The data in Table 5.1 give the price-to-earnings ratio (PE) for samples of stocks on the NYSE and NASDAQ exchanges. Is there evidence that the typical PE values differ on the two exchanges? (Rather...

The data in Table 5.1 give the price-to-earnings ratio (PE) for samples of stocks on the NYSE and NASDAQ exchanges.

Is there evidence that the typical PE values differ on the two exchanges? (Rather than depending on a logarithmic transformation to achieve normality, as in Example 5.1, use a technique that does not require normality.)

Example 5.1

The price-to-earnings ratio (PE) is a measure that is commonly used to evaluate whether a stock may be overpriced. The data in Table 5.1 represent small random samples of stocks having reported PE on the NASDAQ and NYSE stock exchanges (as of 1/30/2020). Do the two stock exchanges differ with respect to the PE of their stocks? The left panel in Figure 5.1 shows that the PE is very positively skewed but suggests that the values may tend to be higher on the NASDAQ exchange. The right panel is the box plot for the transformed data (LNPE 5 ln(10 1 PE), where adding 10 is necessary because one value is negative). These data are still skewed, but much less so than for the raw data. While this panel also suggests that the typical values are higher on the NASDAQ, we will see that the actual evidence for this is surprisingly weak.