DISCUSSION BOARD 2 1
Variables, Z Scores, Population, and Output
Discussion Board 2
Lynn Evans
School of Business, Liberty University
BUSI820: Quantitative Research Methods
April 2 , 2023
nd
Variables, Z Scores, Population, and Output Assignment 2
Variables, Z Scores, Population, and Output
D2.3.1. If you have categorical, ordered data (such as low income, middle income, high
income) what type of measurement would you have? Why?
A categorical variable is a nominal variable and are often used to represent data that
cannot be easily quantified. Some examples of these types of variables include gender, race, or
even marital status. However, some categorical variables can also be used to represent data that
can be quantified, such as income levels or graphical regions. Morgan et al. (2020) indicates that
“categorical terms sometimes used interchangeably with nominal, but we think nominal is better
because it is possible to have it ordered, discrete categories” (p.50). A categorical variable is also
known as a qualitative variable and represents groupings of some kind while being recorded as
numbers where the numbers represent categories rather than actual amounts.
D2. 3.2 Compare and contract nominal, dichotomous, ordinal, and normal variables. (b) In
social science research, why isn’t it important to distinguish between interval and ratio
variables?
D2.3.2a. Compare and contrast nominal, dichotomous, ordinal, and nominal variables
Analyzing your data may be limited based on the level of measurement of the variable
that is used. A hierarchy of complexity and precision, of the level of measurement, is identified
as low (nominal) to high (normal). Categorical variables are categorized as nominal, ordinal,
dichotomous, or normal. Morgan et al. (2020) identifies that a “nominal variable is the lowest
measurement” (p.50). The nominal variable categories are assigned a number and not used in the
calculations whereas categories may be easy, medium, hard will be assigned 1, 2, or 3
respectively. The ordinal variable, as defined by Morgan et al. (2020), are ordered from high to
low and are mutually exclusive categories and ranks are assigned. For example, college rankings
Variables, Z Scores, Population, and Output Assignment 3
or high school rankings from better to worse would be considered a ordinal variable. Morgan et
al. (2020) continues to elaborate on dichotomous variable that “always have only two levels or
categories. In some cases, they have an implied order, some do not have any categories” (p.50).
These variables do not have an ordered category. For example, age group 0-18 and above 18,
which could be coded as 0 or 1 respectively. Finally, the normal variable are ordered low to high
and have “scores that are approximately distributed” (p.51). These types of variables are
commonly seen in surveys when scoring a customer service agent or cleanliness of a store.
D2 3.2.b. In social science research, why isn’t it important to distinguish between interval
and ratio variables?
The ratio variable is “ordered levels; the different between the levels is equal, and there is
a true zero” while the interval variable is “ordered levels in which the difference between levels,
is equal, but no true zero” (Morgan et al., 2020, p.49). In social science is not important to
distinguish between ratio and interval because the interval data can be used in all the different
types of stats that are available. “SPSS stats terminology supports non-distinction by using the
term scale for both internal and ratio” (Morgan et al, 2020, p.50).
D2 3.3 What percent of the area under the standard normal curve is within one standard
deviation (above or below) the mean? What does this tell you about scores that are more
than one standard deviation away from the mean?
The percentage of area under the standard normal curve is 68 percent within one standard
deviation of the mean (Morgan et al., 2020). If the scores are more than one standard deviation
from the mean, then there are fewer examples at the extreme.
Variables, Z Scores, Population, and Output Assignment 4
D2 3.4 How do z scores relate to the normal curve? (b) How would you interpret a z score
of -3.0? (c) What percentage of scores is between a z of -2 and a z of +2? Why is this
important?
D2 3.4a. How do z scores relate to the normal curve?
Morgan et al. (2020) indicate that the z-score is a numerical representation of the
relationship from the value to the mean in a selected group of values. This is identified by the
number of standard deviations from the mean. Units identified in a standard normal distribution
underneath are identified as the z-score. A z-score of zero indicates that the value quals the mean
score as the standard deviation is x from the mean. Additionally, a z-score of 1.0 indicates that
the value is one unit, one standard deviation, from the mean. Z-scores that are positive indicate a
score above the mean while the negative z-score indicate that the value is below the mean.
D2 3.4b How would you interpret a z score of -3.0?
A z-score of -3.0 indicates that the value is three standard deviations below the mean of
the group and would display to the left in a graphical representation.
D2. 3.4c. What percentage of scores is between a z of -2 and a z of +2? Why is this
important.
The percentage of scores between a z-score of 2 and -2 is 95% whereas -2 is 47.5% and
+2 is 47.5. This is important because the remaining 5% relates to “that ever present probability or
p value of 0.05 needed for statistical significance. Values not falling with two standard deviations
of the mean are seen as relatively rare events” (Morgan et al., 2020, p.62).
Variables, Z Scores, Population, and Output Assignment 5
D2 3.5 Why should you not use frequency polygon if you have nominal data? What would
you use to display nominal data?
A frequency polygon, as identified by Morgan et al. (2020), “is best used with
approximate normal data” and it “connects the points between the categories” but “it can be sued
with ordinal data” (p.56). Because the frequency polygon connects data, the nominal data is not
recommended to be used as the nominal data is defined by numerical categories and has no direct
connection to one another. To display nominal data, graphically, the researcher should use the
Bar Chart. This allows the data to be there are no ordering of the categories or level and the data
is not connected.
Variables, Z Scores, Population, and Output Assignment 6
References
Morgan, G.A., Barrett, K.C., Leech, N.L., & Gloeckner, G.W. (2020) IBM SPSS for Introductory
Statistics: Use and Interpretation. Routledge.
