Statistical Analysis of Data

In order to convert the data collected from the questionnaires into results and conclusions, data analysis is required (Jacob, 1984). The first difficulty to overcome is the understanding and selection of the correct statistical analysis technique to address this particular research (Creswell, 2009; Malhotra, 2007).

The following sections discuss the statistical data analysis methods that could address the research objectives within this research, and identify those that are most appropriate.

4.11.1 Descriptive Analysis

Descriptive statistics provide valuable insights of the information collected in the research as well as the preliminary understanding for further analyses. Prior to doing many of the statistical analysis techniques it is important to check that the collected data is not violating any of the assumptions made by the individual tests (Pallant, 2007).

Descriptive frequency analysis for this research would produce a table of frequency counts, percentages and cumulative percentages for all of the values associated with the variables within the three sections: demographics; online activity; and online shopping motivations. It will indicate the extent of any out-of-range, missing or extreme values (Malhotra and Birks, 2007). A discussion of this primary research analysis will be conducted against the secondary research literature reviews.

4.11.2 Reliability Analysis

It is necessary to examine the reliability of the data obtained to determine whether it is

most common statistical measure of internal consistency is Cronbach’s co-efficient (Creswell, 2009), which identifies the average correlation of the scale items.

Cronbach’s co-efficient values range from 0 to 1, with the level of reliability reflective of the value level (Malhotra, 2007).

4.11.3 Factor Analysis

Factor analysis is a statistical analysis of the underlying structure of a concept (Tabachnick and Fidell, 2007) and has two key methods: exploratory and confirmatory, as defined in the following sub-sections.

4.11.3.1 Exploratory

Exploratory Factor Analysis (EFA) is a class of procedures that reduce and summarise a large set of scale items into factors (groups) of statistically associated scale items (Creswell, 2009; Malhotra, 2007; Pallant, 2007), by identifying underlying patterns of correlation between scale items.

It is used in the following academic research circumstances: to identify underlying dimensions, or factors that explain correlation among a set of variables; to identify a new, smaller set of uncorrelated variables to replace the original set of correlation variables in subsequent multivariate analysis; and to identify smaller set of salient variables from a larger set in subsequent multivariate analysis (Malhotra, 2007). The statistical techniques administered in conjunction with EFA are: Bartlett’s test of sphericity; communality; eigenvalues; factor loadings and Kaiser-Meyer-Olkin (KMO) (Pallant, 2007).

4.11.3.2 Confirmatory

Confirmatory Factor Analysis (CFA) establishes whether factors and the loadings of their scale items conform to what is expected on the basis of a pre-established theory or prediction (Tabachnick and Fidell, 2007). The researcher’s knowledge of related theory and empirical research, understanding of the scale items and any underlying correlations between them can be postulated into factors and statistically tested through CFA (Bryne, 2001; Schumacker, 2002). Higher-Order Confirmatory Factor Analysis can subsequently be used to test the underlying concept of the confirmed factors (Hair et al. 2010).

4.11.4 Relationship Analysis

Statistical data analysis can be utilised to explore relationships that may exist between research variables and factors. This section defines the most commonly used in academic research.

4.11.4.1 Chi-Square and Continuity Correlation Analysis

In order to determine whether two categorical variables are related, the Chi-Square test for independence is used, unless each categorical variable has only two categories in which case Continuity Correlation should be used (Malhotra, 2007). The Chi-Square test for independence compares the frequency of cases found in various scale items of one of the variables across the different scale items of another variable (Pallant, 2007). If the minimum expected cell frequency of the Chi-Square test meets the requirement of being 5 or greater, and the Asymp. Sig. (2-sided) value of the Chi-Square test is 0.05 or smaller, the relationship between the variables is significant (Creswell, 2009; Pallant, 2007).

4.11.4.2 Pearson Correlation Analysis

In order to determine the strength and direction of the linear relationship two continuous variables, Pearson’s correlation coefficients are calculated (Creswell, 2009); the size of which, between –1 and 1 whilst ignoring the sign, indicating the strength of their relationship (Pallant, 2007; Malhotra, 2007). Creswell (2009) specifed that the sign represents either: a positive correlation (as one variable increases, so too dies the other); or a negative correlation (as one increases, the other decreases). An interpretation of the strength of the values between 0 and 1 is provided by Cohen (1988):

r = 0.10 to 0.29 or r = -0.10 to –0.29 small r = 0.30 to 0.49 or r = -0.30 to –0.49 medium

r = 0.50 to 1.00 or r = -0.50 to –1.00 large

4.11.4.3 Spearman’s Rank Order Correlation Analysis

Spearman’s Rank Order Correlation (rho) is a statistical technique that measures the strength of the relationship (association) between two ordinal (rank order) variables (Malhotra, 2007), the size of which, between –1 and 1 whilst ignoring the sign, indicating the strength of the relationship (Creswell, 2009; Pallant, 2007). Creswell (2009) specifed that the sign indicates: whether there is a positive correlation (as one variable increases, so too does the other); or a negative correlation (as one increases, the other decreases).

4.11.6.4 Multiple Regression Analysis

If the predictive ability of a set of independent variables on one continuous dependent measure is required, a more sophisticated extension of correlation is required through Multiple Regression (Malhotra, 2007). Multiple Regression compares the predictive ability and identifies which set of variables is most effective in predicting a dependent variable (Creswell, 2009), i.e. exploring many-to-one relationships (Pallant, 2007).

4.11.4.5 Canonical Correlation Analysis

Canonical Correlation examines the relationship between two groups of variables (Tabachnick and Fidell, 2007), i.e. explores many-to-many relationships (Pallant, 2007). Sets of independent variables and dependent variables represent canonical variables of which multiple canonical dimensions between their relationships can be identified (Dunteman, 1989); the first of which most reflects the relationship between the canonical dimensions (Tabachnick and Fidell, 2007). Relationship between the canonical variables is of statistical interest if its Canonical Correlation is 0.3 or higher (Duntman, 1989), and the canonical variables are significantly associated by Canonical Correlation if p<0.05 (Tabachnick and Fidell, 2007).

4.11.4.6 Structural Equation Modelling

Structural Equation Modelling (SEM) is ‘a collection of statistical techniques that allow a set of relationships between one or more independent variables, either continuous or discrete, and one or more dependent variables, either continuous or discrete, to be examined’ (Tabachnick and Fidell, 2007, p.676) and is commonly utilised in social science and consumer behaviour research (Shim et al. 2001; Kim and Park, 2005). SEM uses a comprehensive mathematical technique to explore relationships between factored variables (Schumacker and Lomax, 2004). Causal

relationships between variables identified through confirmatory statistical analysis are transformed by a series of structural equations into a structural theory, providing a clear conceptualisation of the theory under investigation (Byrne, 2001).

Confirmatory Factor Analysis (CFA) is utilised to confirm whether the data collected for the research study is consistent with the system of variables defined with the hypothesised theory (Byrne, 2001; Tabachnick and Fidell, 2007). The identification of any misfit results in modification of the measurement (CFA) model to increase the accuracy of the hypothesis testing and SEM model fit when re-tested (Joreskog and Sorbom, 1997; Byrne, 2001). Alternative statistical techniques that can determine the goodness-of-fit are: model chi-square, relative chi-square, RMSEA, EVCI, CFI, NFI, RMR, GFI, and Hoelter’s Critical N.

4.11.4.7 Comparison and Evaluation of the Techniques to Explore Relationships This section has identified the most commonly adopted statistical techniques that explore relationships between research variables. The exploration of relationships between two variables can be conducted through: Chi-square; Pearson’s Correlation;

and Spearman’s Rank Order Correlation (rho). The exploration of the relationship of a set of independent variables on one continuous dependent variable (many-to-one relationships) can be conducted through Multiple Regression. The exploration of the relationship between two groups of independent and dependent variables (many-to-many relationships) can be conducted through Canonical Correlation. Finally, the exploration of the relationship between one or more independent variables and one or more dependent variables (interrelated relationships) can be conducted through Structural Equation Modelling.

4.11.5 Conclusion of Data Analysis Methods

The research objectives of this research stipulate the identification, analysis and conceptualisation of the plus size fashion online shopping motivations research concept. Descriptive analysis and reliability analysis are vital foundation stages of statistical data analysis and are hence, appropriate to this research.

Factor Analysis has the most appropriate statistical data analysis techniques considering the research objectives and research methods to be adopted in this research. This is due to it ability to identify, allow analysis of and test factors of plus size fashion online shopping motivations whilst also enabling the test of its underlying concept and structure. Exploratory Factor Analysis, Confirmatory Factor Analysis and Higher-Order Confirmatory Factor Analysis will be conducted.

Testing the relationships between the variables would require further identification of independent and dependent variables surrounding plus size fashion online shopping motivations; for example, purchase intentions; that would not correlate to the research objectives. Hence, these statistical data analysis techniques would be appropriate for further research aims and objectives developed upon the conceptualisation of this research.

4.12 Plus Size Fashion Online Shopping Motivations Research Design Framework