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Along the x-axis to be equal. This has also led to some grievous errors in histograms published in archaeological reports. Two kinds of situations in which this often occurs involve chronological scales and grain-size distributions. Commonly, archaeologists want to show change is some variable, such as settlement intensity, over time but we are often forced to assign observations to intervals of time that are not equal in length. Let us say, for example, that we want to show how the number of sites (our indirect measure of human population perhaps) varies over a period of many centuries, but we can date the sites much more precisely in recent times than we can in more ancient ones, and this is reflected in our grouping of sites into “periods” or “phases” of varying numbers of years (an interval scale).
The standard error of the mean is simply the ratio of the standard deviation to the square root of the sample size (n). Consequently we can represent it algebraically as but in samples, since we can only estimate must estimate SE as, we Finally, it is important to mention that when, as often happens in archaeology, we are interested in densities, such as the number of lithics per square meter, or the number of radiocarbon decays per five minutes, the standard deviation is rather different. We will return to this point in discussion of the Poisson distribution in chapter 6 and radiocarbon dates in chapter 15.
If we need to draw a histogram with unequal intervals manually, the procedure is the same as before but with a small complication. We need to transform the data into a ratio 26 The Archaeologist’s Laboratory measurement, such as “sites per year” for the first example or “soil mass per mm” for the second. This will give us the heights we need to preserve the proportionality of area when the bars’ widths are made proportional to the number of years of each period or the size increment between screens.