Data Analysis Assumptions

138 attitudes (cosmopolitanism and consumer ethnocentrism). Hypothesis 2 was tested by performing a one-way between-group MANOVA, with Cosmopolitanism and Consumer Ethnocentrism as dependent variables, followed by planned comparisons for each variable. Prior to performing the MANOVA, recommended grouped data screening steps were followed, to ensure relevant assumptions are met (Tabachnik and Fidell, 2007; Hair et al., 2010)¹⁷. These steps and techniques used are summarised in Table 4-15 below, and the assumptions are discussed in more detail in the next Section 4.4.3. The results of hypotheses 1 and 2 testing are presented and discussed in Chapter 6.

Table 4-15: Data Screening Steps for Analysis of Grouped Data

Assumption Definition Screening Steps Taken

Absence of outliers

Dependent variables should not be highly correlated with each other and should not be made up of variables included as other about the same at all levels of grouping variable

This section reviews the assumptions underlying the multivariate analysis techniques utilised for measure validation and hypotheses testing stages described above.

Considering these assumptions is important since errors in considering the effects of

17 For a detailed discussion of the assumptions please see Section 4.4.3, Data analysis assumptions

139 assumptions violation may invalidate interpretation of statistical inferences and increase the risk of committing a statistical error (known as sampling error), of which there are two types. Type I error is the probability of rejecting the null hypothesis when it is actually true. To safeguard from committing Type I error researchers set the level of significance (alpha) to indicate acceptable limits for error. The Type II error is the reverse, i.e. the probability of not rejecting the null hypothesis when it is actually false.

Type II error is inherently related to the power of statistical inference. A general rule of thumb is that one should strive to achieve power level of 0.8 at the desired level of significance (Hair et al., 2010).

Normality is a fundamental assumption of multivariate analysis as the majority of the analysis techniques are underpinned by it. Assessment of normality is conducted utilising either graphical or statistical methods, seeking to assess such characteristics of the variables’ distribution as skewness and kurtosis. When a distribution is perfectly normal, skeweness and kurtosis equal zero. While this is rarely achieved in social sciences (West, Finch and Curran, 1995), assessment of skewness and kurtosis statistics is important to evaluate that there are no radical departures from normality. One should bear in mind that with large samples (i.e. < 200 cases) the detrimental effects of nonnormality are reduced since the larger sample sizes increase statistical power by minimising sampling error. In particular, as per Tabachnik and Fidell (2007), in a large sample a variable with statistically significant skewness does not make a substantive difference to estimating variance but one should bear in mind that in some techniques it may contribute to violations of other assumptions.

Linearity refers to assumption of a straight line relationship between two variables that generally underpins marketing research. Although some relationships in marketing studies can be non-linear, such as for example price and satisfaction (Campo and Yague, 2008), in absence of clear evidence to the contrary, linearity is assumed. This same assumption is made in this study.

Multicollinearity and singularity refer to extremely high (above .70, suggesting multicollinearity) or perfect (1, suggesting singularity) correlations between variables (Tabachnik and Fidell, 2007). If multicollineairy or singularity are detected, this

140 indicates that variables contain redundant (i.e. similar) information or are expressions of the same phenomenon.

Homoscedasticity and Homogeneity of Variance. Homoscedasticity assumption refers to approximate equivalence in variability of scores of two continuous variables.

Homogeneity of variance is equivalent to homoscedasticity assumption in analysis of grouped data where one of the variables is metric. Homoscedasticity is related to normality since, when assumptions of multivariate normality are met, the variance will be approximately equivalent. Heteroscedasticity (failure of homoscedasticity) can be caused by nonnormality of the variables but not necessarily, it may also be caused by the fact that one variable is related to some form of changes in the other variable. As noted by Tabachnik and Fidell (2007), heteroscedasticity is not fatal to analysis of ungrouped data since the linear relationship between the variables is still captured but in grouped data analysis, violations of homogeneity of variance require careful attention.

Outliers. An outlier is a case with an extreme score on one variable (univariate outliner) or a strange combination of scores of two or more variables (multivariate outlier – Tabachnik and Fidell, 2007; Hair et al., 2010). Four common reasons for detection of outliers are 1) data entry error; 2) error in specification of missing data values; 3) the case is not the member of population intended to be sampled; 4) the case is the member of the population but the distribution of the variable in the target population is more extreme than the normal distribution. To specify, reasons 1 and 2 were screened in this data set as part of data handling. Therefore, when screening for outliers in the analysis stage, reasons 3 and 4 were applied to considerations.

A final consideration is the type of analysis technique intended since different estimation methods have varying levels of sensitivity to departures from assumptions and, consequently, may require different approaches. Results of data screening are reported as they were applied in different stages of the analysis process.

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