Exploratory factor analysis (EFA)

The large number of potential variables derived from the questionnaire and HEIDI (summarised in Appendix V) makes their analysis complicated and therefore EFA was employed to determine whether several items form a single latent variable.

Variables were grouped by theme to form constructs where good theoretical reasons existed to suspect that some variables represented a smaller set of latent variables based on questionnaire

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items (e.g. measure of accuracy, gaming behaviours, budget methods, etc.) and an EFA was conducted in SPSS on each construct using principal axis factoring and varimax (orthogonal) rotation. Cronbach’s alpha was used to test the internal reliability of each construct.

Whilst the constructs were selected based on the researcher’s view of what variables might be sensibly brought together, the optimal number of factors under each construct was determined by the eigenvalue. A value greater than one means that the factor explains more variance than the single item. Whether the factor is considered to be appropriate is determined by the Kaiser-Meyer- Olkin (KMO) measure of sampling adequacy, Bartlett’s test of sphericity and the Anti-image correlation.

Factor loadings were identified together with the extraction sums of squared loadings. The loading measures the relationship of each variable to the factor, with high loadings making the variable representative of the factor. The squared factor loadings indicate the percentage of the variance in the original variable explained by the factor (Hair et al., 2010). Where collinearity between the variables in the construct was too high SPSS indicated that no extraction was possible for the factor. Also, in those cases where a single factor was identified from the construct the output was in the form of unrotated squared loadings only.

The results are presented in Appendix VI, with data for the appropriateness criteria shown in separate columns.

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Table 6.1 Criteria for an acceptable factor

Test Criteria Definition

Kaiser-Meyer-Olkin (KMO) ≥0.5 Ratio of the squared correlation between variables to the partial correlation between variables

Bartlett test of sphericity <0.05

Whether the diagonal element of the variance- covariance are equal and whether the off-diagonal elements are approximately zero

Anti-image ≥0.5 Diagonals used to measure sampling adequacy Eigenvalue >1.0 Amount of variation explained by a factor Cronbach’s alpha for EFA >0.6 Test for internal reliability

A rule of thumb to denote an acceptable level of internal reliability for Cronbach’s alpha is usually 0.7 (Bryman & Bell, 2011), but 0.6 is deemed to be satisfactory for exploratory analysis (Hair et al., 2010).

The main SPSS output of the factor analysis in Appendix VI is to identify for individual constructs how much of each item within a construct forms a factor (i.e. the percentage of rotation sums of squared loadings), if any. These percentages are shown in the second to last column. The items which load highly on to a factor represent a theme within the construct. However, in order for a factor to be valid it must satisfy the criteria set out in Table 6.1. The data for assessing these criteria are shown in the columns headed KMO, Bartlett’s test of sphericity, Anti-image correlation, Eigenvalue and Cronbach’s alpha. Any data not meeting the criteria are signalled in red text.

A maximum number of three factors were found for each construct and the unrotated loadings for each of the factors is shown under columns headed ‘Factor 1 loadings’, ‘Factor 2 loadings’ and ‘Factor 3 loadings’. By default, SPSS shows only loadings above the suppressed output of 0.3 or less and so there are blank spaces for many of the loadings. The factor loadings are the correlation of each item to the factor. High loadings make the item representative of the factor. The figures before rotation are not particularly important for interpretation (Field, 2013). Factor rotation leads to a simpler and more meaningful factor pattern and involves turning the reference axes of the factors until the variance from earlier factors is redistributed to later ones (Hair et al., 2010). Many

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of the constructs resulted in a single factor only however. Thus, each column for the factor loadings shows which combination of items from the construct form a factor.

Factors meeting the appropriateness criteria are summarised in Appendix VII together with factor loadings. Cronbach’s alpha revealed eight valid factors. For these valid factors, the source data for the variables was combined and divided by the number of variables to arrive at the ‘combined’ factor data, which is an approach used in other EFA studies such as Coetzee and Erasmus (2017). No weighting of individual variables was used as there were common scales for those variables combined (e.g. 10-point Likert scales, etc.). Factors were given a meaningful name and used for testing correlation including multiple regression analysis.

A valid factor for accuracy (COMA) comprised of a construct of the perceived accuracy of budgeting, forecasting and student number estimating would appear appropriate. All three variables should have a close relationship if an institution is to demonstrate that it has coherent financial planning. An inconsistent approach to any would likely result in variances which are difficult to sensibly explain.

Other valid constructs might also have been anticipated for the number and qualification of central finance staff engaged on budgeting and forecasting, the change in time spent on financial planning, and the number of variables and linkages in scenario models. It is therefore perhaps unsurprising that the EFA confirms the latent association between the variables in each construct. The remaining valid constructs which deal with strategy, participation and environmental issues affecting forecasting might not have been anticipated due to the variability of institutional processes and views in these areas. For strategy, this would indicate that respondents viewed the budgeting process as contributing to the achievement of the longer-term objectives of the organisation. Participation by a range of departments in constructing institutional forecasts for other income, staff costs and other operating expenses indicates consistency in the approach adopted which also appears to be applicable in terms of which areas of an institution played a major, minor or no role in setting student number forecasts. Many respondents also expressed similar views as to the effect of the uncertain environment on forecasting in terms of whether accuracy had deteriorated, forecasts quickly became obsolete, were more difficult to produce and were subject to more scrutiny by outsiders in terms of the governing body.

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