Overview
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 scholarly citations from the textbook in the latest APA format and a corresponding list of references, including any additional scholarly sources. The textbook remains the only required source, and citations are only necessary if you are referencing specific material. Additional scholarly sources are optional, not required. The minimum word count for the 8 short-answer discussion replies is 100 words to ensure meaningful engagement.
Discussion Thread: Variables, Z Scores, Population and Output
Maximus Dobrev
BUSI820_B01_202630
May 31, 2026
Discussion No. 2
Barrett et al. (2026) emphasizes that appropriate statistics depend on variable type, research design, and whether the question concerns group differences or associations. The following responses use financial trading examples to clarify the concepts in the discussion questions.
D2.3.1 Ordered Categorical Data
Categorical, ordered data such as low income, middle income, and high income are measured at the ordinal level. Ordinal variables have a meaningful rank order, but the distance between categories is not necessarily equal. For example, in trading, stocks may be classified as low-risk, moderate-risk, and high-risk. These categories can be ranked, but the risk difference between low and moderate risk may not equal the difference between moderate and high risk.
D2.3.2 Nominal, Dichotomous, Ordinal, and Normal Variables
D2.3.2.a Comparison and Contrast
Nominal variables are unordered categories, such as stock sector: technology, healthcare, energy, or financials. The categories differ, but they are not ranked. Dichotomous variables have only two categories, such as profitable/unprofitable trades, win/loss outcomes, or options expiring in the money versus out of the money. Ordinal variables are ranked categories, such as sell, hold, and buy ratings. The order matters, but the spacing between ratings is not equal.
Normal/scale variables are quantitative variables that can often be analyzed with parametric statistics when assumptions are met. Trading examples include daily returns, portfolio value, volatility, drawdown, or Sharpe ratio. Barrett et al. use these distinctions to guide selection of statistics such as correlation, regression, t tests, ANOVA, and nonparametric alternatives.
D2.3.2.b Interval and Ratio Variables
In social science research, the distinction between interval and ratio variables is often less important because both are commonly treated as scale variables. Interval variables have equal units but no true zero, while ratio variables have equal units and a meaningful zero. In finance, portfolio value and trading volume are ratio variables because zero means none exists. However, for many analyses, the more important issue is whether the variable can be treated as continuous and whether statistical assumptions are satisfied.
D2.3.3 Standard Normal Curve and One Standard Deviation
Approximately 68% of scores under the normal curve fall within one standard deviation above or below the mean. This means that scores outside one standard deviation are less typical, but not necessarily extreme.
In trading, if a portfolio’s average monthly return is 1% with a standard deviation of 3%, then returns from −2% to 4% are within one standard deviation. A return outside that range may deserve attention, but it does not automatically mean the strategy has failed. Barrett et al. similarly caution that statistical findings should be interpreted with practical significance, effect size, and context in mind.
D2.3.4 Z Scores and the Normal Curve
D2.3.4.a Relationship of Z Scores to the Normal Curve
A z score shows how many standard deviations a score is from the mean. A z score of 0 is at the mean, positive values are above the mean, and negative values are below the mean. In trading, a stock return with a z score of +2.0 is two standard deviations above its average return, suggesting an unusually strong move.
D2.3.4.b Interpretation of Z = −3.0
A z score of −3.0 means the score is three standard deviations below the mean. This is an unusually low value. In portfolio terms, a −3.0 z score could represent a severe trading loss relative to historical performance. It should prompt review, but it may reflect either a valid market shock or a data problem.
D2.3.4.c Scores Between Z = −2 and Z = +2
Approximately 95% of scores fall between z = −2 and z = +2 in a normal distribution. This matters because scores outside that range are relatively uncommon. In trading, returns beyond ±2 standard deviations may be treated as risk-management signals or potential outliers, but they still require practical interpretation.
D2.3.5 Frequency Polygons and Nominal Data
A frequency polygon should not be used with nominal data because it connects categories with lines, implying order or continuity. Nominal categories do not have a natural sequence. For example, stock sectors such as technology, healthcare, energy, and financials should not be connected with a line because one sector does not naturally progress into another.
A bar chart is better for nominal data because it displays each category separately. In trading research, a bar chart could show the number of trades by sector, broker, order type, or strategy type without implying that the categories are continuous.
References
Barrett, K. C., Leech, N. L., Gloeckner, G. W., & Morgan, G. A. (2026). Selecting and interpreting inferential statistics. In IBM SPSS for introductory statistics: Use and interpretation (7th ed., pp. 71–91). Routledge. doi:10.4324/9781003355908-3