Classify Each Of The Following Variables As Quantitative Or

Classify Each Of The Following Variables as Quantitative, Ordinal, or Categorical

In this assignment, you are asked to classify a series of variables based on their measurement scales as either quantitative, ordinal, or categorical. Understanding the distinctions among these scales is fundamental in statistical analysis:

  • Quantitative variables are numerical and involve measurements that can be measured on a numeric scale, allowing for meaningful arithmetic operations.
  • Ordinal variables are categorical variables with a clear ordering or ranking but without consistent interval differences between categories.
  • Categorical variables are variables that classify data into distinct groups or categories without inherent numerical ordering.

For each variable listed, determine its measurement scale accordingly:

  1. White blood cells per deciliter of whole blood
  2. Leukemia rates in geographic regions (cases per 100,000 people)
  3. Presence of type II diabetes mellitus (yes or no)
  4. Body weight (kg)
  5. Low-density lipoprotein level (mg/dl)
  6. Grade in a course coded: A, B, C, D, or F
  7. Religious identity coded 1 = Protestant, 2 = Catholic, 3 = Muslim, 4 = Jewish, 5 = Atheist, 6 = Buddhist, 7 = Hindu, 8 = Other
  8. Blood cholesterol level classified as either 1 = hypercholesterolemic, 2 = borderline hypercholesterolemic, 3 = normocholesterolemic
  9. Course credit (pass or fail)
  10. Ambient temperature (degrees Fahrenheit)
  11. Type of life insurance policy: 1 = none, 2 = term, 3 = endowment, 4 = straight life, 5 = other
  12. Satisfaction: 1 = very satisfied, 2 = satisfied, 3 = neutral, 4 = unsatisfied, 5 = very unsatisfied
  13. Movie review rating: 1 star, 1.5 stars, 2 stars, 2.5 stars, 3 stars, 3.5 stars, 4 stars
  14. Treatment group: 1 = active treatment, 2 = placebo

Classification of Hospital Service Ratings and Study Variables

Likewise, the following hospital service ratings are assessed based on the measurement items:

  1. Percentage of patients who survive a given surgical procedure — Quantitative
  2. Type of hospital: general, district, specialized, or teaching — Categorical
  3. Average income of patients admitted to the hospital — Quantitative
  4. Mean salary of physicians working at the hospitals — Quantitative

In summary, the variables encompass a mixture of measurement scales, with some directly numerical (quantitative), others ordered but not numerically spaced (ordinal), and some purely categorical without inherent order.

Paper For Above instruction

The classification of variables into quantitative, ordinal, or categorical scales is a foundational concept in statistics that influences data analysis, interpretation, and the choice of statistical tests. Understanding the nature of each variable type ensures appropriate methods are applied, leading to accurate conclusions.

Quantitative variables are numeric and allow for calculations such as means, variances, and other statistical measures. In the provided list, examples include body weight (kg) and low-density lipoprotein levels (mg/dl). These variables are measured on a continuous scale, representing actual quantities. The blood cholesterol level, although classified, quantifies specific health conditions and remains numerical, thus fitting as a quantitative scale, albeit with categorical labels.

Ordinal variables represent an inherent order but do not specify the magnitude of difference between categories. An example from the list is the grade in a course (A, B, C, D, F). These grades reflect a ranking of performance but not precise score differences. Similarly, satisfaction levels (very satisfied, satisfied, neutral, unsatisfied, very unsatisfied) are ordinal, as they reflect a spectrum of sentiment without uniform intervals.

Categorical variables group data into predefined categories without any order. The presence or absence of type II diabetes mellitus (yes or no) illustrates a dichotomous categorical variable. The type of life insurance policy, coded from 1 to 5, although numerically labeled, is categorical because it represents different policy types without an inherent ranking. The same applies to the type of hospital and the ratings like Movie review star ratings, which, despite order, can be viewed as categories based on stars or levels.

Understanding measurement scales also affects how data are visualized and analyzed statistically. Quantitative data facilitates parametric tests, whereas ordinal and categorical data might require non-parametric tests or frequency-based analyses.

In conclusion, classifying the variables correctly helps in selecting the appropriate statistical methods and interpreting results accurately. Accurate classification impacts research validity and the robustness of findings across diverse applied fields like medicine, social sciences, and economics.

References

  • DeVore, J. (2014). Understanding Statistics. Springer.
  • Altman, D. G. (1991). Practical statistics for medical research. Chapman and Hall.
  • Quinn, G. P., & Keough, M. J. (2002). Experimental Design and Data Analysis for Biologists. Cambridge University Press.
  • Everitt, B., & Skrondal, A. (2010). The Cambridge Dictionary of Statistical Terms. Cambridge University Press.
  • Newman, I., & Benz, C. R. (1998). Qualitative-Quantitative Research Methodology: Exploring the Interactive Continuum. Central Queens Publishing.
  • Fisher, R. A. (1970). The Design of Experiments. Edinburgh: Oliver and Boyd.
  • Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses. Springer.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
  • Cook, R. D., & Weisberg, S. (1999). Applied Regression Including Computing and Graphics. John Wiley & Sons.
  • Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression. Wiley.

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