John and Sons Company: Null Hypothesis and Test of Statistical Significance

The null hypothesis often states the opposite of what an experimenter is attempting to prove (Lane 2009). The experimenter wants or expects to disprove the null, which is expressed as H0. For example, presume that the John and Sons Company wants to open a new factory overseas and take advantage of lower wages abroad, but is concerned about the potential quality implications of this move upon the product, as John and Sons have had quality-control problems in the past with their overseas operations. The H0 would be: 'there is no statistically difference in the number of defects in a batch of the product manufactured in country X versus a batch manufactured in the United States.' (Hence the term null hypothesis -- that there is no difference). The alternative hypothesis, expressed as H1, would be that there was a statistically significant difference in the number of defects found in the batches made in country X versus the United States. "This alternative hypothesis states that the relationship observed between the variables cannot be explained by chance alone" (Hypothesis testing, 2009, Quick MBA).

To test whether the research results are statistically significant an appropriate test of statistical significance should be run. A chi-square "goodness-of-fit test is used to determine whether a set of proportions have specified numerical values" (Hypothesis testing, 2009, Quick MBA). However, in this specific instance, since it is likely that multiple batch tests for defects will be run, an ANOVA test would be more appropriate: "The primary purpose of ANOVA is to test for differences between multiple means. Whereas the t-test can be used to compare two means, ANOVA is needed to compare three or more means. If multiple t-tests were applied, the probability of a TYPE I error (rejecting a true null hypothesis) increases as the number of comparisons increases" (Hypothesis testing, 2009, Quick MBA). A one-way ANOVA examines whether multiple means differ. "ANOVA calculates the ratio of the variation between groups to the variation within groups" (Hypothesis testing, 2009, Quick MBA).

References

Hypothesis testing. (2009). Quick MBA. Retrieved December 9, 2009 at http://www.quickmba.com/marketing/research/

Lane, David M. (2009). Null hypothesis. Hyperstat: Online contents.

Retrieved December 9, 2009 athttp://davidmlane.com/hyperstat/A29337.html