Page 125 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

104 3 Estimating Data Parameters

A: The histogram and box plot of the ART data (n = 150 cases) are shown in
Figure 3.11. The sample median and sample mean of ART are med ≡ w = 263 and
x = 324, respectively. The distribution of ART is clearly right skewed; hence, the
mean is substantially larger than the median (almost one and half times the
standard deviation). The histogram of the bootstrap distribution of the median with
m = 1000 resamples is shown in Figure 3.12. We compute:

w boot = 266.1210
SE boot = 20.4335

The bias w boot − w = 266 – 263 = 3 is quite small (less than 7% of the standard
deviation). We therefore compute the bootstrap confidence interval of the median
as:

w t ± 149 . 0 , 975 SE boot = 263 ± 1.976×20.4335 = 263 ± 40

40
n 900 x
35 800
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600
25
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x 0
a 0 0 100 200 300 400 500 600 700 800 900 b ART
Figure 3.11. Histogram (a) and box plot (b) of the ART data.

500
n
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x*
0
180 200 220 240 260 280 300 320 340
Figure 3.12. Histogram of the bootstrap distribution of the median of the ART data
(1000 resamples).