Be able to analyze statistics, which can be used to support or undercut almost any argument.
— Marilyn vos Savant
INTRODUCTION
There are only a few instances when anyone has all the information needed to make a decision. The choices made by an eye care practitioner are no different. However, the lack of data does not mean that informed decisions cannot be reached during the process. The proper use of statistics can provide the necessary support in these uncertain times. Statistics is the collection and use of data to aid in the selection of the best option. The successful provider understands how and when to incorporate this science to excel in business.
The application of statistics can be used in all aspects of business. The practitioner encounters it numerous times throughout the day. Obvious examples include areas where numbers are frequently used such as in finance with return on investments and negotiations with reservation points. The extent of statistics does not end there. In fact, statistical theories and methods are also evident in human resources with employee reviews and marketing with website analytics. It is in these unexpected areas that the incorporation of statistics creates a strategic advantage to the user over the competition.
This chapter takes a logical approach to the use of statistics in the life of eye care practitioners. The first section lays the basic groundwork to be used throughout the rest of the discussion. This leads to sections where various real-life situations are presented along with different types of statistics that can be applied to make the best decisions. The aim is to orient doctors with sound statistical theories to employ in day-to-day activities where these decisions can significantly impact the practice.
WHAT IS STATISTICS?
Solid decision making in any venture requires the ability to effectively take information that is gathered and use it in a strategic manner to make choices. This premise assumes that the underlying facts are accurate and correctly represent the desired data to be analyzed. The entire process falls apart without reliable information. Simply stated, garbage in equals garbage out.
However, it should not be assumed that all information can be lumped into either being good or bad. The reality is that most information is useful if its parameters are understood and applied properly into a given situation.1 The best analogy is that sometimes a cut just needs a bandage, but in other instances, it is best to use sutures. The ability to gather and understand data for applications in decision-making situations can make the difference between success and failure.
The pressing issue becomes why we even need to go through this exercise to obtain data to run statistics in the first place. All the necessary information can be obtained and an intelligent decision can be made if enough time and effort is used. Although in theory it makes sense to wait until a complete set of data is available, the reality is that this either is not possible to do or would be so laborious to deem it cost ineffective. The value of statistics becomes evident when given these constraints on data collection. Statistics allows the use of collected information from an appropriate sample from a larger group to make educated decisions about the entire targeted population.
The takeaway is that statistics, if understood and used properly, can support or detract from a choice when confronted with options in a given situation. Furthermore, a clear understanding of the different statistical calculations and their applications help the decision makers remain flexible to the various situations that might be presented. This thoughtful analysis allows the best use of their resources (bandage or sutures) to address their needs.
STATISTICS IN EYE CARE
The value of statistics in eye care is illustrated by the fundamental role that numbers play in the decision-making process for any organization. Accurately collecting data and thoughtfully generating key numbers differentiates a company from its competitors. The former is a time-tested organization that continually improves by making solid choices based on facts. The latter is an underachieving company that learns from making costly mistakes first by relying on emotions. Successful eye care practitioners need to demonstrate the following capabilities in statistics: understanding basic statistics, using parametric testing, identifying non-parametric testing, and applying regression analysis.
Understanding Basic Statistics
Importance
Understanding numbers and their applications through statistical analysis is a required skill set for any successful person. In particular, the use of statistics allows individuals to rely on what is truly happening in a situation instead of being influenced by emotions. The capability to separate factual information from those affected by feelings allows practitioners and their businesses to make less mistakes. It avoids knee-jerk reactions in challenging situations while fostering a more logical and calmer approach to problem solving.
The best companies utilize these objective metrics to be more efficient and effective throughout their organizations. A strong knowledge in this discipline also enables a thoughtful critique of how numbers are derived. This prevents the problems from trusting misleading information and identifies areas of limitations that need to be considered when assessing situations.
Keywords
Statistics: The study of the collection and analysis of data
Descriptive statistics: A type of statistics that describes the collected data set used for analysis
Discrete: A data point that has a limited number of possible values
Continuous: A data point that has an infinite number of possible values
Graphical method: The use of graphs to represent data
Numerical method: The use of numbers to represent data
Mean: A method to calculate an average of a data set by adding the values of the data points and dividing by the number of data points
Median: A method to calculate an average of a data set by sequencing the data points in numerical order and then picking the number in the middle of the group
Mode: A method to calculate an average of a data set by selecting the value that appears the most
Range: A description of a data set that is defined by its extreme values
Standard deviation: A description of a data set that expresses the degree to which there is dispersion of the set’s values
Variance: A description of a data set that is the mean of the squared distances for each point to the population’s mean
Distribution: The way in which the data points are spread out
Normal distribution: A traditional or bell spread of a distribution
Skew distribution: A loop-sidedness of a distribution
Percentile: A measure in statistics in which a given percentage of data points fall below or above a certain value
Probability: A measurement in statistics to describe the odds of an event occurring
Combinations: The number of ways objects from a set can be grouped together regardless of the order
Permutations: The number of ways objects from a set can be grouped together where the order does matter
Applications
Statistics are utilized in a wide range of medical and business applications. The type of statistics selected in a given situation will be affected by what information is available. The validity and subsequent usefulness of the resulting calculations depends on the accuracy of the data points measured and collected. The successful eye care practitioner understands these fundamental properties of statistics and strategically applies them in the right conditions.
The effective use of statistics begins with a characterization of the data set that is obtained. This is known as descriptive statistics. The data points can be discrete or continuous, and expressed in a graphical and numerical methods. Examples of these would be to either plot out the intraocular pressure (IOP) readings from one patient on a graph or write them out, respectively.
A useful calculation to describe the data set is the average for the group of values. This meaning of average, however, can take on several meanings. It is important to understanding what type of calculation was used to determine that number. This is especially true if this information will be used to make a decision because it can change the choice that is selected. Consider the following list of IOP readings in mm of mercury placed in ascending order from a patient after he is started on a prosta-glandin analogue: 12, 12, 12, 13, 15, 15, 16, 16, and 17. The mean is 14, median is 15, and mode is 12. Each of these can be stated as the average but can characterize the data set in a different manner. The consequence is that there can be a misinterpretation of what is meant by average. This can lead to a suboptimal decision.
Additional statistics about this data set could provide the practitioner more information that can be valuable in certain settings. This includes the range, which is 12 to 17, the standard deviation is 1.9, and the variance is 3.9. These calculations provide sophistication to the average. The range provides the minimum and maximum values with which the IOP has been measured. The standard deviation gives an idea of how deviated each measurement is from the mean, or in other ways, how close they are to the mean. The variance provides an understanding of how much variability is in the measurements.
A smaller standard deviation translates to most measurements being near the mean, and a smaller variance expresses less variability between numbers. In this situation, it means the IOPs are close to the mean and do not vary much. A larger standard deviation and variance represents a large spread of numbers away from the mean and different from one another. This is useful information for the provider to know beyond just the mean IOP.
Another approach to interpret this information is to view its distribution. In a normal distribution, the values follow a traditional bell curve with most numbers near the center and tapering off in both directions. Sometimes these numbers do not follow such a balanced distribution and can appeared to have a skew distribution (Figure 11-1). This influences the mean, median, and mode. A different view of this information is to examine the numbers by percentile. This application provides the practitioner an idea of which IOP values are grouped together when the numbers are broken up into percentage groups. For example, the top 25% had IOPs of 16 to 17. The bottom 50% had values of 12 to 15.
Figure 11-1. Visual representation of the different types of averages.
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