CHAPTER 2

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CHAPTER 2 SOLUTIONS TO PROBLEMS

- Interval/Ratio level measurement - in the social sciences, it is at times difficult to unequivocally designate a variable as either interval or ratio. Both answers seem reasonable. It is also a quantitative variable.
- Interval/Ratio. It is a quantitative variable.
- Interval/Ratio. It is a quantitative variable.
- Nominal - unless the offenses are arranged in order of severity in which case you could reasonably argue that it was ordinal. Qualitative.
- Nominal. Qualitative.
- Interval/Ratio. Quantitative.
- Ordinal if the grade was a letter grade (e.g. A, B, C, etc.), because in this instance we would only have order (An A is a better grade than a B, etc.) but it would be classified as an Interval/Ratio level variable if it were in the form of a grade point average. Both would be quantitative variables.
The values of ordinal level variables are not only categorical in nature, but the categories also have some type of relationship to each other. So in addition to the quality of a nominal level variable, values of ordinal level variables have the added distinction of meaning and order. That is, there is some inherent and logical order to the categories which represent the values of a variable measured at the ordinal level.

In addition to being able to rank order values in terms of its relationship to another value, interval level variables allows us to quantify the exact numeric relationship between values. To be classified as an interval level variable, the categories of the variable must have an equal and known quantity. The zero point on an interval scale, however, is arbitrary.

Ratio level variables have all of the qualities of interval level variables, but in addition, the calibrations which allow us to measure the numerical difference between values are based on a natural or true zero point. Although many variab les we use in criminological research do have a true zero point (e.g. prior felonies, sentence length received, a person's age, income, etc.) this level of measurement is perhaps more pertinent to the physical sciences. For our purposes here, then, we wil l not split hairs in trying to distinguish between interval and ordinal levels of measurement.
In this study, you would be trying to predict future drunk driving behavior and you believe that previous arrests would have some impact on this behavior. Arrest is therefore the independent variable and future drunk driving behavior is the dependent variable.
In this case, you are trying to predict levels of fear. You believe gender has some impact on an individual's perception of this fear. Therefore, gender would be used as the independent variable used to predict levels of fear which is t he dependent variable.
To compute age-specific rates of anything, you must utilize both age-specific numerators and denominators. In this case, you would use the number of violent victimizations committed against 14-18 years olds as the numerator and the tota l number of 14-18 years in the population as the denominator. In addition, you would usually multiply this ratio by some base number like 1,000 or 100,000 to ascertain a rate of victimization per 1K or 100K 14-18 year olds.
The most elementary way of presenting information is to present the counts or frequencies of the phenomena you are interested in; this is usually referred to as the frequency count. These simple counts would be fine if we were not interested in making comparisons across counts. In most cases, however, we are interested in such comparisons. To more accurately make comparisons, it is important to control for the size of the populations you are comparing. To do this, it is necessary to calculate rates of some occurrence. Rates are derived by dividing the observed number of an occurrence or phenomenon by the total number that could have been observed within the population of interest. One example which illuminates the importance of ra tes over counts is when you are making comparisons across different demographic categories such as race, age, geographical location, etc. For example, when you examine the number of violent victimizations occurring for blacks and whites in the U.S., it ma y appear from the simple counts that whites are more likely to become the victims of violence compared to blacks. When the population is controlled, however, the reverse is found. Therefore, the original conclusion you would reach when using counts as the comparison is actually false. The counts indicate that there are more victimizations against whites, but this is because there are more whites in the population to become victimized. When this number of victimizations is standardized and based on the tot al number of all potential white victims, the rate of victimization is actually lower than similar rates of victimization against blacks.

 
			f		Proportion	Percent
_________________________________________________________________

Less than $10		16		.029		2.9%
$10-$49			39		.072		7.2
$50-$99			48		.089		8.9
$100-$249	        86		.159		15.9
$250-$999		102		.188		18.8
$1,000 or more		251		.463		46.3
________________________________________________________________
		N=542	                1.0		100%

The units of analysis are juvenile males offenders. The researchers thought sexual and physical abuse in childhood would be related to the type of offense committed by juvenile offenders. The presence of sexual or physical abuse in chil dhood histories would therefore be the independent variable and type of offense committed would be the dependent variable.
The units of analysis would be the 50 states of the U.S. We would select unemployment rates for the 50 states as the independent variable and select types of crime rates (e.g. violent, property, etc.) within the states as the dependent variable. This scenario would presume state levels of unemployment to affect state levels of crime.
This is a bit tricky. What we would ultimately have is aggregate data on police response times for several police departments. Even though the data originally came from individual incidents of crime, we are only using this data to make comparisons across jurisdictions. Jurisdictions are therefore the units of analysis.

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