Discussion 2: Variables, Z Scores, Population and Output
BUSI820
Liberty University
If you have categorical, ordered data (such as low income, middle income, high income)
what type of measurement would you have? Why?
The type of measurement that would be considered as categorical, ordered data is ordinal.
Ordinal typically consists of three or more controlled levels that have a change within the
importance among groups of neighboring levels that are not equivalent. When the sharing of
frequency within scores is not dispersed normally it can be categorized as ordinal. Low income is
more inferior than middle income, the information is not considered as interval or normal due to
the breadth among low-, middle-, and high-income groups that are not equivalent. Although
categorical is often linked to nominal, if the groups considered as controlled the variable should
be analyzed as if it is ordinal (Morgan et al., Although categorical is often linked to nominal, if
the groups are considered as controlled the variable should be analyzed as if it is ordinal (Morgan
et al., 2019).
D2.3.2. (a) Compare and contrast nominal, dichotomous, ordinal, and normal variables. (b)
In social science research, why isn’t it important to distinguish between interval and ratio
variables?
a) Nominal variables are the smallest level of calculation pertaining to numbers that are
delegated for each group, they represent the designation of the group and have no specific
order or value. This level within a variable is considered as controlled, informal, or
equally barring groups. Dichotomous variables typically have two levels which are often
coded in SPSS as 0 or 1. They are primarily implicit variables that can be utilized as self-
governed variables in addition to other variables that are normally allocated. Ordinal
variables are the levels within a variable that are placed and distorted. Greater numbers
indicate that an interval that is rated more advanced within distinct groups are not equal.
It focuses on if the frequency represents each group or value that is allocated into a bell-
shape, normal curve with increased responses in the middle groups and less in the lower
and higher groups. Normal variables have levels that are controlled based on low to high.
The skewness is typically lower than the value of one. Numerous normal variables are
incessant, and if they are not there is the assumption that there is to be a minimum of five
ordered values or levels, and they have an implied and fundamental constant character.
b) In social science research, is not important to determine interval and ratio variables as
they incorporate quantitative calculations. In social science research, it is not important to
determine interval and ratio variables as they incorporate quantitative calculations. Each
variable is tackled the same through the utilization of scale within SPSS. The intervals
and ratio can be exposed to statistical methods that involve the mean, standard deviation,
correlation, and regression evaluation (Morgan et al., 2019).
D2.3.3. What percent of the area under the standard normal curve is within one standard
deviation of (above or below) the mean? What does this tell you about scores that are more
than one standard deviation away from the mean?
“When a study uses a continuous outcome variable, one needs an estimate of the
underlying standard deviation (σ) of the observational error component, in order to interpret the
results” (Walter et al. 2022, p.1, para.1). Normal distribution obeys a bell-shaped normal curve
and is built upon the standard deviation of the mean which is approximately 68%. The area of
percent within the traditional normal curve is within one standard deviation which is about 34%
above and 34 % below, and the actual percentage is 34.13%. About 32% of the scores fall within
several standard deviations apart from the mean (Morgan et al., 2019).
D2.3.4. (a) 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?
a) Z scores are identified as the normal distribution that reflects the amount of standard
deviations. It shows how the curve is to the right of the z-score value. It serves as a
form of distribution that has a mean of zero and a standard deviation of one. Z-scores
resemble percentiles within the normal curve, which allows for the distinguishing of
the number of scores above or below a particular z-score. Their correlation to the
normal curve signifies the amount of standard deviations a score is from the mean.
b) A z-score of -3.0 refers to the score of three standard deviations which falls
underneath the mean. The score is substantially less than the mean value, which
means that it is distant from the mean.
c) The percentage of scores between a z of –2 and a z of +2, are estimated to be about
95% of the scores that fall within its span. This indicates that 95% of the scores are in
two standard deviations below or above the mean (Morgan et al., 2019).
D2.3.5. Why should you not use a frequency polygon if you have nominal data? What
would be better to use to display nominal data?
Frequency polygons were created to be specifically utilized with normal distribution or
scale data due to its representation of the information to constantly expand in value throughout a
graph. Methods that are more effective that can be used to show nominal data are the bar chart or
frequency distribution (Morgan et al., 2019).
References
Morgan, G.A., Barrett, K.C., Leech, N.L., & Gloeckner, G.W. (2019). IBM SPSS for Introductory
Statistics: Use and Interpretation, Sixth Edition (6th ed.).
Walter, S. D., Rychtář, J., Taylor, D., & Balakrishnan, N. (2022). Estimation of standard
deviations and inverse‐variance weights from an observed range.Statistics in
Medicine,41(2), 242-257.Ihttps://doi.org/10.1002/sim.9233
