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Chapter 2

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Sociology 2205A/B
William Marshall

Statistics – Chapter 2 2.1 – Percentages and Proportions - percentages and properties supply a frame of reference for reporting research results in the sense that they standardize the raw data: percentages to the base 100 and proportions to the base 1.00 - proportions: f / n - percentage: f/n x 100 - f = frequency, or the number of cases in any category - n = the number of cases in all categories Figure 2.1 - when working with a small number of cases (like fewer than 20), report the actual frequencies rather than the percent - percentages can change drastically with relatively minor changes in the data - always report the number of observations along with proportions and percentages - this permits the reader to judge the adequacy of the sample size and helps to prevent the researcher from lying with statistics - you should be extremely suspicious of reports that fail to state the number of cases that were tested 2.2 – Ratios and Rates - they provide some additional ways of summarizing results simple and clearly - ratios are especially useful for comparing categories of a variable in terms of relative frequency f˅1/f˅2 - f˅1 = the number of cases in the first category - f˅2 = the number of cases in the second category - example on 37 - ratios tell us exactly how much one category outnumbers the other - ratios are often multiplied by some power of 10 to eliminate decimal points (5.32 = 532) - rates are the number of actual occurrences of some phenomenon divided by the number of possible occurrences per some unit of time - rates are usually multiplied by some power of 10 to eliminate decimal points - the crude death rate for a population is defined as the number of deaths in that population (actual occurrences) divided by the number of people in the population (possible occurrences) per year  this quantity is then multiplied by 1,000 - page 39, formula 2.3 – Frequency Distributions Introduction - frequency distribution is a table that summarizes the distribution of a variable by reporting the number of cases contained in each category of the variable  very helpful and commonly used way of organizing and working with data - table 2.4 - the categories of the frequency distribution must be exhaustive and mutually exclusive 2.4 – Frequency Distributions for Variables Measured At The Nominal and Ordinal Levels - for the nominal level variables, construction of the frequency distribution is typically very straightforward - for each category of the variable being displayed, the occurrences are counted and the subtotals, along with the total number of cases (n) are
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