Null Hypothesis

STATISTICAL CONCEPTS and ILLUSTRATION:

1. Null Hypothesis:

A null hypothesis is a statement proposing that no (statistically significant) relationship or difference exists between population variables of interest. The null hypothesis provides a basis for statistically testing propositions that theorize such relationships or differences to exist. For instance, I may propose that since the US produces more than three times as much oil and gas as compared to Canada (U.S. Department of Energy, 2012), US oil & gas firms are larger, and hence have greater market capitalization, than their Canadian counterparts. The variables of interest here are the average market capitalization of US oil & gas firms, and the average market capitalization of Canadian oil & gas firms. An example of a corresponding null hypothesis is “There is no difference in average market capitalization between US oil & gas firms and Canadian oil & gas firms”. Mathematically, this null hypothesis may be expressed as

μUSO&GMktCap – μCanadaO&GMktCap  = 0. (μ represents population mean).

I can now test this null hypothesis by computing the difference in average market capitalization between a sample of US oil & gas companies, and a sample of Canadian oil & gas companies, and using an appropriate statistical test to infer if the difference is significantly greater than (or lesser than) zero for the respective populations.

There are over 500 publicly traded oil & gas companies in each of the US and Canada (CreditRiskMonitor.com, 2013).  I use two samples comprising 52 US oil & gas companies and 46 Canadian oil & gas companies respectively, from the 2013 Sustainalytics database. Sustainalytics (established in 1993) is a sustainability research and analysis company.  It covers over 1200 North American companies across 24 industry sectors, and provides market capitalization data (in millions of US dollars) for each company. The coverage is balanced and includes industry leaders as well as laggards, with respect to economic, social and environmental performance indicators (Sustainalytics, 2013). Hence, I contend that the sample is reasonably representative of the oil & gas industry population for the US and Canada.  I use the independent samples t-test to test the null hypothesis, since US oil & gas companies and their Canadian counterparts represent independent groups, and market capitalization is a ratio variable. (Note: The sample sizes are small and per the K-S test results, which are not shown for brevity, the assumption of normality does not hold. Hence, for these samples, I tested the null hypothesis using a non-parametric test (Mann Whitney U test) as well as a parametric test (independent samples t-test). Test results are not shown for brevity; however, both test results are significant, hence I use the parametric t-test.)