Condence Intervals, Error Bars, and p Values
This chapter presents more about CIs, including some beautiful pictures and two further approaches to CI interpretation. The main issues are
• Error bars, and how they can show various types of information in figures
• Cat’s-eye pictures that show the beautiful shape of a CI • The fourth approach to interpreting CIs-in terms of their shape • The relation between CIs and p values • The fifth approach to interpreting CIs-with reference to p values • One-sided CIs, which correspond to one-tailed NHST
Does Figure 4.1 show the mean number of ice creams consumed by 10-yearolds or the median response time to a red stoplight? What do the error bars represent? These are good questions, and Figure 4.1 fails to provide answers. I’ll refer to the simple graphic shown on the column and dot in Figure 4.1 as error bars, or sometimes simply bars. Error bars define a range of values around a point estimate such as a mean. The trouble is that bars can be used to depict various different types of ranges. When you see Figure 4.1, what questions spring to mind? Probably the
most basic concern is the dependent variable, what it measures, and what its values mean. Ice creams or braking times? Then we need to know what the column and the big dot are reporting-perhaps the sample mean, a median, or a frequency? Labels on the figure or the figure caption needs to give clear answers to these questions. Seeing the error bars should prompt an additional question, because,
although the error bar graphic is familiar, it is, unfortunately, ambiguous.