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If we assign experimental units that have high values of that lurking variable into one treatment group, that group will be either advantaged or disadvantaged, depending if there is a positive or negative relationship. We would be quite likely to conclude that treatment is good or bad relative to the other treatments, when in fact the apparent difference would be due to the effect of the lurking variable. That is clearly a bad thing to occur. We know that to prevent this, the experimental units should be assigned to treatment groups according to some randomization method.

Some elementary data analysis tools are: ◦ Order Statistics. The data when ordered smallest to largest. y[1] , · · · , y[n] . ◦ Median. The value that has 50% of the observations above it and 50% of the observations below it. This is y[ n+1 ] . 2 48 DISPLAYING AND SUMMARIZING DATA It is the middle value of the order statistics when n is odd.

This underlying GRAPHICALLY DISPLAYING A SINGLE VARIABLE 35 population distribution1 would generally be reasonably smooth. There is always a trade-off between too many and too few groups. If we use too many groups, the histogram has a "saw tooth" appearance and the histogram is not representing the population distribution very well. If we use too few groups, we lose details about the shape. 4 shows histogram of the Earth density measurements by Cavendish using 12, 6, and 4 groups, respectively.

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