3.2 METHOD
3.2.12 Statistical tests applied in the study
The Chi-Square Test, the Analysis of Variance and the Independent Samples Test were applied in this study with p<0.05. This therefore means that the finding has a 5% (0.05) chance of not being true, which is the converse of a 95% chance of being true. The chi-square test was used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. The ANOVA (Analysis of Variance) was used to analyse the differences between group means and their associated procedures. It provides a statistical test of whether or not the means of several groups are equal and is useful in
comparing/testing three or more means i.e. groups or variables for statistical significance. The p-values computed are presented in Table 4.5.
Inferential statistical analysis is concerned with the testing of hypothesis. The independent T-test is the most appropriate parametric test for a comparison of the means. This tests any significant difference between the two variables. Primary data was collated and analysed and comments and concluding discussions are thereafter based on the results obtained (Lind, Marchal and Mason, 2004). Inferential statistical analysis allows the researcher to draw conclusions about populations from sample data. The most important application in the social sciences of the statistical theory around sampling distributions has been significance testing or statistical hypothesis testing.
The traditional approach to reporting a result requires a statement of statistical significance. A p-value is generated from a test statistic. A significant result is indicated with “p <0.05.” The choice of the value of 0.05 as the level of significance is in fact totally arbitrary, but has become enshrined as a standard in statistics.
A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution when the null hypothesis is true, or any in which the probability distribution of the test statistic (assuming the null hypothesis is true) can be made to appropriate a chi-square distribution as closely as desired by making the sample size large enough. Specifically, a chi- square test for independence evaluates statistically significant differences between proportions for two or more groups in a data set.
The completed survey questionnaires were analysed using a professional statistical analysis package viz. the Statistical Package for the Social Sciences (SPSS). The SPSS evolved from mere statistical software to a very powerful management tool. The capabilities of the SPSS software package for analysis make it an indispensable part of every decision-making process of a company (Wagner, 2007). It is a data management and analysis programme and is generally regarded as the market leader in this respect. It is an effective tool for profiling the spending patterns of different groups of visitors to a major event such as the Comrades Marathon. It was released in its first version in the 1968, and is amongst the most widely used programmes for analytical analysis in the social sciences. It is also used by market researchers, health
researchers, survey companies, government, education researchers and others. It is a
comprehensive and flexible statistical analysis and data management system and takes data from almost any type of file and uses them to generate tabulated reports, charts, plots of distribution,
trends and descriptive statistics, and conducts complex statistical analyses (Green et al, 1996).
Inferential and differential statistical methods were employed in the survey in order to analyse the data gathered. The data were presented using graphs and tables.
Economic impact analysis incorporates specific tools that can be both differential and inferential.
Differential techniques of economic impact analysis contribute useful measures of economic activity that provide context for decision-making. These include industry measures such as export-base multipliers. Inferential techniques of economic impact analysis attempt to use available data on past and present economic activity to estimate impacts of change and to
forecast future activity. Examples of these techniques include input-output analysis. In the past, input-output models have been the primary means of translating spending effects into income and employment effects. Input-output tables are at the core of input-output models and show a complete set of accounts for an event. The use of the input-output model can expand the usefulness of the tables used to a significant extent.
The first step of an economic assessment for this event is to define the levels of spending brought about by the event. Once these are defined, the use of the input-output model requires two further steps. Firstly, one or more columns of expenditures must be estimated that represent the additional spending generated by the event. This might include a column for visitors to the event and a separate column with several different categories might be considered for visitor spending.
Secondly, an input-output model must be used to calculate the GDP and import effects of these expenditure patterns.
Chi-square tests were conducted to determine statistical differences between the two cities. In this way the percentage of responses across the categories was compared between the two cities.
Categories with 0 percentages were omitted. When the p-value is greater than 0.05 that is the significant level, it would imply that the null hypothesis is true. Hence, the null hypothesis is not rejected that is the finding is not statistically significant at the 5% level. At the significant level the results are only 5% likely to be acceptable. When the p-value is less than or equal to the significant level, the null hypothesis is rejected and the finding is statistically significant at the 5% level.