Biostatistics Summary

Chapter 17: Biostatistics

  • Biostatistics Definition
    • The application of data analysis and interpretation in health care research.
    • Typically relies on computers for statistical computations.
    • Researchers may hire statisticians to ensure robust analysis.
    • Data analysis aims to interpret results, answering research questions or testing hypotheses.

Data Analysis

  • Purpose
    • Applies statistical tests to organize, describe, and summarize data.
    • Essential for verifying research questions or hypotheses.

Interpretation of Study Results

  • Elements of a Valid Study

    • Adequate time duration
    • Sufficient number of participants
    • Appropriate measurements
    • Correct statistical tests utilized.

  • Statistical Symbols

    • Refer to textbook (Table 17-1, p. 211) for symbols and meanings.

Types of Data/Data Categorization

  • Item of Data
    • A singular piece of data.
  • Data Set
    • A collection of data items.
  • QUANTITATIVE Data
    • Numerical values (e.g., pocket depths, number of sealed teeth).
    • Can be displayed as counts, percentages, and means.
  • QUALITATIVE Data
    • Non-numerical; cannot be quantified.
    • Example: Patient survey responses on dental visit satisfaction.

Variables

  • CONTINUOUS (QUANTITATIVE)
    • Numeric, can be fractional.
    • Infinite measurements on a continuum (e.g., height, weight).
  • DISCRETE (QUANTITATIVE)
    • Numeric whole numbers with finite values (e.g., number of children).
  • CATEGORICAL (QUALITATIVE)
    • Non-numeric, organized into groups (e.g., ethnicity, gender).
  • DICHOTOMOUS (QUALITATIVE)
    • Only two categories (e.g., male/female).

Scales of Measurement

  • Importance
    • Determines which statistics to apply for data analysis.

4 Scales:

  1. Nominal
    • Categorizes data without rank (e.g., toothpaste types).
  2. Ordinal
    • Data with order but unequal intervals (e.g., plague classification).
  3. Interval
    • Equal distances without an absolute zero (e.g., temperature).
  4. Ratio
    • Equal distances with an absolute zero (e.g., number of teeth).

Categories of Statistics

  • Descriptive Statistics
    • Summarizes quantitative data (central tendency, frequency tables).
    • Not used for conclusions.
  • Inferential Statistics
    • Generalizes findings from samples to populations.

Measures of Central Tendency

  • Mean
    • Average, sensitive to outliers.
    • Formula: M = rac{ ext{Sum of all scores} }{ ext{Total number of scores} } .
  • Median
    • Middle value when numbers are ordered.
  • Mode
    • Most frequently occurring score.
    • Bimodal: Two modes; Multimodal: More than two modes.

Measures of Dispersion

  • Definition
    • Indicates variation within data.
  • Range
    • Distance between highest and lowest scores.
  • Standard Deviation (SD)
    • Measurement of deviation from the mean SD = ext{sqrt( Variance )} .
  • Variance
    • Average deviation of scores from the mean.

Distribution

  • Describes data dispersion; shown through graphs.
  • Normal/Gaussian Distribution
    • Bell curve where most scores occupy the center.

Empirical Rule

  • Suggests that almost all data within a normal distribution falls within three standard deviations of the mean.

Skewness

  • Negative Skew: Left skewed, with lower scores predominating.
  • Positive Skew: Right skewed, with higher scores predominating.

Types of Graphs

  • Chart Types:
    • Polygon, Pie chart, Bar graph, Scattergram, Histogram, Line graph.

Correlation

  • Studies relationship between variables, quantifiable as a correlation coefficient r , ranging from -1 to +1.

  • Positive Correlation: Both variables increase together.

  • Negative Correlation: One variable increases while the other decreases.

  • Correlation Coefficient Interpretation:

    • 0.00 - 0.25: Little association
    • 0.26 - 0.49: Weak
    • 0.50 - 0.69: Moderate
    • 0.70 - 0.89: High
    • 0.90 - 1.00: Very High

Statistical Decision Making

  • Null Hypothesis: No association between variables (accepted unless evidence suggests rejection).
  • Positive/Research Hypothesis: Suggests a relationship or effect.

Accepting or Rejecting the Hypothesis

  • Based on alpha (p-value):
    • p <= 0.05: Statistically significant.
    • p > 0.05: Not significant.

Inferential Statistics

  • Generalizations about a population from sample data.
  • Parametric Data: T-tests, ANOVA for means comparison.
  • Nonparametric Data: Chi-square test for frequency counts.

Data Research and Results

  • Validity: Internal vs. external validity.
  • Reliability: Consistency of study results.
  • Significance: Statistical vs. practical significance.