The spatial analysis conducted in the quantitative phase of research provides additional strengths. An assumption of most statistical analysis is that the observations are independent of each other and that there is no spatial pattern within the data.
Observations that are not independent can affect the statistical rigour and affect the ability to judge significance. As Rogerson (2010, p. 257) argues “understanding the effects of spatially dependent observations in statistical analysis provides an important motivation for learning more about spatial patterns.” A primary component of spatial analysis is that of spatial autocorrelation. Spatial autocorrelation is based on one of the tenants of
geography, Tobler’s (1970, p. 236) First Law, where “everything is related, but near things are more related than distant things.” Spatial autocorrelation measures the degree of dependency among observations in a geographic space (Getis, 2008). Positive spatial autocorrelation indicates that there is clustering; for example, a pattern of nearer
municipalities having similar brands. Oppositely, negative spatial autocorrelation would indicate that neighbouring jurisdictions tend to have different brands. Finally, no
autocorrelation would describe a random pattern of branding. The measure of spatial autocorrelation can be identified at both a global scale and a local one. This method of analysis, therefore, provides an approach to identifying and understanding underlying structures to a phenomenon.
4.3 Methodology
Two research questions were investigated:
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RQ6: Does the local spatial pattern of place brands identify clusters of similarly-branded municipalities?
Both RQ5 and RQ6 consider the distribution of place brands in municipalities across Ontario, and measure the local and global spatial autocorrelation to determine whether these brands show a pattern of clustering, dispersal, or random distribution. Due to the pattern of municipalities in Ontario, with a spatially confined economic core of cities and a periphery seemingly focused on tourism and agriculture, the hypothesis for this research objective is that: the pattern of place branding will demonstrate clusters of municipalities
with similar brands. To examine the research hypothesis, the local and global spatial
autocorrelation of place brands within the province was examined. As a result, the statistical hypothesis, both locally and globally is defined as:
HO : There is no spatial autocorrelation amongst brands, and therefore no clusters
exist
HA : Spatial autocorrelation is occurring and clusters of like brands exist
The dataset was developed from the content analysis (see Chapter 3), utilizing categorical data that identified the primary brand for each municipality (either culture, agriculture, industry, nature, recreation, heritage, or none). This differs from the dataset used in quantitative analysis phase, as it considers only the primary place brand for each municipality based on the occurrence and the prominence and of the visual imagery. From a semiotic perspective, it is considering the main theme of each visual identity. As each municipalities brand is placed into one of seven discrete classes, the resulting data set is categorical.
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4.3.1 Join-Count Statistic
Due to the categorical nature of the dataset, a join-count statistic for spatial autocorrelation was applied to appraise the research hypothesis (Getis, 2008). Join-count pattern analysis considers the brand of a municipality, as well as the brands of its
neighbours, connected by a join, to identify patterns of clustering or dispersal (Cliff and Ord, 1970; Getis, 2008). It examines whether the observed brand in a municipality is independent of the brands of the neighbouring municipalities (Rey, 2001). This compares the nature of each join between neighbours (for example, industry-industry, industry- culture; see Table 4.1 for a summary of relationships within the dataset), and compares the total number of observations (OJ) of each relationship with an expected total (EJ) based on occurrence within the population of 414 municipalities (n; summarized in Table 3.1 in Chapter 3). The municipalities examined in this study were represented as a
contiguous set of polygons derived from the 2011 Statistics Canada census subdivision dataset (Figure 4.1) and their relationship was quantified through a Queen’s case weight matrix.
Table 4.1: Place brand dimensions and probability of occurrence
Culture Agriculture Industry Recreation Environ. Heritage None
Culture 0.00 Agriculture 0.01 0.02 Industry 0.00 0.02 0.01 Recreation 0.00 0.02 0.01 0.01 Environment 0.02 0.05 0.04 0.04 0.12 Heritage 0.01 0.02 0.02 0.02 0.05 0.02 None 0.00 0.01 0.01 0.01 0.03 0.01 0.01 ________________________________________________________________________
101 The join count is defined as:
𝐽𝑜𝑖𝑛𝑠 [𝑍] = 𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 [𝑂𝐽]−𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑[𝐸𝐽]
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 [𝐸𝑆] (4.1)
Where EJ:
𝐸𝐽𝑠𝑎𝑚𝑒 𝑏𝑟𝑎𝑛𝑑 = 𝑘𝑝𝑏𝑟𝑎𝑛𝑑12 (4.2)
𝐸𝐽𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑏𝑟𝑎𝑛𝑑= 2𝑘𝑝𝑏𝑟𝑎𝑛𝑑1𝑝𝑏𝑟𝑎𝑛𝑑2 (4.3)
Where k is the total number of observed joins within the dataset, and p is the probability of a brand occurring, derived from occurrence rates observed in the data. The standard deviation of the expected joins (ES) is:
𝐸𝑆𝑠𝑎𝑚𝑒 𝑏𝑟𝑎𝑛𝑑 = √𝑘𝑝𝑏𝑟𝑎𝑛𝑑12 + 2𝑚𝑝 𝑏𝑟𝑎𝑛𝑑13 − (𝑘 + 2𝑚)𝑝𝑏𝑟𝑎𝑛𝑑14 (4.4) 𝐸𝑆𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑏𝑟𝑎𝑛𝑑= (4.5) √2(𝑘 + 𝑚)𝑝𝑏𝑟𝑎𝑛𝑑1𝑝𝑏𝑟𝑎𝑛𝑑2− 4(𝑘 + 2𝑚)𝑝𝑏𝑟𝑎𝑛𝑑12 𝑝 𝑏𝑟𝑎𝑛𝑑22 Where: 𝑚 = 0.5 ∑𝑛𝑖=1𝑘𝑖(𝑘𝑖− 1) (4.6)
The join-count analysis was completed at both the global and local level, testing the null hypothesis that spatial dependency was not occurring at a confidence of α = 0.05. The global level considered the overall pattern of spatial autocorrelation within Ontario, and identified which place brand dimensions showed indications of clustering through the rejection of the null hypothesis. The global autocorrelation result was also used to
identify specific neighbouring-brand relationships that showed evidence of clustering. Second, the local analysis identified specific municipalities that had a significant number of neighbours with similar brands. Clusters of three or more municipalities showing positive autocorrelation of these same brand dimensions were isolated as potential locations for inter-jurisdictional cooperation. This final step ensures that territories of
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greater size were being suggested. Further, due to the small number of joins at a local level (ranging from zero to ten), the threshold of three adjacent municipalities reduces the risk of areas with few neighbours (i.e. zero or one) being identified
Figure 4.1: An overview of the community place brands in Ontario