Quantitative data analysis

It is worth noting that one of the unsolved issues in quantitative data analysis is the question of when parametric rather than non-parametric tests should be used. “The term Parameter points to a measurement that identifies the distribution of the population, like the mean and variance.” (Bryman and Cramer, 2002, p. 115).

Some authors (for example, see: Bryman and Cramer, 2001) have argued that parametric tests are only suitable when data meets the following three conditions (Bryman and Cramer, 2002):

 The level or scale of measurement is interval or ratio scaling, that is, more than ordinal.

 The distribution of the population scores is normal

 The variances of both variables are equal or homogeneous.

Bryman and Cramer (2001, p. 115) reported that “non-parametric tests are so called because they don’t depend on assumptions about the valuable form of the division of the sampled population”. This type of test is called a distribution free test (see also: Kotrlik and Higgins, 2001). These tests attempt to avoid reliance on any particular assumptions with respect to the form of the implied parameters or their distribution. It is worth mentioning that with interval or percentage data, a parametric test is more suitable, while a non-parametric test is more suitable for nominal and ordinal data.

Therefore, non-parametric tests were used in this study, particularly the Chi square (2) test, correlation coefficient and frequency distribution. These tests are suitable for analysing the data, especially the data collected through the questionnaire, because of the categorical nature of the data. These tests are also suitable for achieving the aims of this study.

The chi-square (2) test is possibly the most frequently used hypotheses. It is a non-parametric test, and is suitable for use in a wide range of situations when the data are categorical. Moore (1995) stated that the chi-square (2) test is used to identify whether two repeated distributions

differentiate importantly from one another (Moore, 1995). This test is a test of statistical significance, meaning that it allows the researcher to ascertain the probability with which the observed relationship between two variables might have arisen by chance (Kotler, 2001).

With one degree of freedom (two categories), the expected frequencies for each category should be at least 5 before the test can be applied, but with more than one degree of freedom (more than two categories), some researchers, such as: (Bryman and Cramer, 2001) and (Howitt and Cramer, 2000), suggest that the only conditions in which the chi-square should not be used are when any expected frequency is smaller than 1 or when more than 20% of the expected frequencies are less than 5. In these situations, they suggest either combining categories or using alternative tests, such as the binomial test.

The popularity of the chi-square test may be due to the relative ease of conducting this test. In addition, it is useful in a wider variety of research situations than other tests.

The correlation coefficient is used to measure the strength of the relationships between two variables (strong or weak) and the type of this relationship (positive or negative). It lies between - 1 and +1. Thus, it supplies data on the strength and the direction of relationships. The closer the correlation coefficient is to +1, the higher the positive association. This means that the two variables increase and decrease at the same time. The closer the correlation coefficient is to -1, the higher the negative association. In this case, the two variables tend to move in opposite directions. The closer the correlation coefficient is to 0, the lower the degree of association between the two variables (for example, see: (Bryman and Cramer, 2001).

It is worth noting that Pearson’s r must be used with interval and ratio data, and the relationship between the variables must be linear. Spearman’s rho and Kendall’s tau must be used with nominal and ordinal data. The interpretation of the results of the method is typical for Pearson’s r. Moreover, unlike Pearson’s r, Spearman’s rho and Kendall’s tau are non-parametric methods, which mean that they can be used in a wide variety of contexts since they make fewer assumptions about variables (for example, see: Bryman and Cramer, 2001 and Fielding, Gilbert and Gilbert, 2006).

Frequency distributions are used as a statistical tool for describing the data for a single variable. (Fielding, Gilbert and Gilbert, 2006) stated that this tool allows the researcher to ascertain how

many and what percentage of the sample fall into a particular category. So, it allows the comparison of information between groups of individuals. This is considered a popular method for describing variables.

It is worth noting that the most commonly used computer software for survey data analysis is SPSS, the Statistical Package for Social Sciences. A program, like SPSS, has two main components: the data analysis facilities and the data management facilities (for example, see: Fielding, Gilbert and Gilbert, 2006). So, the SPSS program is considered a very important tool for researchers as it plays an important part in presenting and analysing data.

The chi square (2) test will be used to examine the importance of the association between a DSS and the effectiveness of the admission system in Saudi universities. In addition, the correlation coefficient will be used to measure the strength of the relationships between DSS and the effectiveness of admission system in Saudi universities. The researcher will use Spearman’s rho, because this is commonly used by other researchers. In addition, this test is suitable for analysing the data collected by the survey method used in this study (nominal and ordinal data). Descriptive statistics (frequencies, percentages of responses) will also be used to describe the research variables. This will lead to a good picture of the current admission systems in the Kingdom of Saudi Arabia. Consequently, it will help in establishing the proposed admission system. The researcher selected these tests, because these tests are adequate for achieving the study objectives and testing their hypotheses.