Quantitative Data Analysis

Data collected through questionnaire surveys and PWMF validation questionnaires (except open-ended questions) were analysed using quantitative techniques that will be described in forthcoming sections. The data analysis techniques depend on the type of data collected and their scales of measurement: nominal, ordinal, interval and ratio.

Therefore, the identification of data scales of measurement is essential prior to a statistical analysis of collected data.

The data generated from different questions of the questionnaire survey in this study belongs to different scales of measurements: data of question number 1.2, 2.1 and 3.1 were considered as nominal data; and experience of the respondents and number of employees of the company were regarded as ratio data. However, a difficulty was raised when deciding the scale for the question data generated using a rating scale;

whether those data are considered as ordinal or ratio for the analysis purpose. In this pursuit, it was examined how the data generate through rating scale(s) needs to be treated.

One of the most common rating scales is the Likert scale. As with other scales, the Likert scale is also used either as a summated scale or as an individual scale item.

However, whether it is an ordinal or an interval is a subject of much debate (Achyar, 2008). Further, Hodge and Gillespie (2003) stated that treating the Likert scale either as interval or even ratio is unclear, if not doubtful. The Likert scale is widely used in measuring attitude and image (Jacoby, 1971) and often considers as an interval scale.

However, some argued that the Likert scale is ordinal in nature; for the reason that, summing ordinal data will not make it interval (Achyar, 2008). Because of the ordinal nature, Elene and Seaman (2007) stated that the Likert scale is most suitable being analysed by non-parametric procedures such as frequencies, tabulation, chi-squared statistics, and Kruskall-Wallis H test.

Clason and Dormody (1994) noted that it is not a question of there being right or wrong ways to analyse data generated from the Likert scale, the main concern needs to be whether it is directed to answering the research questions/objectives meaningfully.

Adams et al. (1965, p.100) also mentioned that “nothing is wrong per se in applying any statistical operation to measurements of given scale, but what may be wrong, depending on what is said about the results of these applications, is that the statement about them will not be empirically meaningful or else that it is not scientifically significant”.

The rating scales used in the questionnaire survey and framework validation questionnaire of this study were on a 5 point scale. Despite literature arguments on the appropriateness of scale length, the selection of 5-point scale was mainly based on its popularity in use. Furthermore, the 5 point scale enables respondents to express neutrality. Therefore, the 5-point scale helps to eliminate forced choice for a favorable response (i.e. minimise positive response bias). The question data based on the rating scale were analysed considering the data type as „ordinal‟.

2.9.1.1 Data analysis software

A number of computer software applications have been developed in order to aid the steps of data analysis. However, computer aided software needs to be used with caution as they have both strengths and limitations (Lee and Fielding, 1991). One of the main advantages of computer aided software is its ability to rapidly handle large volumes of data. By using computer aided software, data can be easily manipulated and displayed in a number of ways (Robson, 2002). This makes the data analysis process more comprehensive, transparent and replicable thus increasing the reliability and validity of the analysis. Importantly, if the computer aided software is used with care, to assist the tedious tasks of data handling such tools can enhance the data analysis process. The SPSS (Statistical Package for Social Science) is one of the most widely used software packages for statistical data analysis. Thus, it was decided to use SPSS software for the quantitative data analysis in this research, expecting that the use of SPSS software makes the data analysis process more comprehensive, transparent, replicable, and also increases the reliability and validity of the analysis.

Two versions of SPSS software were used for the data analysis of this research due to software up-grade processes in Loughborough University: SPSS version 16 to analyse questionnaire survey data; SPSS version 17 to analyse PWMF validation questionnaires. The following steps were taken when entering data;

 Data coding and data entering were conducted as specified by the SPSS guidelines.

 Double entry to achieve error free data (such as to avoid data duplication and entering wrong data).

2.9.1.2 Descriptive statistics

Descriptive statistics, as the name implies, describe or summarise the data (Tan, 2002). Descriptive statistics for surveys include counts (numbers or frequency);

proportions (percentages); measures of central tendency (the mean, mode and median); and measures of variation (range and standard deviation) (Fink, 2006). The most common descriptive statistics are the mean and standard deviation for the data analysis process. However, mean and standard deviation are invalid parameters for descriptive statistics whenever data are on ordinal scales. Consequently, parametric methods with calculations based on mean and standard deviations would also be invalid for analysing ordinal data (Jakobsson, 2004). This was confirmed by many authors namely Siegal (1956); Tan (2002); Thorkildsen (2005); and Doig and Groves (2006). They further explained that mean and standard deviations found on the scores themselves are in error to the extent that the successive intervals (distances between classes) on the scale are not equal. If parametric techniques of statistical inference are used with such data, any decisions about hypotheses are doubtful. As a result, probability statements derived from the application of parametric statistical tests to ordinal data are in error to the extent that the structure of the method of collecting the data does not have a similar appearance but is genetically different to arithmetic.

As Siegal (1956) stated and Doig and Groves (2006) demonstrated in a student perceptions survey, the allowable operations on the ordinal data resulting from a survey are:

 transformed data on an interval scale;

 the median response to each category; or

 the proportion of responses in each category.

The allowable operation resulting on ordinal data is to transform the data mathematically (i.e. order-preserving transformation) on an interval scale (e.g.

transformed the raw ordinal data into logits (log odds units) using Masters‟ Partial Credit Model; Rasch Model (Doig and Groves, 2006; Hardigan and Carvajal, 2007). An order-preserving transformation is a form of transformation that preserves the ranking

of the raw data and produces an interval scale, one that allows the operations of ordinary arithmetic and statistic (i.e. means, standard deviations, parametric tests) operations.

Statistically, the most appropriate way of describing the central tendency of scores in an ordinal scale is the median, since the median is not affected by changes of any scores, which are above or below it as long as the number of scores above and below remains the same (Siegal, 1956, Doig and Groves, 2006). However, the median provides a minimal amount of useful information. Doig and Groves (2006) confirmed the above demonstrating that the respondents‟ responses missing from the median approach is any indication of the distribution of the responses and there is no way in which a particular respondent‟s response pattern can be discerned from a form of summary information (i.e. a median distribution chart).

The other operation for reporting ordinal data is the proportion of responses in each category, which is considered as being the most popular method and more informative than the use of median, yet less informative than transformed data on an interval scale (Fink, 2010). This method allows the reporting of a pattern of endorsement of the survey; propositions of categories which do not provide any information on individual respondents or even about sub-groups of respondents. However, non-parametric approaches can be used along with this method to provide information on various aspects (Doig and Groves, 2006), especially to gain such missing information (i.e.

information on individual respondents or even about sub-groups of respondents).

In this research, the transformation data on an interval scale was not undertaken for the purpose of ordinal data of the questionnaire survey considering the complex procedure of transforming data on an interval scale. Furthermore, the main objective of the questionnaire survey was to capture a broad view on the issues associated with the relationship between CPS and waste generation, as such a simple and meaningful data representation approach was a priority. Hence, the proportion of responses in each category along with non-parametric tests was considered the main data reporting method in the questionnaire survey and framework validation questionnaire. Mostly, descriptive statistics were used in this research to analyse data related to different questions by computing counts (numbers or frequency) and proportions (percentages) used as appropriate. Therefore, statistical analysis techniques considered in this study were non-parametric procedures. However, taking a pragmatic view means considering in the analysis to answer research questions meaningfully.

2.9.1.3 Missing data analysis

Missing values can result in misleading interpretations and may reduce the precision of calculated statistics (SPSS version 16). Therefore, missing value analysis was conducted for each question of the questionnaire survey as it helps to address several concerns caused by incomplete data. The results of missing value analysis are shown in the Appendix 2.4 for questionnaire data while there were not missing values recorded for the framework validation questionnaire. If missing data values are less than 10% of total data for each section of the question, then the statistical analysis was presented based on a score of non-missing values as the appropriate index while keeping the total sample at unchanged (Bryman and Cramer, 2005).

2.9.1.4 Kruskal - Wallis H test

The non-parametric tests for multiple independent samples are useful for determining whether or not the values of a particular variable differ between two or more groups.

The Kruskal-Wallis test is a one-way analysis of variance by ranks. It tests the null hypothesis that multiple independent samples come from the same population. It is appropriate when the test variable is ordinal or when its distribution does not meet the assumptions of standard ANOVA (SPSS version 16). Unlike standard ANOVA, the Kruskal-Wallis test does not assume normality, and it can be used to test ordinal variables. The only assumptions made by the test are that the test variable is at least ordinal and that its distribution is similar in all groups. Thus, the Kruskal-Wallis H test was used to ascertain whether any difference was present between responding groups for the questionnaire survey (i.e. procurement managers, sustainability/environmental managers and quantity surveyors). However, the same test was not undertaken for the framework validation questionnaire due to the small sample size of the framework validation respondents.

The Kruskal-Wallis statistic measures (chi-square) the extent to which the responding group ranks differ from the average rank of all groups. The degrees of freedom (df) for the chi-square statistic are equal to the number of groups minus one. The asymptotic significance (Asymp. Sig.) estimates the probability of obtaining a chi-square statistic greater than or equal to the value of significant, if there are truly no differences between the group ranks (SPSS, version 16). The value of the asymptotic significance level is greater than 0.05, which indicates that there is no difference between respondents‟ views mean ranking of groups (Tan, 2002; Bryman and Cramer, 2005;

Ilozor, 2009).

2.9.1.5 Internal reliability test (Cronbach‟s Alpha)

Several measures were taken to ensure the reliability of both the questionnaire survey and framework validation questionnaire data from the questionnaire design stage (section 2.7.6). In this research, Cronbach‟s Alpha values were considered to test how internally reliable the question data of the questionnaire survey was. Cronbach's Alpha calculates the average of all possible split half (split half reliability the items in a scale are divided into two groups either randomly or odd-even basis) and the relationship between respondents‟ (scores for the two halves is computed) reliability coefficients (Tan, 2002; Bryman and Cramer, 2005; Bryman, 2008). The value of this measure varies between 0 (i.e. denoting no internal reliability) and 1 (i.e. denoting perfect internal reliability) (Bryman, 2008). To compare groups, the reliability coefficient of 0.5 or above is acceptable (Fink, 2006; Bryman, 2008). According to Nunnllay (1978) as well as many writers are accepted that at or over 0.7 (Tan, 2002), the more internally reliable is the scale.