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Describing Data: Statistical and Graphical Methods¹

¹ From the Department of Surgery, University of Michigan Medical Center, Ann Arbor. Received January 14, 2002; revision requested March 2; revision received May 20; accepted June 14. Address correspondence to the author, Department of Surgery, University of Pennsylvania Health System, 4 Silverstein, 3400 Spruce St, Philadelphia, PA 19104-4283 (e-mail: seema.sonnad@uphs.upenn.edu).

View larger version (14K): [in a new window]   Figure 1. Line graph shows the mean, median, and mode of a skewed distribution. In a distribution that is not symmetric, such as this one, the mean (arithmetic average), the median (point at which half of the data lie above and half lie below), and the mode (most common value in the data) are not the same.

View larger version (18K): [in a new window]   Figure 2. Box plot demonstrates low variation. A high-variation box plot would be much taller. The horizontal line is the median, the ends of the box are the upper and lower quartiles, and the vertical lines are the full range of values in the data. (Reprinted, with permission, from reference 1.)

View larger version (25K): [in a new window]   Figure 3. Line graph shows change in MR signal intensity in the cerebrospinal fluid (CSF) collected during oxygen inhalation over time. Signal intensity in the quadrigeminal plate cistern increases more gradually, and equilibration is reached at 15-20 minutes after the start of oxygen inhalation. (Reprinted, with permission, from reference 3.)

View larger version (26K): [in a new window]   Figure 4a. Bar graphs. (a) Use of a scale with a maximum that is only slightly higher than the highest value in the data shows the differences between the groups more clearly than does (b) use of a scale with a maximum that is much higher than the highest value.

View larger version (19K): [in a new window]   Figure 4b. Bar graphs. (a) Use of a scale with a maximum that is only slightly higher than the highest value in the data shows the differences between the groups more clearly than does (b) use of a scale with a maximum that is much higher than the highest value.

View larger version (44K): [in a new window]   Figure 5. Bar graph shows the underestimation rate for lesion size with vacuum-assisted and large-core needle biopsy. Underestimation rates were lower with the vacuum-assisted device. It is helpful to label the bars with the value. (Reprinted, with permission, from reference 4.)

View larger version (27K): [in a new window]   Figure 6. Bar graph shows the diagnostic adequacy of high-spatial-resolution MR angiography with a small field of view and that with a large field of view for depiction of the segmental renal arteries. (Reprinted, with permission, from reference 5.)

View larger version (19K): [in a new window]   Figure 7. Histogram represents distribution of calcific area. Labels on the x axis indicate the calcific area in square millimeters for images with positive findings. (Reprinted, with permission, from reference 6.)

View larger version (28K): [in a new window]   Figure 8a. Representative histogram and frequency polygon constructed from hypothetical data. Alternate ways of showing the distribution of a set of data are shown (a) with both the histogram and the frequency polygon depicted or (b) with only the frequency polygon depicted.

View larger version (20K): [in a new window]   Figure 8b. Representative histogram and frequency polygon constructed from hypothetical data. Alternate ways of showing the distribution of a set of data are shown (a) with both the histogram and the frequency polygon depicted or (b) with only the frequency polygon depicted.

View larger version (20K): [in a new window]   Figure 9. Stem and leaf plot constructed from data in Table 4. Step one shows construction of the stem, and step 2 shows construction of the leaves. These steps result in a sideways histogram display of the data distribution, which preserves the values of the data used to construct it. The number 9 appears on the stem as a place saver; the lack of digits to the right of this stem number indicates that no values began with this number in the original data.

View larger version (16K): [in a new window]   Figure 10. Box plots present follow-up data for serum creatinine concentration. Left: Within 72 hours after injection of a gadolinium chelate (group 1 baseline creatinine clearance, <80 mL/min [<0.50 mL/sec]). Right: Within 120 hours after injection (group 2 baseline creatinine clearance, <30 mL/min [<0.50 mL/sec]). (Reprinted, with permission, from reference 7.)