 # Research 101: Index and Correlation

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In part three of our series into the world of research, we will take a look at some of the most popular and often misused concepts in research and statistics. Whether you are a researcher, account executive or even an art director, it is important to understand the meaning and application of these concepts as they can have significant impact on how data is interpreted as well as how marketing decisions are made.
First, lets discuss indices. The first lesson is knowing when you use ‘index’ or ‘indices.’ Index is singular form of the word, while indices represents the plural. Easy enough, right? In statistics and marketing research, an index number most commonly represents an indicator of average percentage change in a series of figures where one figure, called the base, is assigned an arbitrary value of 100 and the other figures are adjusted in proportion to the base. In other words, numbers less than 100 would mean those items are below average in relation to the base number while those exceeding 100 would be considered above average. The most challenging part of dealing with indices is knowing how to interpret their meaning. Let’s look at example. An index number of 110 can be inferred to mean that this figure is 10% above the “base” average, while an index of 90 would represent a figure 10% below the base average. An index may also be read in exponential form. Thus, an index number of 110 means that figure is 1.1x above the base. This method is often used when the figures represent the likelihood of events. A third way to interpret an index is by index points. These points simply refer the difference between the indices.

Another common, but often misused, concept in marketing research is understanding the difference between correlation and causality. Correlation is one of the easiest descriptive statistics to understand and is one of the most widely used. The term correlation literally means co-relate and refers to the measurement of a relationship between two or more variables. A correlational coefficient typically ranges between –1.0 and +1.0 and provides two important pieces of information regarding the relationship: intensity and direction.

Intensity refers to the strength of the relationship and is expressed as a number between zero (meaning no correlation) and one (meaning a perfect correlation). These two extremes are rare as most correlations fall somewhere in between. A correlation of 0.30 may be considered significant and any correlation above 0.70 is almost always significant. Direction refers to how one variable moves in relation to the other. A positive correlation (or direct relationship) means that two variables move in the same direction, either both moving up or down. For example, high school grades and college grades are often positively correlated in that students who earn high grades in high school tend to also earn high grades in college. A negative correlation (or inverse relationship) means that the two variables move in opposite directions; as one goes up, the other tends to go down. For instance, depression and self-esteem tend to be inversely related because the more depressed an individual is the lower his or her self-esteem. As depression increases, then, self-esteem tends to decrease.

Now the biggest make a researcher can make is to assume that every correlation represents causality. A classic example of this is the correlation between ice cream consumption and murder rates in the U.S. It is true that as ice cream consumption increases, more murders occur, but could it be true that ice consumption leads to more murders. Of course not. The truth is that often two variables are related only because of a third factor, which is weather in this case. When the weather is hot, people are more inclined to buy ice cream. When the weather is hot, people are also more prone to violent acts. With this example in mind, please remember that correlation does not imply causation. Researchers like to identify the relationships that exist between variables as clients often get excited about these relationships and make marketing decisions based on those relationships. It is important that researchers take time to identify why a relationship exists. Sometimes the best tool in a researcher’s toolkit is common sense, and the same holds true when dealing with correlations and causality.
Tune in next month for another edition of Research 101.