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I ve already talked about quantitative and qualitative measurement, and, not surprisingly, these two approaches to security metrics produce different types of data stemming from the observations being made Just like the research methods used to produce the data, neither type of data is intrinsically better or preferable to the other Deciding which data is best depends on your understanding the questions that the data is supposed to help you answer Understanding more about these data types can help you make decisions regarding which might better support your security metrics
Quantitative Data
Quantitative data is expressed with numbers and analyzed statistically Numerical data can reflect things that you can actually count, such as the number of installations of a particular OS in your network environment or the number of reconnaissance scans against your network perimeter in the past month Numbers can also reflect changes in state along some scale, such as the temperature in your data center or the severity rating of an identified vulnerability Scientific measurement identifies four major types or scales of data: nominal, ordinal, interval, and ratio
3:
Understanding Data
Nominal Data The nominal scale is the simplest, and sometimes the most misleading, scale for quantitative data Nominal data is not really about numbers at all, but has to do with categories Numbers are often used as labels for the categories involved, but this is not required For example, say you are identifying the types of OS you have in your environment for a security review You might assign OS type according to the nominal scale in Table 3-1 The choice of numbers to represent OS types is arbitrary You could have just as easily used letters (A, B, C ) or abbreviations of the OS name as your data, but numbers are often the first choice for nominal data sets In nominal data sets, the fact that the data is represented as a number does not convey any meaning regarding the target of observation other than the category to which it is assigned It does not measure anything intrinsic But you can count the instances of categorical data, how many of Type 1, Type 2, and so on, are observed For analytical purposes, this means that you can use nominal data to build frequency distributions and perform cross-tabulation if you have more than one set of nominal data It is not appropriate to use statistical techniques such as the mean (commonly called the average, although the two are different), or the median (the middle value) on nominal data directly (how do you average three separate categories ), although mode (the most frequent value) works okay I will cover these analytical techniques in detail in later chapters For now, remember that the numbers associated with nominal data are used to divide your observations into different buckets they do not indicate anything particularly quantitative about the things that go into those buckets Ordinal Data Ordinal data uses numbers to describe a more complex relationship between the targets of observation than is found in nominal data Where nominal metrics describe whether or not something falls into the same category as something else, ordinal data involves the rank order of those observations A simple example is the order in which contestants finished in a race (first, second, third, and so on) A security example includes the risk rankings obtained in a risk matrix analysis (for instance, a 1 3 rating of
Category Value 1 2 3 4 5 6
Operating System Windows XP Windows Vista HP-UX Solaris Linux Mac OS X
Table 3-1 Nominal Categories for OS Type
IT Security Metrics
risk severity and likelihood scores reflecting low, medium, and high) Ordinal data does not provide any information regarding the amount of difference between the rankings, such as how much faster the winner of the race was compared to the runner up By the same token, a security risk ranking of 10 does not mean that the risk is twice that of something ranked as a 5 To this extent, ordinal data remains somewhat categorical, but the buckets are now arranged in numerical order in a way that means something in the context of the scale Analysis techniques for ordinal data are much like those of nominal data, involving counts of which observations fall into which ranks and the distribution of the data Although people often do it, it is still inappropriate to apply means or averages to ordinal data, because the ordinal scale does not give any insight into the differences between ordinal rankings (Think of a race that results in a close finish for first and second place, followed by a distant third) The mode (the value most often observed) still works fine with ordinal data, and the median (the middle value observed) can be applied as well Ordinal data may also be compared against other nominal or ordinal data in tabular fashion, as in the example risk scoring summary in Table 3-2, which shows ratings observed in a survey of ten security administrators Analysis shows the most frequent risk scores given to each data type Interval Data Where ordinal data describes a ranking relationship, but with no real measure of the distance between individual rankings, interval data involves increases in rank in which the distance between the ranks is measured in some sort of standard unit Thus the amount of difference between ranks means something Measures of temperature on the Celsius and Fahrenheit scales are good examples of interval data, because the difference between 10 degrees and 20 degrees is the same as the distance between 0 degrees and 10 degrees on each scale (but not necessarily between the scales) Another example would be the Common Vulnerability Scoring System (CVSS) scores used to measure the severity of security vulnerabilities Unlike ordinal severity scores that reflect low/medium/high rankings, CVSS scores range from 0 to 10 with the assumption that the difference between 3 and 4 on the scoring scale is mathematically equivalent to the difference between 5 and 6 The reason is pretty simple If standard
Risk of Data Loss or Corruption (Summary of Scores) Data Type User data Financial data Customer data Intellectual property 1 Low 3 1 2 5 2 Medium 5 4 7 3 3 High 2 5 1 2 Mode 2 Medium 3 High 2 Medium 1 Low
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