396 Statistical Methods
7 Click OK. StatPlus generates the histograms shown in Figure 10-3.
Figure 10-3
Multiple
histograms
of prices
in each cityWhat do these histograms tell you about the analysis of variance as-
sumptions? One of the assumptions states that the population variance is
the same in each group. If one city has prices that are all bunched together
and another has a very wide spread of prices, unequal variances can be
a problem. The plot shows a tendency for the spread to be larger when
the prices are higher. In particular, New York seems to have the highest
mean price and the biggest spread, and Chicago is second in both mean
and spread. In this situation it sometimes helps to replace the response
variable with its logarithm. Exercise 7 requests that you replace Price
with the log of price and to see what effect this has on the analysis. If
you find there that the assumptions seem valid but that the results are
essentially the same, then that tends to validate the original analysis. Here
we continue with the analysis using Price as the response variable, even
though there is a question about the equal variance assumption. Generally
speaking, it is easier to interpret the analysis on Price rather than its loga-
rithm or some other transform.
What about the assumption of normal data? The analysis of variance is
robust to the normality assumption, so only major departures from normality