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Welcome to the first installment of a series of articles on statistics in the laboratory. Our primary goal is to teach you how to interpret and understand statistics, such as method validation; a secondary objective is to help you learn how to calculate your own statistics using Excel. If you are fond of your Texas Instruments calculator, please let us know and we can help you with the statistics on it; our examples in this series will use Excel. The following are the topics that at this point we propose to cover:
I. Descriptive Statistics
a. The Middles
i. Mean
ii. Median
iii. Mode
b. The Variation
i. Range
ii. Average Deviation
iii. Standard Deviation
iv. Standard Deviation Index (SDI)(Z-score)
c. Statistical Charts - I (Charts will be intermittently discussed as appropriate in the text.)
i. Bar Chart
ii. Pie Chart
iii. Normal Curve
II. Drawing Conclusions from Data
a. Differences between Means
i. Unpaired T-test
ii. Paired T-test
b. Chi Square
c. Statistical Charts - II
i. Scatter plot
ii. Difference plot (Bland-Altman)
d. Regression
i. Slope
ii. Intercept
iii. Correlation Coefficient (r)
iv. Coefficient of Determination (R2)
e. Data Source
III. Pulling It All Together
a. Assessing Linearity
b. Analytical Method Validation
c. Reference Interval (Reference Range)
d. Clinical Method Validation
e. Quality Control
This being said, we strongly encourage (urge) you to comment on this and make suggestions on what you would like to see discussed, as we see this as a you-based series. As you have questions or concerns, let us know: davidplaut@yahoo.com.
We begin with the first descriptive statistic: the Mean.
Descriptive Statistics - The Middles
Imagine walking into work one Monday morning and seeing a note reading, "Good morning. Please take a look at these data of the blood test values from the health fair on Saturday and get back to me with your thoughts. Thanks."
Table 1: Blood test values from Health Fair, 31.10.2010
Consider what your response would be without statistics. Statistics help us understand, clarify, interpret and present sets of data.
We start with some simple but useful descriptive statistics - those which describe, rather than compare, a data set. These first three statistics are measures of the "middle" or measures of central tendency.
The Mean
The mean is a simple statistic to understand and calculate. The mean (occasionally referred to as the arithmetic mean or average) is one of three common measures of the middle or central tendency. The mean is found by adding each of the data points and dividing by the number (n) of points. For example:
In this case, there are 13 data points, of which the sum is 107.4. Dividing by 13, we have 8.3, which is rounded to one decimal place. The mean for the 100 points in Table 1 is 64.55. This is useful information, but there is probably more we wish or need to know about the data set.
The next installment will include interpretations of the mean. See you in two weeks. In the meantime, we look forward to your questions and comments: davidplaut@yahoo.com
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