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1. Identify the proper scale for each of the following measures: LOC McCabe s cyclomatic number Average depth of nesting Maximum depth of nesting 2. Show that the temperature scales of Celsius and Fahrenheit are an interval scale using the Celsius temperatures of 20, 30, and 40 degrees. 3. Show that McCabe s cyclomatic number satis es the representational theory of measurement. 4. Show that McCabe s cyclomatic number is an interval scale measure. 5. Calculate McCabe s cyclomatic number on the following source code. Draw a control ow graph. Label the regions with Roman numerals. read x,y,z; type = scalene ; if (x == y or x == z or y == z) type = isosceles ; if (x == y and x == z) type = equilateral ; if (x >= y+z or y >= x+z or z >= x+y) type = not a triangle ; if (x <= 0 or y <= 0 or| z <= 0) type = bad inputs ; print type;
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1. Explain why the height example satis es the criteria for valid metrics. Criteria 1: Di erent people can be di erent heights. Criteria 2: Any two people that we feel are related in height, their numerical heights would agree. Criteria 3: Each additional height on a person matches the increase in numerical height. Criteria 4: Di erent people can be the same height. 2. A study of grade school children found a high correlation between shoe size and reading ability. Does this mean that shoe size is a good measure of intelligence No, shoe size correlates well with age. Age correlates well with reading ability. Neither would be a good measure, since neither would satisfy the representation condition. 3. Explain why is money a ratio scale measure and not just an interval scale. Money has a well-understood notion of zero. In all monetary systems, there is a zero and it is equivalent to zero in all other systems. The intervals are xed. Thus, if you have twice as much in U.S. dollars as I do, it will still be twice as much if we convert both our monies into British pounds (assuming no conversion penalties and using the same exchange rate). 4. Explain why GPA is not sound by measurement theory. For grade points to be averaged, then grade points must be an interval scale. This implies that the di erence between values is comparable. That is, the di erence between an A and a B is the same as the di erence between a D and an F. Normally, this is not even considered when allocating grades. 5. Why is complexity not readily measurable Complexity is not well de ned. There are many aspects to complexity, and each person may have a slightly di erent interpretation of what is complex. In fact, complexity could be considered the interaction between a person and the code. 6. What is the advantage of having a partial order on the empirical relation system The empirical relation system must have an accepted relation. It is often easier to nd a partial order that is well accepted, whereas nding agreement on all cases might be di cult. 7. Why is the number of decisions plus 1 an important method for calculating McCabe s cyclomatic number It would be very time-consuming to have to construct the control ow graph for large programs. 8. Why is monotonicity an important characteristic of a size or e ort metric such as Halstead s e ort metric If adding more code can cause the value of the e ort metric to decrease, then the metric s behavior is not understandable. It may also mean that the metric can be manipulated.
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