MATH 105 WAN Directed Reading 5

Question 1

In the first two paragraphs of Understanding Types of Variables, the author points out that information about types of variables affects your choice of _________________. The type of calculations that make sense depend on variable type. With some variables it only makes sense for one case (or individual or subject) to have one response while with other variables multiple responses per case make sense. Even the choice of tools (table/graphs) for
_____________________________ is affected by the variable and number of responses.

Answer 1

Comparisons/Presenting Numbers

Question 2

____________variables take on values that take on negative, zero, and positive values. They can be compared using the mathematical operation of _______________________ but cannot be compared using __________________.
Summarize the temperature example, indicating the comparison that is and is not appropriate.

Answer 2

Interval/Subtraction/Division

Question 3

_______________ variables can be compared using _______________
______ and ____________________ because:

Summarize the distance example showing that both comparisons are appropriate.

Answer 3

Ratio/Subtraction/Division
A value of zero can be interpreted as the lowest possible value
Ratio variables can be interpreted two ways; if A is 2 miles from B but C is 4 miles from B, C is 2 miles farther than, or twice as far as, A

Question 4

Categorical variables are of two types. ____________ variables are those where the categories have order. The three examples provided for this type of variable are:

____________ variables are those where the categories have no inherent order, such as:

Answer 4

Ordinal (Ordered)
Letter grades, Income grouped into ranges of several thousand dollars (units must be specified), Likert-type items
Nominal (Named)
Gender, Race, Religion

Question 5

Summarize the paragraph on regrouping continuous/quantitative variables into categorical variables. Use the age example in your summary.

Answer 5

Categorical variables of continuous variables, like grouping age into 5 or 10 year age groups, can simplify information, or indicate whether values reach a cutoff like retirement age

Question 6

When each case/individual can have only one valid value for a categorical variable, then every case/ individual should fall into: _____________________________________________
__________.
Mutually exclusive categories are ________________________.
Exhaustive categories _________________________________________
___________________.
Explain why the categories “under 18 years”, “18‐64” and “65 and older” are mutually exclusive and exhaustive to someone that does not understand those terms.

Answer 6

One group/Nonoverlapping/Encompassing all possible responses
These categories are mutually exclusive, because someone can only be one age at a given time, and exhaustive, because everyone has an age in one of these categories

Question 7

Discuss the Census Bureau problems (and their solutions) that were finally addressed in 2000.

Answer 7

There were questions on what race you were, but some people considered themselves biracial, so the answers weren’t mutually exclusive until multi-race categories were implemented. There were also questions that treated hispanic race and hispanic origin as different characteristics, so for people who believed they were the same, the questions weren’t exhaustive

Question 8

What are some ways than “other” categories are used?

Sometimes the “other” category misses out important information. What can be done in the data collection process to avoid this problem?

Answer 8

To allow for answers researchers didn’t anticipate, or to allow researchers to later combine uncommon responses instead of creating separate categories for reasons mentioned by only a small share of respondents.
Allow respondents to specify what “other” means in their case

Question 9

In the health insurance example, a “family” is a case/individual. Summarize this example to illustrate how a variable might have no answer, only one answer or multiple answers depending on the situation of any specific case/individual.

In situations where answers can
vary from none to many, the categories are not ___________________ or
_________________________. In the situation where many individuals had multiple responses, when you add up all the responses, they can _______________ the numbers of case/individuals. If none of the responses apply for some individuals, it is possible that the number of responses could be __________________ the number cases/individuals.

Answer 9

A family can have the same health insurance for everyone, different health insurance for different people, or no health insurance at all, depending on the family’s situation.

Mutually Exclusive/Exhaustive/Exceed/Less Than

Question 10

Self‐contained Tables (as well as charts/graphs) are those that are labeled so the audience can:

Using the title, row and column headings and notes, the audience should be able to discern (list all):

Answer 10

Understand the information without reference to the text

The purpose of the table, the context of the data (the W’s), the location of specific variables within the table, units of measurement or categories for every number in the table, data sources, definitions or pertinent terms and abbreviations

Question 11

The title of each table (chart/graph) should convey:

Answer 11

The specific topics or questions addressed in that table

Question 12

If there are multiple tables/charts/graphs, the individualized titles should:

Answer 12

Differentiate the titles from one another and to convey where each fits in the overall scheme of your analysis

Question 13

Summarize the information in each of the following paragraphs:

a) Topic
b) Context
c) Units

Answer 13

Include the major components of the relationships illustrated in that table, and use summary phrases or name broad conceptual categories

Specify the context of the data by listing the W’s in the table title; where and when the data was collected, and the restrictions on who is included in the data. Name institution or name of specific study if necessary

State the units of measurement, level of aggregation, and system of measurement for every variable in the table. Generalize units for the table, and if the same units apply to most numbers in the table, specify in the title, or the column or row headings if there’s not enough space

Question 14

Copy the “best” title, then identify the part of that title that indicates the topic, then the parts that give context.

Answer 14

Means and Standard Deviations for Soil Components, 100 Study Sites, Smith County, 1990
Topic: Means and standard deviations
Context: 100 study sites, Smith County, 1990

Question 15

If units of measurement differ across rows/columns, mention them in the labels. Different variables often have different units. COMPLETE: Do not assume that the units of measurement will be self‐evident once the concepts are named:

Answer 15

Without labels, readers might erroneously presume that age was measured in months or years, or weight or length reported in British rather than metric units

Question 16

Summarize the paragraph on abbreviations, acronyms, and codes.

Answer 16

Minimize use of abbreviations or acronyms in headings, and don’t use “alphabet soup” variable names or numeric codes-your audience won’t understand the variable names and they don’t need to know the numeric codes

Question 17

Summarize the problems of the table in the poor example and the strengths of the better example. (Page 126)

Answer 17

The acronyms don’t convey the meaning of the variable in the poor example, but the labels clearly identify the concepts in each row

Question 18

If the wording of the question is critical for real understanding of a variable (the concept is too complex to be fully summarized with a few words), what should be done?

Answer 18

Refer them to an appendix that contains the pertinent part of the original data collection instrument

Question 19

What are the 4 bullets summarizing the anatomy of a chart/graph?

Answer 19

Displaying sample composition in terms of the key variables in the analysis

Portraying bivariate or three-way associations among variables

Facilitating visual hypothesis-testing with the addition of confidence intervals around point estimates

Showing the sensitivity of results to alternative assumptions

Question 20

Summarize the information in each of the following paragraphs:

a) Chart Titles
b) Axis Titles and Axis labels
c) Legends
d) Data Labels

Answer 20

Specify the W’s in each chart title and use the title to differentiate the topic of each chart from other charts and tables in the same document

Give each axis a title to identify its contents and include labels (short phrases) for categories or values along each axis (include 5 or 10 of these)

Use legends to identify the series or categories of variables not labeled elsewhere in the chart

Use data labels sparingly, only to complement the general depiction of the chart

Question 21

Summarize the details on the section on pie charts

Answer 21

Use pie charts to display how parts add up to the whole; they can only be used for one single-response variable per chart with a mutually exclusive value. Don’t use pie charts to compare averages or rates across groups or time periods, to contrast measures of quantitative comparison, to present multiple-response variables, and avoid skinny slices