Understanding Statistical Concepts

Population and Elements

Population: All persons included in a study.

Elements: People or things within the population.

Variables

Variables: The focus of the study.

Quantitative Variables

Expressed in numeric values.

Discrete

Numerical values expressed in whole numbers (no decimals).

Continuous

Numerical values that can include decimals.

Attribute Variables

Values expressed in text.

Ordered

Have an accepted order.

Unordered

Do not have an order.

Data Sources

Primary Sources: First-hand information (interviews, surveys).

Secondary Sources: Reflections of primary sources (censuses, registers).

Statistical Tables

Data is collected and organized into tables.

Absolute Frequency: Number of times a value appears.

Relative Frequency: Absolute frequency divided by sample size.

Absolute Cumulative Frequency: Sum of appearances of a value or lesser values.

Graphs

Axes should start at 0, with equal intervals.

Column Graph

Rectangles represent values; intervals are not continuous.

Bar Graph

Similar to column graph, but axes are rotated.

Line Graph

Points connected by lines show value changes.

Proportion Graph

Uses percentages to represent variable frequency.

Dispersion Graph

Shows dispersion between observed values.

Measures of Centralization

Arithmetic Mean: Sum of values divided by sample size.

Median: Central value in an ordered series.

Mode: Most frequent value.

Quartile: Points dividing frequency into four equal parts.

Measures of Dispersion

Mean Deviation: Average difference between values and the mean.

Variance: Squared deviations to eliminate negative signs.

Standard Deviation: Square root of the variance.

Coefficient of Variation: Deviation from the mean expressed as a percentage.

Lorenz Curve: Shows concentration in a frequency distribution.

Bivariable Associations

Independent Variable: Not modified by another variable.

Dependent Variable: Affected by the independent variable.

Form: Relationship pattern in a coordinate system.

Strength: Significance of the relationship.

Correlation Coefficient: Measures strength and direction of a relationship.

• Spearman’s C: For ordinal values.
• Pearson’s C: For actual values.

Multivariate Analysis

Factor Analysis

Reduces data size while retaining maximum information.

Confirmatori

• Spatial information array
• Correlation matrix
• Factor array, extraction of factors
• Rotation of factors
• Interpretation of factors

Exploratory

• Variable selection
• Measures of similarity or distance
• Clustering algorithm, hierarchical methods