisation. However, scholars such as Bruck (2010), Cram (2006:5), Eugster, Kakkar and Roegner (2000:133), Hinterhuber (2004:765) and Pratt (2007) believe that the pricing function in organisations has largely been neglected by managers and academics and that price is generally set by guesswork and not by scientific means. This article maintains that the pricing function in an organisation can be successfully managed through the implementation of a pricing plan. A critically important step in the pricing plan is to select a pricing strategy or combination of pricing strategies to set the price of a product or service. A number of nonparametric statistical tests are available to assist management in the selection of the most suitable pricing strategy, or combination of pricing strategies, when determining the price of a product or service. The aim of this article is to demonstrate the use of statistical methods in selecting a pricing strategy as part of a comprehensive pricing plan. The article contains an analysis of selected literature, while taking a descriptive and statistical approach to demonstrate the use of statistical methods in selecting a pricing strategy.

This study aims to investigate the important indicators that contribute to happiness among Beijing residence. The residents of Beijing were taken as the target population for the survey. A questionnaire was used as the main statistical instrument to collect the data from the residents in Beijing. In so doing the investigation employs Factor analyses and chi-square analyses as the main statistical tools used for the analyses in this research. The study found that Beijing residents gained greater happiness in the family, interpersonal relationships, and health status. The analysis also shows that generally, the residence of Beijing feels happier and also in terms of gender basis, females in Beijing feel happier as compare to their male counterpart. It will find that gender, age and education are statistically significant when dealing with happiness.

The purpose of this study was to describe the predictors of evacuation intention among coastal residents in the State of Florida and to determine if there are meaningful segments of the population who intend to evacuate when told to do so by governmental officials because of a major hurricane. In the America’s and the Caribbean, 75,000 deaths have been attributed to hurricanes in the 20 th century. A well planned evacuation can reduce injury and death, yet many people do not have an evacuation plan and do not intend to evacuate when told to do so. The study used secondary data from the Harvard School of Public Health, Hurricane in High Risk Areas study, a random sample of 5,046 non-institutionalized persons age 18 and older in coastal counties of Texas, Louisiana, Mississippi, Alabama, Georgia, North Carolina, South Carolina and Florida. Surveys for the State of Florida were segregated and used in this analysis, resulting in a study sample of 1,006 surveys from 42 counties. When asked if they would evacuate in the future if told to by government officials, 59.1% of Floridians surveyed said they would leave, 35.2% said they would not leave and 5.6% said it would depend. In Florida, 65.7% of the population had been threatened or hit by a major hurricane in the last three years and 26.6% of those had left their homes because of the hurricane. Of those whose communities were threatened by a hurricane, 83.3% of the communities were damaged and 33.8% experienced major flooding associated with the hurricane. Bivariate statistics and logistic regression were used to explore the interactions of predictors and evacuation intention. The best predictor of evacuation intention was prior evacuation from a hurricane (chi-square= 45.48, p < .01, Cramer’s V = 0.266). Significant relationships were also demonstrated between evacuation intention and worry a future hurricane would hit the community (chi-square = 22.75, p < .01, Cramer’s V = 0.11), the presence of pets (chi-square = 6.57, p < .01, Cramer’s V = 0.084), concern the home would be damaged (chi-square = 19.41, p < .01, Cramer’s V = 0.10), belief the home would withstand a major hurricane (chi-square = 19.55, p < .01, Cramer’s V = 0.10), length of time in the community (chi-square = 26.59, p < .01, Cramer’s V = 0.12), having children in the household (chi-square = 11.13, p < .01, Cramer’s V = 0.11), having a generator (chi-square = 17.12, p < .01, Cramer’s V = 0.13), age (chi-square = 24, p < .01, Cramer’s V = 0.16) and race (chi-square = 12.21, p = .02, Cramer’s V = 0.12). Logistic regression of the predictors of evacuation intention resulted in significant relationships with previous evacuation experience (OR = 4.99, p < .001), age 30 to 49 compared to age over 65 (OR = 2.776, p < .01), the presence of a generator (OR = .447, p < .01), having a home not very likely to be damaged compared to a home very likely to be damaged (OR =.444, p = .018), and experiencing poor prior government and voluntary agency response to previous hurricanes compared to excellent response (OR = .386, p < .027). Chi-squared Automatic Interaction Detection (CHAID) was used to identify segments of the population most likely and least likely to evacuate when told to do so. Those most likely to evacuate had evacuated due to a previous hurricane. Those least likely to evacuate when told to do so had not evacuated in a previous storm, do not own a generator and are over the age of 65. Information from this study can be used in planning for evacuation response by governmental entities. Available demographic information can be used to determine numbers of persons likely to evacuate before a storm. The results of this study can be used to inform a marketing strategy by government officials to encourage evacuation among those who say they would not evacuate when told to do so. Further research is needed to determine additional characteristics of the populations who say they will and will not evacuate when told to do so.

This research was conducted to identify whether South African 3 star and above hotels are interested in forming alliances. The objective of this study was to group South African independent 3 star and above hotels on the alliance framework continuum, namely; cooperation, collaboration, coordination and coadunation; and to identify whether South African independent 3 star and above hotels are interested to progress from one simple form of alliance to the next complex, formal type of alliance. Hypotheses were proposed to determine the significance of the differences in preference of South African 3 star and above independent hotels. Thus, this study is descriptive in nature, to test the proposed hypotheses. An extensive investigation into the relevant literature was done. An empirical study was also conducted and the measuring instrument consisted of a selfadministered questionnaire. The population selected consisted of managers of these South African 3 star and above independent hotels. The major findings included: South African independent 3 star and above hotels seem to prefer niche personality and potential non-financial relationship, while they try to avoid economic and cultural integration with a partner firm and not interested in shared management control with the partner firm. Besides, four factors confirmed the alliance continuum developed by Bailey and Koney (2000), namely; cooperation, coordination, collaboration and coadunation. Friedman’s test indicated that there is significant difference among the different dimensions of alliance formation, namely; cooperation, collaboration, coordination and coadunation and that South African independent 3 star and above hotels are interested to form cooperation form of alliances mostly, followed by coordination form of alliances. South African independent 3 star and above hotels are neutral on whether to form collaboration type of alliances and they are not interested to involve in the coadunation form of alliances. Chi-square test indicated that there is no significant difference on the opinion of the respondents on whether the hotel they work for needs to progress from simpler form of alliances into more formal and complex format of alliances. However, those who preferred that their hotel has to progress from simpler form of alliance are higher in number than those who did not prefer. It was, inter alia, recommended that as South African 3 star and above hotels choose lower form of alliance, value chains seem the most applicable form of alliance. Hotels could share a name, reservation information and some basic IT facilities (point of sale IT reservation equipment and back office IT equipments). Finally, the study concludes by recommending that South African independent 3 star and above hotels should take alliances as an option for growth and justification of expenditures and decide the level of alliance continuum they want to engage in. / Dissertation (MBA)--University of Pretoria, 2012. / Gordon Institute of Business Science (GIBS) / unrestricted

Using a variance-stabilizing transformation of the non-centralχ² distribution and Wald's sequential probability ratio test, procedures have been developed for sequential analysis of categorical data group-wise. These procedures' enables (i) a simple hypothesis to be used for the alternative hypothesis instead of the composite hypothesis commonly used in goodness-of-fit tests, contingency tables, and Mood's non-parametric generalization of the one-way analysis of variance, (ii) calculation or a power function, and (iii) calculation of the greatest expected ASR's and the non-centrality parameter requiring this sample size in addition to the ASN's when the null or alternative hypothesis is true. Application of these procedures to the three types of analysis given in (i) give the right decisions with sample sizes near the calculated ASN’s. The ASN's for when the expected number of groups equals one compare favorably with those obtained by Jackson (1959) using Bhate’s conjecture and those obtained empirically by Appleby (1960). In general, the sequential approach will require smaller sample sizes than fixed sampling if the non-centrality parameter is equal to or less than the group size and the group size is large enough to meet minimum expectation requirements. / M.S.

This study compared the results for McNemar's test, the t test for related measures, and the chi-square test of independence as cell sized varied in a two-by-two frequency table. In this study. the probability results for McNemar's rest, the t test for related measures, and the chi-square test of independence were compared for 13,310 different combinations of cell sizes in a two-by-two design. Several conclusions were reached: With very few exceptions, the t test for related measures and McNemar's test yielded probability results within .002 of each other. The chi-square test seemed to equal the other two tests consistently only when low probabilities less than or equal to .001 were attained. It is recommended that the researcher consider using the t test for related measures as a viable option for McNemar's test except when the researcher is certain he/she is only interested in 'changes'. The chi-square test of independence not only tests a different hypothesis than McNemar's test, but it often yields greatly differing results from McNemar's test.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This dissertation examines the measurement of business concentration by the Herfindahl- Hirschman Index (HHI). In the course of the examination, a modification to this method of measurement of business concentration is proposed, in terms of which the accuracy of the conventional depiction of the HHI can be enhanced by a formulation involving the Gini index. Computational advantages in the use of this new method are identified, which reveal the Ginibased HHI to be an effective substitute for its regular counterpart. It is found that theoretically and in practice, the proposed new method has strengths that favour its usage. The practical advantages of employing this method are considered with a view to encouraging the measurement of business concentration using the Gini-based index of the HHI. / AFRIKAANSE OPSOMMING: Hierdie verhandeling ondersoek die meting van sakekonsentrasie deur middel van die Herfindahl- Hirschman-indeks (HHI). ‘n Wysiging aan hierdie metode word voorgestel, deur middel waarvan die akkuraatheid van die konvensionele voorstelling van die HHI verhoog word, deur ‘n formulering wat die Gini-indeks betrek. Die berekeningsvoordele van hierdie nuwe metode word geïdentifiseer en dit word aangetoon dat die Gini-gebaseerde HHI ’n doeltreffende plaasvervanger vir sy meer bekende teenvoeter is. Daar word bevind dat die voorgestelde nuwe metode teoretiese en praktiese sterkpunte het wat die gebruik daarvan ondersteun. Die praktiese voordele van die voorgestelde metode word oorweeg met die oog op die aanmoediging van die gebruik van die Gini-gebaseerde HHI-indeks as maatstaf van sakekonsentrasie.