The student must then post 1 reply to another student’s post. The reply must summarize the student’s findings and indicate areas of agreement, disagreement, and improvement. It must be supported with Original Papers

The student must then post 1 reply to another student’s post. The reply must summarize thestudent’s findings and indicate areas of agreement, disagreement, and improvement. It must besupported with scholarly citations in the latest APA format and corresponding list of references.The minimum word count for Integrating Faith and Learning discussion reply is 250 words. 

Quantitative Analysis: Variables, Z Scores, Population, and Output 

D2.3.1 Type of Measurement 

Categorical, ordered data such as “low income, middle income, high income” is considered an ordinal level of measurement. Ordinal data allow researchers to rank values in order but do not assume equal distances between categories (Morgan et al., 2019). For example, the gap between “low” and “middle” income may not equal the gap between “middle” and “high” income, yet the order is meaningful. This distinction matters because using the wrong level of measurement in analysis may produce misleading results. 

D2.3.2 Variable Comparisons 

D2.3.2.a Nominal, Dichotomous, Ordinal, and Normal Variables 

Nominal variables are categorical with no order (e.g., gender). Dichotomous variables are a subtype of nominal variables with only two categories, such as yes/no (Morgan et al., 2019). Ordinal variables involve ranked categories, while normal variables refer to continuous data distributed in a bell-shaped curve (Dat & Tham, 2025). Normal variables are crucial in statistics because many inferential tests assume normality. 

D2.3.2.b Interval vs. Ratio Variables 

In social sciences, researchers often do not distinguish between interval and ratio variables because most statistical analyses treat them similarly (Morgan et al., 2019). Both scales assume equal intervals, while ratio additionally has a true zero point. Alessandro and Asmerilda (2020) explain that ordinal and continuous distinctions, rather than ratio versus interval, have more practical implications for choosing statistical tools. 

D2.3.3 Standard Normal Curve 

Approximately 68% of the area under the standard normal curve falls within one standard deviation of the mean (Morgan et al., 2019). This indicates that scores beyond one standard deviation are less common and represent greater deviation from average performance. In practice, this helps researchers interpret probabilities and identify unusual cases. Recognizing such deviations can guide policy, interventions, and deeper analysis. 

D2.3.4 Z Scores 

D2.3.4.a Relation to Normal Curve 

Z scores express how many standard deviations a score lies above or below the mean, aligning scores across different normal distributions (Morgan et al., 2019). 

D2.3.4.b Interpretation of –3.0 

A z score of –3.0 indicates the value is three standard deviations below the mean, an extremely rare occurrence. Such cases are usually considered outliers requiring further investigation. 

D2.3.4.c Percentage Between –2 and +2 

About 95% of scores lie between z = –2 and z = +2 (Morgan et al., 2019). This matters because it shows the range where the vast majority of scores fall, supporting decisions such as identifying outliers. In research, this principle emphasizes stewardship of data, being careful to account for the 5% that falls outside of expected ranges, echoing Keller’s (2012) point that integrity in work requires diligence even in rare or difficult cases. 

D2.3.5 Data Display 

Frequency polygons are inappropriate for nominal data because they assume ordered categories and continuity. Instead, bar charts or pie charts are better options to visualize nominal data (Morgan et al., 2019; Alessandro & Asmerilda, 2020). Choosing appropriate displays respects the integrity of the data and ensures truthful representation. From a faith perspective, Keller (2012) reminds us that our work, even in statistics, reflects God’s order and should be done with excellence and honesty. 

References 

Alessandro, B., & Asmerilda, H. (2020). Goodman and Kruskal’s gamma coefficient for

ordinalized bivariate normal distributions. Psychometrika, 85(4), 905–925.

https://doi.org/10.1007/s11336-020-09730-5Links to an external site. 

Dat, T., & Tham, A. W. (2025). Accuracy comparison between feedforward neural network,

support vector machine and boosting ensembles for financial

risk evaluation. Journal of Risk and Financial Management, 18(4), 215.

https://doi.org/10.3390/jrfm18040215Links to an external site. 

Keller, T. (2012). Every good endeavor: Connecting your work to God’s work. Dutton. 

Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2019). IBM SPSS for

introductory statistics: Use and interpretation (6th ed.). Routledge.