*Dave Sutherland 0000-00-00 00:00:00*

Did Your Expert Use Correlation Analysis? Your expert may present opinions based on statistical analysis. While you will not need to become an expert on statistical analysis, it is helpful if you understand some basic statistical tools. One such tool is correlation analysis. There are a variety of tools to test for relationships that may exist among data sets, such as sales, cost of goods sold, etc. Think back to the time when your client emphatically proclaimed, “Sales would have gone up, because we’ve been spending a ton on advertising!” This is an interesting statement. The client assumes that there is a causal relationship between how much they spend on advertising and sales. The assumption is that the more they spend on advertising, the more their sales increase. This may be true, but it may not. Businesses incur expenses in order to generate sales. Understanding how these different variables relate to one another is important. In fact, if a relationship exists, predictions can be made. Experts try to visualize, describe, and quantify these relationships. One of the simplest ways to visualize the strength of the relationship between two variables, such as sales and advertising costs, is to create a graph. This type of graphical representation shows each variable relative to the other. As is evident in this example, the data points are relatively close together and are upward-sloping. Visually, it appears that both sales and advertising expense are related; however, what the picture does not show is the strength of the relationship. One way to quantify the strength of the relationship between the two variables is to determine the “sample correlation coefficient.” The sample correlation coefficient is a statistic that measures the strength of the relationship. In our example, it is the strength of the relationship between sales and advertising expenses. The measurement will lie somewhere between “-1” and “1.” An amount of (or close to) zero implies that the variables are not related. Using our example of sales and advertising expenses, a value of 0.00 would imply that there is no apparent relationship between the amount spent on advertising and sales. An amount close to “1” implies a “strong positive correlation”. In other words, as advertising expense increases, sales increase as well. Conversely, an amount close to “-1” is said to possess a “negative correlation” or as advertising expense increases, sales likely decrease1. It is not enough to establish that the relationship is positive, negative, or no correlation. The expert needs to identify how significant the relationship is between the two analyzed variables. A significance test proves mathematically that the results did not occur by chance. Statistical analysis performed properly can be very powerful. Performed poorly, it can be disastrous.

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