250216 - 3.1 VARIABLES- CLASSIFICATION, SCALES, PROPERTIES

Presentation at the Course ‘Biostatistics MSN823’ Level 2 Year 1 Faculty of Nursing, Princess Noura bint Abdulrahman University. By Prof. Omar Hasan Kasule Sr. MB ChB (MUK), MPH (Harvard) DrPH (Harvard)

 

CLASSIFICATION OF VARIABLES:

• Quantitative/numerical and qualitative/categorical.
• Quantitative/numerical are either discrete (possible values countable and sample space can be listed) or continuous (an infinite number of possible values in a continuum).
• Qualitative/categorical are nominal, ordinal, and rank.
• Nominal data is data whose values are labels and not numbers.
• Note that the nominal and ordinal can become discrete if counted.
• Ordinal data is qualitative data that has numerical values
• Note also that more than 10 discrete outcomes can be represented by a continuous model.

 

EXERCISES:

1. List class data variables that are discrete and those that are continuous.
2. Identify class data variables that are ordinal.

 

PRESENTATION AND DISCUSSION:

• Identify the main variables in the following article and discuss their classification: Hisham Aljadhey, Yousef Asiri, Yaser Albogami, George Spratto, Mohammed Alshehri. Pharmacy education in Saudi Arabia: A vision of the future. 2017 Jan;25(1):88-92. It is available as a free PMC article from PubMed.

 

SCALES OF RANDOM VARIABLES:

• Numerical variables are on 2 scales: interval and ratio.
• Distinction between ratio and interval: ratio test (two numbers) and the true zero test (not found in the interval scale).

 

PRESENTATION/DISCUSSION:

1. Identify and discuss 2 examples of the use of the interval scale in pharmacy practice.

 

SIX PROPERTIES OF RANDOM VARIABLES:  

1. Expectation
2. Variance
3. Correlation (scale-free measure of dependence)
4. Covariance (scale-dependent measure of dependence between variables),
5. Skew
6. Kurtosis.

 

EXERCISES:

1. Estimate the expectation, variance, skew, and kurtosis of age, height, and weight in the class data set: Analyse > descriptive statistics > descriptives > drag age, weight, and height into the variables window > in options check: mean, std deviation, variance, standard error of the mean, range, minimum, maximum, kurtosis, skewness > OK
2. Compute the correlation for weight and height: analyze > correlate > bivariate > drag height and weight into the variables window > chosose all 3 correlation coefficients (Pearson for normally distributed data , Kendall tau-b & Spearman for non normal data) > choose 2 tailed > choose flag significant correlations > OK
3. Compute the covariance for weight and height

 

 

FIGURE MEAN and 95% CONFIDENCE INTERVALS-1

 

 

 

FIGURE MEAN and 95% CONFIDENCE INTERVALS-2

 

INTERQUARTILE RANGE

 

 

FIGURE OF SKEWNESS

 

FIGURE OF KURTOSIS

 

 

FIGURE OF LINEAR CORRRELATION

 

FIGURE OF VARIANCE

FIGURE OF COVARIANCE

 

TYPES OF VARIABLES IN INFERENCE:

• Independent / determinant / cause.
• Dependent /result /outcome.
• Confounding eg ice dream drownings.
• Interaction variables

 

Presentation/discussion:

1. Identify the independent, dependent, and confounding variables in the following article: Mohammad J Al-Yamani et al. Epidemiological Determinants For The Spread Of Covid-19 In Riyadh Province Of Saudi Arabia.  Saudi J Biol Sci. 2021 Dec 20. doi: 10.1016/j.sjbs.2021.12.032. Online ahead of print. Free copy available onPMC via pubmed.

 

TRANSFORMATION OF VARIABLES:

• Linear transformations: standard normal is x-µ/std dev,
• Non-linear transformation, eg, logarithmic.
• Purpose of transformations: normalize skewed data, allowing use of the t-test.