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 === Example 1: highest annual batting average in the National League. === We consider here the maximum batting average obtained by any National League player in each of the years 1901-1990. Because batting average is a time series, data certainly are not independent and we must beware of temporal trends. If we were to ignore the possibility of temporal trends, we would conclude that the data exhibit moderately normal behavior (Figure 8a), with slight positive skewness and, according to Chauvenet’s criterion, one anomalously high value of 424 that could be excluded. Ignoring temporal trends, we would predict at a 68% confidence level (1σ) that the maximum 1991 batting average would be 352±21 (Table 6).

Plotting batting average versus time (Figure 8b), however, we see immediately that the departures from the mean were nonrandom. Batting averages decreased rapidly during 1901-1919, peaked during 1921-1930, and decreased gradually since then. What accounts for these long-term