Bank X is interested in determining if a correlation exists between online and total sales. Unfortunately, it would not be appropriate to investigate such a correlation since correlative analysis requires that the variables be independent (Moles & Terry, 1997). Since online sales are a subset of total sales, the two variables are related. Since a correlation calculation cannot be done on these two variables, Bank X must change its research question. They are still interested in understanding what effects online sales, so it makes sense to ask if there is a correlation between online sales and in-store sales. In other words, subtracting online sales from total sales generates another variable that can be used for the correlation calculation.
The correlation coefficient describes the relationship between two independent variables using a scale of -1 to +1. A negative correlation coefficient indicates an inverse relationship in which an increase of one variable results in an increase of another. A positive correlation coefficient, on the other hand, describes two variables that are increasing together (Moles & Terry, 1997). The U.S. Department of Commerce (2004) provides quarterly data on retail sales in the United States. Comparing the online to in-store retail sales information for 19 quarters from 1999 to 2004 produces a correlation coefficient of 0.790. A regression analysis of the same data verifies that calculation by creating a line of a best that results in the same correlation coefficient. Since this coefficient exceeds the critical value for a 99% confidence level with this size data set, it can be said with 99% confidence that there is a correlation between online and in-store retail sales.
This is similar to an analysis we performed at a regional Internet Service Provider, ISP X. Like most ISPs, ISP X tracks usage in each market to determine how individual users are affecting the resources of each market. Since ISP X offers different speed plans, there was an interest from executive management whether there was a relationship between purchased download speed and heavy resource usage. The theory was that people who plan to use their Internet connection more would buy higher speed plans in order to gain faster access to more data. After analyzing the top 100 users in 4 different markets, we were unable to reject the hypothesis that there was no correlation between speed plan and resource usage. Therefore, we had to conclude that there was not enough evidence to support the claim that higher available download speeds resulted in more bandwidth resource usage.
Moles, P. & Terry, N. (1997). Correlation. The Handbook of International Financial Terms. Retrieved April 27, 2009.
U.S. Department of Commerce. (2004). Retail E-Commerce Sales in Second Quarter 2004 Were $15.7 Billion, up 23.1 Percent from Second Quarter 2003, Census Bureau Reports. United States Department of Commerce News. Retrieved May 4, 2009.