Biostatistics and Data Analysis in Dental Hygiene

Introduction to Biostatistics and Data Analysis

• Definition of Biostatistics: The application of data analysis and interpretation specifically within the context of healthcare research.
• Role of Technology: Most contemporary computations are performed using dedicated computer programs. Researchers must possess the knowledge to input data correctly and accurately interpret the generated results.
• Scope of Data Analysis:
  • Involves the application of various statistical tests to organize, describe, summarize, and analyze gathered data.
  • Aimed at answering researchers' specific questions or testing formulated hypotheses.
  • Requires critical thinking to explain the meaning and practical application of findings.
  • Involves identifying factors that could have influenced results and drawing inferences from sample data to the broader population.
• Applications in Dental Hygiene:
  • Demonstrating patient response to dental hygiene therapies.
  • Testing clinical products and specific treatment regimens.
  • Determining the specific oral health needs of target populations.
  • Evaluating oral health treatments, prevention strategies, and educational programs.
• Importance of Research Knowledge for the Dental Hygienist:
  • Understanding the epidemiology of diseases.
  • Developing and practicing evidence-based therapies.
  • Implementing effective public health programs.
  • Practicing evidence-based dentistry to ensure clinical decisions are supported by data.

Potential Causes of Invalid Research Results

• Low Sample Size: Utilizing an insufficient number of subjects can undermine the statistical power of the study.
• Duration Issues: Studies that are too short in duration may not capture the true effects of an intervention.
• Tool Errors: Using incorrect or uncalibrated measurement instruments.
• Procedural Errors: Utilizing incorrect procedures during the data collection or intervention phase.
• Statistical Misapplication: Applying incorrect statistical tests to analyze the gathered data.

Categorization and Types of Data

• General Definition: Data refers to the specific information collected by a researcher.
• Qualitative Data:
  • Definition: Data that reflects the quality or nature of variables rather than numerical counts.
  • Ordering: Can often be rank-ordered (e.g., a list of patient responses regarding what they liked most vs. least).
  • Categorical Variables: Variables with no numerical representation (e.g., hair color, ratings of "good" or "bad").
  • Dichotomous Variables: Variables that place subjects into exactly two distinct groups (e.g., female/male, yes/no, pass/fail).
• Quantitative Data:
  • Definition: Data represented by numbers and expressed as counts, percentages, and means.
  • Examples: Pocket depths, number of teeth with sealants.
  • Continuous Variables: Variables derived from a large or infinite number of measures. These can be expressed in fractions (e.g., height, weight).
  • Discrete Variables: Measurements consisting of distinct and separate units expressed in whole numbers only (e.g., the number of children, DMFT score).

Scales of Measurement

• Nominal Scale:
  • Organizes data into mutually exclusive categories.
  • Categories have no inherent rank or numerical value.
  • Dental Hygiene Example: Patient classification (Pediatric, Adult, Geriatric) or hair color (brown, black, blonde, gray).
• Ordinal Scale:
  • Organizes data into mutually exclusive categories that possess a specific rank order.
  • However, the difference between the ranks is not necessarily equal in value and has no true numerical meaning.
  • Dental Hygiene Example: Shades of tooth whiteness ($A1$, $A2$, $B1$, $B2$) or the difficulty level of dental hygiene patients categorized as $0$, $1$, $2$, $3$, and $4$.
• Interval Scale:
  • Possesses all characteristics of the ordinal scale, but includes equal distances between units of measurement.
  • Critically, it has no absolute zero point, meaning values can be negative.
  • Example: Temperature measured on the Fahrenheit scale.
  • Dental Hygiene Example: Periodontal probe measurements (though often debated, primarily categorized here for distance equality).
• Ratio Scale:
  • Possesses all characteristics of the interval scale plus an absolute zero point.
  • The presence of a $0$ score indicates the total absence of the variable.
  • All arithmetic operations can be applied to ratio data.
  • Examples: Money, height, weight, number of teeth, or number of participants enrolled in a community program.

Descriptive vs. Inferential Statistics

• Descriptive Statistics:
  • Procedures used to summarize, organize, and describe quantitative data.
  • Utilizes tables and graphs for visualization.
  • Includes measures of central tendency, measures of dispersion, and frequency distribution tables.
• Inferential Statistics:
  • Procedures used to make inferences or generalizations about a larger population based on data collected from a sample.
  • This process is also known as making statistical decisions.

Measures of Central Tendency and Practice Examples

• Mean: The arithmetic average of a data set. Symbolized as $\bar{x}$ or $M$.
• Median: The exact midpoint of the data set when arranged in order.
• Mode: The value that occurs with the greatest frequency.
  • Bimodal: The data set contains two modes.
  • Multimodal: The data set contains more than two modes.
• Practice Array 1: Data set ($2, 2, 3, 4, 5$)
  • Median: $3$
  • Mode: $2$
  • Mean: $3.2$
• Practice Array 2: Data set ($2, 2, 3, 3, 4, 5, 6$)
  • Median: $3$
  • Mode: $2$ and $3$
  • Array Type: Bimodal
  • Mean: $3.6$

Measures of Dispersion (Variability)

• Definition: Measurements that describe how much variation is present within a group of data.
• Range: Calculated by subtracting the lowest score from the highest score. It is the simplest but least helpful measure because it is heavily affected by extreme outliers.
• Variance: Represents the average squared distance of each individual score from the calculated mean.
• Standard Deviation (SD): The square root of the variance. It is considered the most common and useful measurement of dispersion.

Normal Distribution and the Empirical Rule

• Gaussian Distribution: Also known as the normal distribution, it forms the theoretical foundation for statistical comparisons.
• Characteristics: A symmetrical, unimodal, bell-shaped curve where the Mean, Median, and Mode are exactly equal.
• The Empirical Rule (Standard Normal Distribution):
  • Approximately $68\%$ of data points fall within one standard deviation ($1\,SD$) of the mean.
  • Approximately $95\%$ of data points fall within two standard deviations ($2\,SD$) of the mean.
  • Approximately $99.7\%$ of data points fall within three standard deviations ($3\,SD$) of the mean.
• Curve Width: The larger the numerical value of the standard deviation, the wider and flatter the distribution curve appears.

Skewed Distributions

• Definition: An asymmetrical distribution of scores where the curve is distorted or pushed to one side, often caused by small sample sizes, non-random sampling, or extreme outlier scores.
• Positive Skew: The curve is shifted toward the left, meaning there are more scores in the lower range. The "tail" of the curve points toward the higher values (right).
• Negative Skew: The curve is shifted toward the right, meaning there are more scores in the higher range. The "tail" of the curve points toward the lower values (left).
• Identification: Skewness is identified by comparing the mean and the median.

Frequency Distributions and Graphing Techniques

• Frequency Distribution Tables: Show the number of times each score or item occurs. Data should be understandable without additional explanation.
  • Ungrouped: Data presented in ascending or descending order with the frequency for each individual score.
  • Grouped: Data presented in ranges (intervals) with the frequency of scores falling into those ranges.
  • Cumulative: The frequency of occurrence of scores up to and including a specific value.
• Bar Graph: Used for categorical data. The length of the bar corresponds to frequency. A cluster bar graph can compare multiple groups.
• Histogram: Similar to a bar graph but with bars touching (side by side). Used for interval, ratio, or ordinal data treated as continuous.
• Frequency Polygon: A line graph representing continuous frequency data, created by connecting the midpoints of histogram bars.
• Scattergram: A plot showing the relationship between two variables, illustrating how one variable's level changes as the other changes.
• Pie Chart: Represents parts of a whole (represented as percentages). Generally more acceptable for lay audiences than for technical scientific publications.

Correlation and the Correlation Coefficient ($r$)

• Definition: Correlation measures the strength and direction of a relationship or association between two variables.
• The $r$-value: Signifies the correlation coefficient, ranging from $-1$ to $+1$.
  • Strong Relationship: Values closer to $-1$ or $+1$. ($r = -0.90$ is as strong as $r = +0.90$).
  • Weak Relationship: Values closer to $0$.
  • Perfect Relationship: Exact values of $+1$ or $-1$.
  • No Relationship: A value of $0$.
• Positive Correlation: A direct relationship. As variable $x$ increases, variable $y$ also increases; as $x$ decreases, $y$ decreases.
• Negative Correlation: An inverse relationship. As variable $x$ increases, variable $y$ decreases; as $x$ decreases, $y$ increases.

Inferential Statistical Tests and Decision Making

• Null Hypothesis: Statistical decisions are made to either reject or accept the null hypothesis based on probability.
• Probability Value ($p$-value):
  • Evaluates the possibility that the results occurred by chance without intervention.
  • Threshold: The commonly accepted $p$-value in oral health research is equal to or smaller than $0.05$.
  • Significance: If $p \le 0.05$, results are statistically significant. If $p > 0.05$, results are not statistically significant.
• T-test: A statistical test used to determine the hypothetical difference between two mean scores.
• ANOVA (Analysis of Variance): A test used to compare the statistical differences between three or more mean scores.

Research Quality: Validity, Reliability, and Calibration

• Validity: The degree to which an instrument measures what it is intended to measure.
  • Internal Validity: Refers to the accuracy of the study results; affected by study length, sample size, and statistical accuracy.
  • External Validity: Refers to the accuracy of generalizing the study results to the total population; affected by how well the sample represents that population.
• Reliability: The extent to which a measurement method performs consistently, yielding the same results in the same population upon repetition.
• Calibration: The process of establishing a relationship between a measuring device and the units of measurement to ensure consistency among examiners.
  • Inter-examiner Reliability: Consistency between different examiners. Calibration increases this.
  • Intra-examiner Reliability: Consistency within the same examiner over time.

Topics Excluded from Assessment

• For examination purposes, the following specific concepts are not tested from this chapter:
  • Degrees of Freedom
  • Type I or II Error
  • Spearman Rank-Order Correlation
  • Pearson Product-Moment Correlation Coefficient
  • Regression Analysis
  • Confidence Intervals
  • Parametric and Nonparametric Statistics