Category: P-values. A p-value is a measure of evidence commonly used in hypothesis testing. These pages describe some of the controversies associated with the use of p-values. Articles are arranged by date with the most recent entries at the top. You can find the theme and closely related categories, definitions, and other resources at the bottom of this page.

Stats: Choosing between two conflicting analyses (May 16, 2007). Someone wrote in and asked about an analysis where there was only a limited amount of data. The simple analysis using an odds ratio produced a significant result (p=0.048). A referee suggested that they run a logistic regression model adjusting for two covariates. These covariates were not imbalanced between the two groups. With the logistic regression model, the p-value changed from 0.048 to 0.06.

Stats: Can the p-value actually equal 1.0? (May 30, 2006). Dear Professor Mean, I have a data set that compares the proportions in two groups. In the first group, the proportion is 19% (5/26). In the second group, the proportion is also 19% (3/16). I computed a p-value of 1.0 for this data, but a referee tells me that a p-value of 1.0 is impossible. How can I convince the referee that he/she is wrong.

Stats: Relationship between sample size and p-values (February 14, 2005). I got a rather basic inquiry about p-values, but it is worth mentioning. Someone had a data set with 9,000 observations and was unhappy with the p-value that he got in a logistic regression model. So just as an experiment, he decided to replicate the data set (copy the entire matrix and paste it immediately below). This gave him a sample size of 18,000 observations. He noted that the odds ratio stayed the same but the p-value got smaller.

Stats: A small p-value does not mean a large difference (February 8, 2005). Someone asked me if the p-value for a t-test indicates the size of the difference between two groups. It turns out that the p-value is related both to the size of the difference and the sample size. In general, a very small p-value might indicate a large difference, a large sample size, or both.

Stats: Confusion about p-values (January 18, 2005). Someone wrote to me with a statement that represents a commonly held, but false belief. He stated, in effect, that a p-value of 0.06 means that there is only a 6% probability that the null hypothesis is true.

Stats: One-tailed p-values (April 12, 2004). Someone asked me how to compute one-sided p-values in SPSS. The output from SPSS always uses two-sided p-values. This was worth an explanation, so I added a new question to the Ask Professor Mean page on how to do this. There is a fierce debate about when you should use one-sided tests.

Stats: One-tailed p-values (April 12, 2004). Dear Professor Mean, SPSS produces two-tailed p-values, but I want a one-tailed p-value. How do I get this?

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This webpage was written by Steve Simon on 2007-09-11, edited by Steve Simon, and was last modified on 2008-07-08. Send feedback to ssimon at cmh dot edu or click on the email link at the top of the page.