P-value > 1?

I was skimming ProQuest today to look for something new to discuss. There are many dissertations with incorrect statistical tests, and misaligned research questions and research designs. But, I found one from a University that so far this year has only one graduate (or at least only one graduate dissertation in ProQuest). In this study, the emerging scholar explored a company’s change in financial value pre- and post-merger or acquisition. While outside my domain, I’ve read enough about financial value creation to at least understand what was going on. Plus, I like reading about how time-series analyses are constructed. For a primer on time-series analysis in R, see Avril Chohan and Tavish Srivastava.

As I reviewed the emerging scholars data analysis I began to be concerned. I saw the term one-way analysis of variance (ANOVA) on p. 59. A one-way ANOVA is used to explore the differences in a variable of interest based on three or more categories. For example, if one where to examine test scores of five 4th-grade courses, that would be a function that a one-way ANOVA could handle. However, the variables in this study are not independent. One of the critical assumptions of a one-way ANOVA is that the variables are independent. For example, the stock price of Google (Symbol: GOOGL) on September 15, 2021 is related to the stock price on both September 14, 2021 and September 16, 2021. In other words, an observation at one point is related to the observation at another point.

There are a many of data analysis approaches, statistical tests, and books written about the analysis of time-series data. In the ANOVA series of tests, which is used to detect changes in a mean value of the variable of interest, a repeated-measure ANOVA could be selected. A repeated-measure ANOVA, sometimes called RMANOVA, measures the mean value of the variable of interest over time. An RMANOVA, at least, should have been considered and attempted. So what does the wrong test have to do with the title of this blog entry?

Three of the results of the one-way ANOVA, which I know is wrong, have p-values listed greater than 1!!! For the record, 11 of the 12 statistical tests had reported p-values > 1 (the highest being 8.94). A p-value means the probability of having a result that is equal to or greater than the result achieved under a specific hypothesis. Thus, does that mean that the null hypothesis was not rejected was with the force of 894% probability? What does that say about the one result which was p < .001?

I get it when faculty aren’t strong in quantitative data analysis. That’s the purpose of textbooks, the library, and the Internet. Maybe even reach out to a few colleagues to refresh a memory or two. But seriously? p > 1!!! Don’t advise students performing quantitative work.

Reference:

Tuggle, J. R. (2021). Evaluating merger activity using a quantitative case study approach to aid in the determination if mergers and acquisitions are a strategic advantage to the creation of financial value for acquiring company shareholders (Doctoral dissertation; Lincoln Memorial University). ProQuest Dissertations & Theses Global: The Humanities and Social Sciences Collection (28650945)