Name University Course Tutor Date Analysis Introduction The following statistical techniques are used to find relationships between one or more variables. In this case, the study of these techniques is to find their significance, uses and limitations as an approach of investigating the financial and operating performance of firms before and after Initial Public Offerings. These statistical methods will be used to study how the performance of most firms does indeed deteriorate after they go public. The markets in question are the Saudi Arabian firms where 52 public offerings made by the Gulf Cooperation Council will be investigated. The Chi-Square Test The Chi-Square test determines the difference between observed frequencies and expected frequencies in one or more categories. Questions like whether the number of objects or individuals that fall in each of these categories differ significantly from the results you expected arise. The difference in results can either be due to sampling errors or it could be the real difference. There are requirements that are needed in order to perform a Chi-Square test. These requirements are the presence of one or more categories, an adequate sample size, a random sample, data recorded in frequency form, quantitative data, and independent observations (Carver & Nash, 2011). The use of prior knowledge about the frequencies observed in a previous test is used to estimate an expected frequency in the current one. The expected frequency i...