Page 54 - Intermediate Statistics for Dummies

06_045206 ch02.qxd 2/1/07 9:42 AM Page 33
Chapter 2: Sorting through Statistical Techniques
The next step is to find a means to relate these numbers to each other in an
easy way. You can do this by using what is called a relative frequency. The rel-
ative frequency is the percentage of data that falls into a specific category of a
qualitative variable. You can find a category’s relative frequency by dividing
the frequency by the sample total (500, using this example) and multiplying
180
by 100. In this case, you have
=
*
500
320
=
. 0 64 100 64=
*
500
You can also express the relative frequency as a proportion in each group by
leaving the result in decimal form and not multiplying by 100. This statistic
is called the sample proportion. If you continue with the same example, the
sample proportion of males is 0.36, and the sample proportion of females
is 0.64.
You mainly summarize qualitative variables by using two statistics — the
number in each category (frequency) and the percentage (relative frequency)
in each category. percent females. . 0 36 100 36= percent males and 33
Statistics for Qualitative Variables
The types of statistics done on qualitative data may seem to be limited; how-
ever, the wide variety of analyses you can perform using frequencies and rela-
tive frequencies offers answers to an extensive range of possible questions
you may want to explore.
In this section, you see that the proportion in each group is the number-one
statistic for summarizing qualitative data. Beyond that, you see how you can
use proportions to estimate, compare, and look for relationships between the
groups that compose the qualitative data.
Comparing proportions
Researchers, the media, and even everyday folk like you and me love to com-
pare groups (whether you like to admit it or not). For example, what propor-
tion of Democrats support oil drilling in Alaska, compared to Republicans?
What percentage of women watch college football versus men? What propor-
tion of readers of Intermediate Statistics For Dummies pass their stats exams
with flying colors, compared to nonreaders? To answer these questions, you
need to compare the sample proportions using a hypothesis test for two pro-
portions (see Chapter 3 or your intro stat textbook).