Statistics

Statistics in Epidemiology and Dentistry

Introduction

• Overview of key topics covered in statistics relevant to biostatistics, epidemiology, and public health focusing on their applications in dentistry.

Applications of Statistics in Epidemiology and Dentistry

• Descriptive statistics: Summarize and organize data.

• Inferential statistics: Make predictions or inferences about a population based on a sample.

Key Concepts in Statistics

Statistics Defined

• Definition 1: Science of assembling and interpreting numerical data (Bland, 2000).

• Definition 2: Discipline concerned with the treatment of numerical data derived from groups of individuals and things (Armitage et al., 2001).

Data

• Data: Items of information; plural form.

Types and Variables in Statistics

Variables

• Definition: Variables are characteristics that can vary among subjects in a study.

• Population: The complete set of specimens or objects (statistical units) that can be studied.

• Sample: A subset of the population used to represent the population in statistical analysis.

• Attribute: A characteristic of a specimen or object.

• Types of Variables:

  • Qualitative (Categorical): Non-measurable characteristics.

  • Nominal: Without order.

  • Ordinal: With order.

  • Binomial: Only two categories (boolean).

  • Quantitative (Numerical): Measurable characteristics.

  • Discrete: Finite, isolated values.

  • Continuous: Infinite range of values; can take on any value within a given range.

Graphical Representations of Data

• Visual aids including bar plots, pie charts, histograms, and box plots are used to represent statistical data distributions clearly and succinctly.

Statistical Distributions

Distributions of Variables

• Distribution: Percentage of specimens or objects falling into each category or interval.

  • Example Distribution - Oral Hygiene:

  • None: 30%

  • Low Hygiene: 32%

  • Medium Hygiene: 18%

  • High Hygiene: 20%

  • Total: 100%

• Diet Distribution Example:

  • Proteins: 34%, Lipids: 43%, Carbohydrates: 23%

Tendency of Data

Measures of Central Tendency

1. Mean (Average): Calculated as $\bar{x} = rac{ ext{Sum of values}}{n}$.

2. Median: Middle value in an ordered sample of numerical values.

3. Mode: Value that occurs most frequently in a data set, can be numbers or categories.

4. Range: Difference between the largest and smallest values, can be misleading if extreme values are present.

5. Centiles: Help to describe the central range of data.

   • 25th centile (Q1), 50th centile (Median), 75th centile (Q3).

6. Interquartile Range (IQR): Distance between Q1 and Q3; indicates variation in data.

Statistical Measures

Standard Deviation and Variability

1. Standard Deviation (SD): Measures the amount of variation or dispersion in a set of values.

   • Formula: $ext{SD} = rac{ ext{Sum of squared deviations}}{n-1}$.

2. Mean Deviation Formula Considered: Square the deviations for accuracy.

Summarization Techniques in Statistics

Types of Summaries

• Qualitative/Categorical Summaries:

  • Nominal, ordinal - example: blood types, stress levels.

• Quantitative Summaries:

  • Binary, discrete, continuous - involves mean, median, and interquartile ranges.

Refreshing Key Concepts

Core Formulas in Statistics

• Mean: $ext{mean} ext{ } ( ext{µ}) = rac{ ext{Sum of observations}}{n}$.

• Variance: $ext{Variance} ( ext{ω}^2) = rac{ ext{Sum of }(X - ext{μ})^2}{N}$.

• Standard deviation: $ext{SD} = rac{ ext{Sum of deviations}}{ ext{N} - 1}$.

Bibliography

• Detels R., Gulliford M., Abdool Karim Q., and Tan C. (2017). Oxford Textbook of Global Public Health (Sixth Edition), Oxford University Press.