12 - Explain and give an example
for each of the following types of variables: (a) equal-interval, (b)
rank-order, (c) nominal, (d) ratio scale, (e) continuous.
a)
Equal-interval is a type of variable
that is quantitative, like for example the temperature in Fahrenheit degrees.
It does not have an absolute zero, like 0 degrees does not mean “no
temperature”.
b)
Rank-order is a qualitative variable
that can be ranked, like for example the levels of authority in a company.
c)
Nominal is a variable that represents
categories, like for example to colors of the cars in a parking lot.
d)
Ratio scale this is a quantitative
variable, and we can perform all mathematical operations with the values. Also,
it has an absolute zero. For example, the age of the students in a classroom.
e)
Continuous represents the variables with
all possible values within a given range, like for example someone’s weight,
which doesn’t have to be an absolute number, it can be 101,5.
15 - Following are the speeds of 40
cars clocked by radar on a particular road in a 35-mph zone on a particular afternoon:
|
30, 36, 42, 36, 30, 52, 36, 34,
36, 33, 30, 32, 35, 32, 37, 34, 36, 31, 35, 20, 24, 46, 23, 31, 32, 45, 34,
37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40
|
Make (a) a frequency table and (b) a
histogram. Then (c) describe the general shape of the distribution.
a)
|
15-19
|
1
|
|
20-24
|
3
|
|
25-29
|
2
|
|
30-34
|
15
|
|
35-39
|
11
|
|
40-44
|
4
|
|
45-49
|
2
|
|
50-54
|
2
|
b)
c) This distribution has as general
shape a bell shape.
19
- Give an example of something having these distribution shapes: (a) bimodal,
(b) approximately rectangular, and (c) positively skewed. Do not use an example
given in this book or in class.
a)
Bimodal: a graph showing the amount of
drinks man and women consume. If the researchers do not separate the two
genders, there will be two spikes in the graph.
b)
Approximately rectangular: all events
have the same chance of happening, like a coin toss.
c)
Positively skewed: a graph showing how
people make more money as they get older.
20 - Find an example in a newspaper
or magazine of a graph that misleads by failing to use equal interval sizes or
by exaggerating proportions.
This graph is misleading because
when we analyze the sale numbers presented on the full-price sales, The Times
had more sales with a margin of less than 10%, unlike what the picture shows
being almost the double.
21) Nownes
(2000) surveyed representatives of interest groups who were registered as
lobbyists of three U.S. state legislatures. One of the issues he studied was
whether interest groups are in competition with each other. Table 1–10 shows
the results for one such question. (a) Using this table as an example, explain
the idea of a frequency table to a person who has never had a course in
statistics. (b) Explain the general meaning of the pattern of results.
a) A simple way to explain the
meaning of frequency is the number of times an event has happened, or how
frequently. A frequency table is very useful because it all allows us to have a
visual demonstration of the repetition of those events.
b) This example shows us that 118
people answered that there is no competition between groups; 342 people
answered with some competition; 131 answered with a lot of competition. The
pattern of results is once again that repetition in events, or in this case,
answers.
22) Mouradian
(2001) surveyed college students selected from a screening session to include
two groups: (a) “Perpetrators”—students who reported at least one violent act
(hitting, shoving, etc.) against their partner in their current or most recent
relationship—and (b) “Comparisons”—students who did not report any such uses of
violence in any of their last three relationships. At the actual testing
session, the students first read a description of an aggressive behavior such
as, “Throw something at his or her partner” or “Say something to upset his or
her partner.” They then were asked to write “as many examples of circumstances
of situations as [they could] in which a person might engage in behaviors or
acts of this sort with or towards their significant other.” Table 1–11 shows
the “Dominant Category of Explanation” (the category a participant used most)
for females and males, broken down by comparisons and perpetrators. (a) Using
this table as an example, explain the idea of a frequency table to a person who
has never had a course in statistics. (b) Explain the general meaning of the
pattern of results.
a) A simple way to explain the
meaning of frequency is the number of times an event has happened, or how
frequently. A frequency table is very useful because it all allows us to have a
visual demonstration of the repetition of those events.
b) This example shows the difference
between men and women and the occurrence of violent acts in their
relationships. The table of frequency allows us to see the pattern of aggressive
reactions people have had in their relationships.
References
Aron,
A., Aron, E. N., & Coups, E. J. (2009). Statistics for psychology (5th ed.). Upper Saddle
River, NJ: Pearson/Prentice Hall.
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