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.