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Using intervals for reporting continuous data saves space and allows readers to more easily understand patterns in the data. For this reason, g rouped data, based on intervals, is often used in presenting data in the form of tables or graphs. We explain how to do this later in this chapter. Calculation of summary measures, such as the mean (average), however, should always be based on the original raw data. This preserves the original interval or ratio level of measurement. Otherwise, calculation of summary measures from grouped data can reduce the level of measurement from the ratio or ordinal level of measurement, depending on the nature of the variable, to ordinal. Any time original numerical data are reduced to intervals some data are, in effect, thrown away because a less powerful level of measurement is substituted for the original ratio or interval level. As a result, less powerful means of statistical analysis have to be used. Both conditions reduce the strength of the conclusions that can be drawn from the results of the analysis. Reduction is more serious when fewer, broader intervals are used. Therefore, narrower intervals are generally preferred over wider ones, and more intervals over fewer ones. Analyzing single variables Frequencies are simply counts of raw data. By themselves, frequencies have little meaning. A frequency acquires meaning through comparison with other frequencies. The fact that there are 2,346 males at a university, for example, does not mean much by itself. But this frequency has meaning when expressed as a proportion or percentage of male students relative to both male and female students at a university. In the context of the entire student body, the number of males now has meaning. The same frequency can be expressed as ratio of males to females or the reverse. Frequencies also take on meaning when expressed as rates at which something occurs. A rate expresses how often something occurs in relation all the chances that the event could occur. Familiar rates are the birth rate or the unemployment rate. The birth rate says how many women in a certain age range had live births in a year relative to the population of the area. The unemployment rate indicates how many persons looking for work can't find a job. These four forms of univariate analysis are used frequently in research reports. Even if you don't use any of these in your own research, you need to know what each is and how to interpret them. Proportion A proportion is a fraction or part of something expressed as a decimal value between 0 and 1.0. At a university with an equal number of male and female students, the proportion of each would be 0.5. As the number of males increased relative to females, the proportion of males would increase. If the number of females increased relative to the males, the proportion of females would increase. A proportion is found by a simple formula: Proportion = f/N Where f is the frequency of the part of the distribution selected for analysis and N is the total number of cases. In a university with 575 females and 2,456 males, the proportion of females would be: Proportion of females = f/N = 575/575+2,476 = 575/3,051 =.1885 Percentage Proportions are converted to percentages by multiplying the proportion by 100. Percent literally means per 100. Percentages reduce a distribution to a base of 100. The formula for percent is: Percent = f/N(100) For the illustration used previously for calculating a proportion, the percentage of females in the university population is: Percent females = f/N(100) = .1885(100) = 18.85 = 18.8%. You will very likely calculate percentages in any research you do. The following guidelines will help ensure calculation of accurate percentages: |