## Measuring statistical relationships

The importance of statistical tests of relationship between variables is that these measures indicate how various factors operating within a market influence and interact with each other. They can indicate how a market works by identifying and quantifying cause-and-effect relationships. These make it possible for a decision maker to predict the outcomes of particular actions that could be taken, because they indicate which variables influence the marketplace and by how much. Armed with this kind of information the decision maker becomes a far more informed operator in the market. He or she can measure which of the marketing and non-marketing variables have what effects in the marketplace, for example, how sales are affected by changes in price, advertising or average daily temperature. It is at this point that marketing decision making becomes more of a science than an art. These are compelling reasons why any commissioner and user of marketing research data should attempt to understand what measures of relationship a research agency should be asked to provide following a research survey, and should appreciate the importance of their implications for decision making once they are available. As in the preceding paragraphs, this subsection will attempt to explain the meaning of statistical measures of relationship without explaining the statistical formulae.

### Correlation analysis

Correlation analysis is a statistical device which measures the degree of relationship in the movement of two sets of variables. This is expressed as a correlation coefficient, which can have a maximum value of +1 and a minimum value of - 1. Perfect positive correlation between two sets of variables is indicated by +1. That is, if there is a movement of 10 per cent on one variable it is accompanied by a movement of 10 per cent in the same direction on another variable, e.g. when the advertising budget is increased by 10 per cent then sales in the subsequent period also increase by 10 per cent. If this were the case (regrettably it is never that simple) then the resulting correlation coefficient calculated for the two variables would be +1. Similarly, if the two variables had a perfect relationship but in opposite directions, say for every 10 per cent increase in price, the sales volumes decreased by 10 per cent (equally unlikely), then the correlation coefficient would be - 1. When changes in one variable are not associated with changes in the other variable, then the correlation coefficient will be calculated as zero and this indicates no relationship between the two sets of variables.

The usefulness of correlation analysis lies in the fact that it indicates which variables appear to have common sets of movement in the market and the strength of association between them. The value taken as significant depends on the sample size but, as a rule of thumb, correlation coefficients above +0.7 or below - 0.7 are generally thought to indicate an increasing degree of association, and therefore to warrant further investigation of the two variables under consideration, for data derived from large samples.

The usual use of correlation analysis in marketing decision making is to attempt to measure the degree of association between those variables that the marketing manager would like to see associated. Correlation coefficients can be calculated for the relationship between company sales volume and variables such as price, level of advertising expenditure, competitive activity, and various consumer variables such as purchase behaviour, income and attitude. Correlation coefficients can also be calculated for variables which, experience suggests, are relevant to sales volume: seasonal factors, economic factors, competitive activity, and so on.

The simplest form of correlation analysis is bivariate correlation analysis, in which only two variables are considered. For most practical marketing applications multiple correlation analysis is more useful, since it indicates association between three or more sets of variables.

It is important for the user of correlation analysis to remember that the statistical technique will simply indicate that there is a statistical relationship in the movement of two sets of data. From this, the assumption is made that there is a cause-and-effect relationship. If a high degree of statistical correlation is found between the amount of money spent on advertising and sales volume, then it is assumed that the high level of advertising support is resulting in high levels of sales. But the statistical technique does not indicate cause-and-effect relationships, it simply indicates related movements in the data. Whether it is appropriate to consider cause-and-effect depends entirely on the subjective application of the user: if a cause-and-effect relationship appears to make sense then it is assumed to be so, if it does not make sense then it is assumed that the correlation is irrelevant. Inevitably, there are dangers in subjective interpretation and common sense is at least as important as statistical technique in interpreting the results.

### Regression analysis

Where correlation analysis is concerned with association, regression analysis is concerned with dependence. That is, if correlation analysis indicates a number of variables that are associated with sales volume, regression analysis makes it possible to predict sales volumes from knowledge about the other variables. This introduces the concept of dependent and independent variables. Movement in the dependent variables depends on movement in the independent variables. The most commonly used dependent variable in practice is sales volume. The independent variables, on which this may depend, are any of the marketing decision variables such as price, advertising, level of distribution and product quality, and non-marketing external variables such as level of income, changes in the weather, and a whole host of other social and economic variables that may influence sales volume in a particular market. Typically, then, correlation analysis and regression analysis are both carried out on the same set of data. Correlation analysis indicates which variables have a relevant association with sales volume, for example. Regression analysis can then be used to predict sales volume given a set of decisions about marketing variables and assumptions about probable movements in external variables.

The most common use of regression analysis in marketing research is for sales forecasting. Since sales volume is normally dependent on a number of variables, it is more common to use multiple regression analysis than simple bivariate regression analysis. Multiple regression, as with multiple correlation, makes it possible to deal with the effect of a number of variables at once, and therefore to cope with a more realistic analysis of actual market movements.

### Multivariate analysis

Multiple correlation and multiple regression analyses form the basis for further complex statistical methods of analysis that can deal with a number of variables at once. These make it possible to cluster respondents who are similar on a number of univariate attributes or to group similar attributes into a smaller number of factors. These techniques are therefore extremely useful in market segmentation studies. They identify and describe market segments, describe and group product attributes, and measure product similarities. The techniques are only briefly introduced here in a non-statistical way. However, readers wishing to obtain the most from the use of quantitative marketing research data should equip themselves with sufficient statistical background to find out more about the use and application of these methods.

Multivariate analysis of data is a highly specialized area requiring thorough statistical knowledge of the range of techniques and their appropriate application. The growth in use of computers for analysis of marketing research data has resulted in the increased use of multivariate analysis, but sometimes in inappropriate ways and on unsuitable data. The purpose of this section introducing the idea of multivariate analysis is simply to indicate that some very useful statistical analytical techniques exist which, if applied in the right way to the right type of data, can provide worthwhile operating knowledge to the marketing decision maker. Research agencies that carry out quantitative research will have statisticians on their staff with whom the possibilities for multivariate analysis applied to a specific problem can be discussed. Four techniques are mentioned here: factor analysis, cluster analysis, multiple discriminant analysis and multi-dimensional scaling.

### Factor analysis

This technique reduces a large number of original variables, such as attitude statements, to a smaller number of factors. Each factor consists of a group of related statements that form a broad dimension of attitude. In a research survey on television programme assessment, 750 viewers used 58 rating statements to describe 61 different programmes. Factor analysis reduced the 58 statements to nine factors. One factor was called 'information' and contained attitude statements about the degree of scientific interest in the programme, whether it made the viewer think, whether it contained education/information or whether it was meant to entertain. The value of this exercise lay in the fact that 58 possible comments about television programmes were reduced to nine main dimensions of thought, which allow viewers to give a rating to any programme.

### Cluster analysis

This technique analyses responses on a large number of variables, for example attitude statements, from a large number of respondents and groups together, or clusters respondents who are similar in the pattern of their responses. Cluster analysis can therefore be used as the basis for identifying segments in the market that exhibit similarities to each other and differences from other clusters in the market. Identification of market clusters and knowledge of the ways in which they are similar can lead to changes in the product or marketing methods used to reach this group.

### Multiple discriminant analysis

The objective of this technique is to classify respondents into two or more groups on the basis of a number of items of information about them. Once respondents have been discriminated into one group or another it may become possible to predict or explain their response to a given marketing situation.

The major discriminating factor between shoppers and non-shoppers in a particular department store was found, through discriminant analysis, to be the perceived price level within the store. Subsequent advertising of lower priced lines resulted in an increase in the number of shoppers._

A variant of this technique is called automatic interaction detection (AID), and is commonly used for market segmentation studies.

### Multidimensional scaling

This technique is used for producing perceptual maps. Consumers rate brands or products by their attributes, by the degree to which brands are seen as similar or by the degree to which one brand of product is preferred to another. These rating questions usually include a rating for the consumer's 'ideal' brand. Multidimensional scaling is applied to the responses, resulting in perceptual maps. An example is shown in Figure 6.3.

These can be used to change product attributes to be nearer the 'ideal' brand, or to suggest advertising messages that will stress the brand attributes nearest to the ideal brand. They indicate the real competitors in a marketplace from the consumer's point of view and so can be used to determine market positioning strategies.

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