Analytical Statistics

The analytical, or inferential, method is the process whereby conclusions and generalisations are derived from the raw data. The process starts from data collection, is followed by descriptive analysis, and completed by analysis of significance and differences. Therefore, the current study employs analytical statistics for two purposes:

to examine the significance of responses, and to make inferences about the population parameters from the sample statistics through hypothesis testing.

5.7.2.1 Testing the Significance of Responses

The significance of the responses towards 50 statements of the questionnaire was examined by using the Wilcoxon Signed Rank Test. For non-parametric sets of data, the Wilcoxon Signed Rank Test can be used as substitute of one sample t-test in parametric statistics (Chan, 2003). The test computes the difference between the sample mean and the hypothesised value. Therefore, the mean score of responses was compared with 3 (the mid score of the 5 point scale) to examine the significance of agreement or disagreement using a Wilcoxon Signed Rank Test.

5.7.2.2 Testing the Hypotheses

Kerlinger (1986) mentioned four different reasons for using statistical analysis, which are:

(i) To reduce a large quantity of data to a manageable and understandable form;

(ii) To aid in the study of the population and samples;

(iii) To assist decision making; and,

(iv) To enable the deduction of reliable inference.

Many statistical tools could be used for analysing the data collected from the questionnaire survey. However, the main objective of the analyses was to investigate current practices of the ACs in Bangladesh. The idea was to generate an indicator to measure the variability of an individual response within a particular distribution. This study aimed to make inferences from sample statistics to the population parameters.

Therefore, hypothesis testing was done to compare the opinions of respondents on the current practice of the ACs in Bangladeshi companies. In order to test the stated hypotheses, the researcher carried out two non-parametric tests, namely: the Kruskal-Wallis One- Way Analysis of Variance Test Score, and the Mann-Whitney U Test. The following discussions briefly introduce these two testing techniques.

A. The Kruskal-Wallis Test

The Kruskal-Wallis Test is the non-parametric version of the parametric ANOVA Test for calculating the difference in the population mean. It is a test of one-way, between-groups analysis of variance that allows a comparison of three or more between-groups (Pallant, 2001). Borg and Gall (1983) stated that the Kruskal-Wallis Test is: "a statistical technique used to compare categorical data. It also gives a comparison of the distribution of individual variables from two or more different groups and produces a measure of relationship, called the contingency coefficient which is similar to the correlation coefficient". In addition, the conditions that should be met for the appropriateness of using the Kruskal-Wallis Test include: the data must be a random sample from a large population, the expected number in each category should not be too small, and the rule of thumb is to demand that at least five counts be expected in each

category (Siegel and Castellan, 1988). When the obtained value of Kruskal Wallis (H) test is significant, this indicates that at least one of the groups is different from at least one of the others. To identify the differing group, Kruskal Wallis pair-wsie comparison (six pairs of four groups²⁴ i.e. 1 &2; 1&3; 1&4; 2&3; 2&4; 3&4) has been conducted.

B. The Mann-Whitney U Test

It is used to investigate the differences between two independent groups. This test compares the medians of the two groups and subsequently evaluates whether the ranks for the two groups differ significantly. The Mann-Whitney U Test is used to test the difference between two independent groups on a continuous measure. In respect of this test, Pallant (2001) noted that it converts the scores on the continuous variable to ranks, across the two groups; and that it then evaluates whether the ranks for the two groups differ significantly. In addition, the Mann-Whitney U Test is more powerful than the median test since it uses the ranks of the cases and it requires an ordinal (ranked) level of measurement. The test has been used in this study to compare means of responses from two groups divided on the basis of educational background, professional qualification and length of experience of the respondents.

5.7.2.3 Regression Analysis

Regression analysis is used to identify the relationship between a dependent variable and one or more independent variable(s). More specifically, regression analysis helps us to understand how the typical value of the dependent variable changes when any one of the independent variables is varied while the other independent variables are held fixed (Allison, 1999). In order to investigate the AC effectiveness in Bangladesh, two multiple regression models have been derived using the questionnaire survey data. In the first model AC characteristics (i.e. composition, authority & resources, diligence, meeting) are independent variables and AC role (weighted average score of three key roles of an AC) is a dependent variable. In the second model, the three key roles (i.e.

role in financial reporting, role in external auditing and role in internal auditing) are

independent variables and AC effectiveness is a dependent variable. The correlations (Spearman) of the variables of the regression models have also been presented to facilitate in ascertaining the association between the variables. The multicollinearity of the regression models has been investigated using the Variance Inflation Factors (VIFs).

It should be noted that there is no hard and fast rule regarding VIF value for determining presence of multicollinearity problem. For weaker models, the researchers paid note if the VIFs were of 4 (four) or more while for stronger models (if explains 50% or more) some researchers accepted VIFs up to 10 (Hair et. al, 1992). In this study, VIFs of 8 (eight) or less have been accepted in examining the multicollinearity problem, considering that the regression models are very strong.

5.7.2.4 Analysing the Significance of Test Results

To analyse the statistical test results in Chapter Six, the researcher has assumed a 5%

level of significance (i.e. a probability or p level of 0.05 or five times out of a hundred has been considered). When the p-value of a statistics is less than the significance level, the value of the statistic is said to be significant. The conventional probability, or p-value, for deciding that a result is not due to chance has been set as equal to, or less than, 0.05 (i.e. five times out of a hundred). If we are willing to accept a 5% chance of making an error, we can construct a 95% confidence interval (Weisberg et al, 1996;

Cramer, 1998). If the probability is less than 0.05, then it is thought unlikely to have been due to chance. If, on the other hand, the probability level of an outcome is above 0.05, then that result is statistically non-significant in the sense that it is considered likely that it could have been due to chance (Cramer, 1998). In other words, the p-value is the probability that the null hypothesis is true. If the p-value is less than 0.05, we would say that the result is significant at the 0.05 level (Weisberg et al, 1996). To sum up, Kinnear and Gray (2000) posited:

(i) If the p-value is greater than 0.05, H is accepted and the result is not significant;

(ii) If the p-value is equal or less than 0.05 but greater than 0.01, H is rejected and the result is significant beyond the 5 per cent level; and,

(iii) If the p-value is less than 0.01, H is rejected and the result is significant beyond the 1 per cent level.