QUALITATIVE AND QUANTITATIVE VARIABLES ✅ INTRODUCTION TO STATISTICS
Random Variables - Classification ✅ INTRODUCTION TO STATISTICS
Qualitative Variables - Nominal and Ordinal
Quantitative Variables
Quantitative variables are characteristics that can be described by numbers, and are classified as continuous or discrete.
– Discrete variables: the variable is evaluated in numbers that are the result of counts and, therefore, only whole numbers make sense. Examples: number of children, number of bacteria per liter of milk, number of cigarettes smoked per day.
– Continuous variables: the variable is evaluated in numbers that are the result of measurements and, therefore, can assume values with decimal places and must be measured by means of some instrument. Examples: mass (scale), height (ruler), time (clock), blood pressure, age.
Qualitative Variables
Qualitative (or categorical) variables are characteristics that do not have quantitative values, but are instead defined by categories, that is, they represent a classification of individuals. They can be nominal or ordinal.
– Nominal variables: there is no ordering among the categories. Examples: sex, eye color, smoker/non-smoker, sick/healthy.
– Ordinal variables: there is an ordering among the categories. Examples: education (1st, 2nd, 3rd grade), stage of the disease (initial, intermediate, terminal), month of observation (January, February,…, December).
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1 Descriptive statistics and exploratory data analysis: graphs, diagrams, tables, descriptive measures (position, dispersion, skewness and kurtosis).
2 Probability. 2.1 Basic definitions and axioms. 2.2 Conditional probability and independence. 2.3 Discrete and continuous random variables. 2.4 Probability distribution. 2.5 Probability function. 2.6 Probability density function.
2.7 Expectation and moments. 2.8 Special distributions. 2.9 Conditional distributions and independence. 2.10 Transformation of variables. 2.11 Laws of large numbers. 2.12 Central limit theorem. 2.13 Random samples. 2.14 Sampling distributions.
3 Statistical inference. 3.1 Point estimation: estimation methods, properties of estimators, sufficiency. 3.2 Interval estimation: confidence intervals, credibility intervals. 3.3 Hypothesis testing: simple and compound hypotheses, significance levels and power of a test, Student's t-test, chi-square test.
4 Linear regression analysis. 4.1 Least squares and maximum likelihood criteria. 4.2 Linear regression models. 4.3 Inference on model parameters. 4.4 Analysis of variance. 4.5 Residual analysis.
5 Sampling techniques: simple random, stratified, systematic and cluster sampling.
5.1 Sample size.