Reference Ranges

In several ways, the reference range (RR, reference interval, normal range) is similar to the descriptive statistics we discussed in the previous column. Here, we will use two examples to bring together the statistics used to summarize a reference range. The first one does not separate the data by age or sex, etc. Example 1 is a set of 40 values with the mean, the median, as well as the minimum, the maximum and the range (maximum - minimum). We have also included the first and third quartiles (Q1 and Q3), the histogram and the cumulative % plot.

Table 1

Figure 1

In this example, we see that the mean and median are the same, suggesting a 'normal' distribution. The histogram also looks 'normal' in spite of the fact that we have only 40 data points. The cumulative % line helps establish the 95% range. Looking at the ±2 SD values we see that, keeping in mind the fact that there are only 40 points, it is similar to the 95% range using the % from the cumulative % line. That is done by looking at the 2.5 and 97.5% points on the y-axis and moving over to the red line then down to the x-axis. (In our small drawing this is not as easy as it is in larger drawings, as you could have in the whole screen using Excel.)

In Example 2 we have again used 40 data points but in this case we have divided them into females and males. This is easily done with Excel using a column with M or 0 for males and F or 1 for females and then sorting the ID, raw data points and M or F to collect the data by sex. (This approach can easily be used if you want to divide the data by age.)

In this Example we have added the t-test to test for a difference between males and females (0.703). The t-value indicates there is no statistical difference between the males and females. We have not drawn nor do we suggest you draw the histograms with so few points.

Table 2

Table 3

In the last installment, we considered some "non-normally" distributed data in looking at children's cholesterol levels. As you remember, the SD of these data to be 47.1, so ±2SD would be between 2.4 and 190.8, which is not 95% range of the data. It is inappropriate to use ±2SD as the calculations indicate. Otherwise, we would lose the top 5 data points. Our suggestion is to eliminate the bottom 2.5% and the top 2.5%. Since we have 60 points, then we would will exclude 1.5 values, so we have chosen to eliminate the bottom 2 values and the top 2 values.

Table 4

Table 5

Without the grayed data, the range is now 173, from 56 to 229.

In the next installment we will discuss in some detail the statistics used in a method comparison. One of the examples will be of methods with different reference ranges. As always, you are invited to send questions and comments to

Interpreting Statistics Archives


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