In a recent e-mail query, someone asked about how they should compare two air pollution monitors that sit side by side and collect data all day. They had the average reading per monitor for each of 50...

In a recent e-mail query, someone asked about how they should compare two air pollution monitors that sit side by side and collect data all day. They had the average reading per monitor for each of 50 days and wanted to compare the two monitors; their first thought was to run a t test between the means of the readings of the two monitors. This question would apply equally well to psychologists and other behavioral scientists if we simply substitute two measures of Extraversion for two measures of air pollution and collect data using both measures on the same 50 subjects. How would you go about comparing the monitors (or measures)? What kind of results would lead you to conclude that they are measuring equivalently or differently? This is a much more involved question than it might first appear, so don’t just say you would run a t test or obtain a correlation coefficient. Sample data that might have come from such a study are to be found on the Web site in a file named AirQual.dat in case you want to play with data.