ClassNotes-Chapter-02

ClassNotes-Chapter-02 - Sven Thommesen 2011 Chapter 2:...

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1 © Sven Thommesen 2011 Chapter 2: Descriptive statistics: graphs and tables [Edited 09/07/10] [Note: some concepts in this chapter depend on concepts introduced in chapter 3.] This chapter discusses different ways of illustrating or representing a given data set by the use of summary tables and graphical devices. Why? Because if you have a large dataset, just staring at the raw data may not be all that enlightening! [Since Microsoft Word doesn‟t draw very good pictures, please look in your textbook for examples of the different graphs.] [Microsoft Excel is capable of generating most of the charts and graphs discussed in this chapter. Your textbook shows how to do it in many cases.] [The OpenOffice free office suite has modules comparable to Word and Excel. Visit http://www.openoffice.org .]
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2 T.1 TABULAR REPRESENTATION OF DATA: QUALITATIVE DATA As mentioned in chapter 1, qualitative data is data where each entity is assigned (placed into) one of a limited number of possible categories, such as male/female, white/black/Hispanic, or brand-of-car-you-drive. The best we can do with such data is to COUNT how many entities in the data set fall into each of the possible categories (the data frequency for that category), then calculate what FRACTION or PERCENTAGE of the total belongs in each category ( relative frequency ). FREQUENCY DISTRIBUTION Let us use as an example the grades given out in a section of BUS-271 in the past. Each entity (that is, each student) was assigned one out of a small number of possible grades: A,B,C,D,F,W. Say that students in the particular class were assigned the following grades: A, B, C, D, F, W, A, B, C, F, W, A, B, C,F, W, A, C, W, A, W, A, W, A, A, A Let us first rearrange the observations so as to group similar grades together. (Since these data are ordinal, there is a natural order in which to list or sort them.) A, A, A, A, A, A, A, A, A, B, B, B, C, C, C, C, D, F, F, F, W, W, W, W, W, W From this, we can make a list of the possible data values (categories) represented in the data set: A, B, C, D, F, W. If we now count how many students received each grade, we have: A 9 B 3 C 4 D 1 F 3 W 6 --- 26 Total number of observations: n = 26
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3 This table is called a “ frequency distribution ”. The number of students who received a given grade is the „frequency‟ for that grade. It should be clear that we can create this kind of frequency distribution for any type of qualitative data, whether nominal or ordinal. For example, in our day-1 survey, the brand of car you drive, or your eye color. (In some cases, the researcher provides the set of possible answers, in other cases nature provides this naturally. But in some cases, especially when we ask human subjects an open-ended question [such as „what is your eye color‟] the set of answers, i.e. the set of categories to be used, must be drawn from the data set itself.) RELATIVE FREQUENCY DISTRIBUTION Adding these all up, we see that we have a total of 26 observations or records in our data set. We can now calculate fractions and percentages: A 9 9/26 = .346 (34.6%) B 3 3/26 = .115 (11.5%) C 4 4/26 = .154 (15.4%) D 1 1/26 = .039 ( 3.9%) F 3 3/26 = .115 (11.5%) W 6 6/26 = .231 (23.1%) Sum = 100.0%
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ClassNotes-Chapter-02 - Sven Thommesen 2011 Chapter 2:...

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