8.5 Biostatistics in Dental Research: Mean, Median, P-values, Sensitivity & Specificity

8.5 Biostatistics in Dental Research: Mean, Median, P-values, Sensitivity & Specificity

Biostatistics is the application of statistical reasoning and mathematical calculations to biological, dental, and public health data. Biostatistical analysis allows researchers and clinicians to summarize sample observations (descriptive statistics) and draw valid conclusions about broader populations (inferential statistics). Mastering biostatistical principles is essential for interpreting dental research findings and answering calculation and conceptual items on the NBDHE.

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Measures of Central Tendency & Skewness

Measures of central tendency identify the single central value around which numerical data cluster.

• Mean: The arithmetic average computed by summing all values and dividing by the total sample size ($n$). The mean is highly sensitive to extreme outliers, which skew its value toward the tail.
• Median: The exact midpoint score when data points are arranged in numerical rank order (50th percentile). The median is unaffected by extreme outliers and is the preferred measure of central tendency for skewed or non-normal distributions.
• Mode: The most frequently occurring score in a distribution. A distribution can be unimodal, bimodal (two peaks), or multimodal.

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|                             SKEWED DISTRIBUTION CURVES                             |
|                                                                                    |
|  POSITIVE SKEW (Right-Skewed): Tail extends right  -->  Mean > Median > Mode       |
|  NEGATIVE SKEW (Left-Skewed):  Tail extends left   -->  Mean < Median < Mode       |
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• Positive Skew (Right-Skewed): Tail extends toward higher positive values. The mean is pulled to the right: $\text{Mean} > \text{Median} > \text{Mode}$.
• Negative Skew (Left-Skewed): Tail extends toward lower negative values. The mean is pulled to the left: $\text{Mean} < \text{Median} < \text{Mode}$.

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Measures of Dispersion & The Normal Distribution

Dispersion describes the spread or variability of scores around the central point.

• Range: Difference between the highest score and lowest score ($Max - Min$).
• Variance: Average of squared deviations from the mean.
• Standard Deviation (SD): The square root of variance; quantifies the average distance that individual scores deviate from the sample mean.

The Normal (Gaussian) Bell Curve & Empirical Rule

In a perfectly symmetrical normal distribution, the Mean, Median, and Mode are all equal at the exact center peak.

+------------------------------------------------------------------------------------+
|                        THE EMPIRICAL RULE (NORMAL BELL CURVE)                      |
|                                                                                    |
|  Mean +/- 1 Standard Deviation (SD)  -->  Encompasses 68.2% of all population data |
|  Mean +/- 2 Standard Deviations (SD) -->  Encompasses 95.4% of all population data |
|  Mean +/- 3 Standard Deviations (SD) -->  Encompasses 99.7% of all population data |
+------------------------------------------------------------------------------------+

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Inferential Statistics & Hypothesis Testing

Inferential statistics test hypotheses to determine whether observed differences between groups represent true biological effects or random chance.

1. The Null Hypothesis ($H_0$)

• The baseline statistical assumption that no real difference, no treatment effect, or no association exists between the study groups (e.g., "There is no difference in plaque reduction between toothbrush A and toothbrush B").

2. Statistical Significance & The p-value

• p-value: The probability that the observed study results occurred purely by random chance assuming the null hypothesis is true.
• Standard Significance Alpha Level ($\alpha = 0.05$):
  • If $p < 0.05$: There is less than a 5% probability that results were due to chance. The researcher rejects the null hypothesis ($H_0$) and concludes that a statistically significant difference exists.
  • If $p \ge 0.05$: Results are not statistically significant. The researcher fails to reject the null hypothesis.

3. Type I vs. Type II Errors

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Diagnostic Test Accuracy: Sensitivity vs. Specificity

Evaluating the validity of clinical diagnostic screening tools (e.g., caries detection dyes, oral cancer screening lights, saliva biomarkers) requires analyzing sensitivity and specificity metrics.

+------------------------------------------------------------------------------------+
|                       DIAGNOSTIC TEST CONTINGENCY MATRIX                           |
|                                                                                    |
|                         DISEASE PRESENT (D+)       DISEASE ABSENT (D-)             |
|   TEST POSITIVE (T+)    True Positive (TP)         False Positive (FP)             |
|   TEST NEGATIVE (T-)    False Negative (FN)        True Negative (TN)              |
+------------------------------------------------------------------------------------+

1. Sensitivity (True Positive Rate)

• Definition: The percentage or probability that a test correctly identifies individuals WHO HAVE THE DISEASE ($D+$).
• Formula: $\text{Sensitivity} = \frac{TP}{TP + FN} \times 100$.
• Mnemonic: SNOUT — A highly Sensitive test, when Negative, rules OUT the disease.

2. Specificity (True Negative Rate)

• Definition: The percentage or probability that a test correctly identifies individuals WHO DO NOT HAVE THE DISEASE ($D-$).
• Formula: $\text{Specificity} = \frac{TN}{TN + FP} imes 100$.
• Mnemonic: SPIN — A highly Specific test, when Positive, rules IN the disease.

3. Predictive Values

• Positive Predictive Value (PPV): Proportion of individuals testing positive who actually have the disease: $\frac{TP}{TP + FP}$.
• Negative Predictive Value (NPV): Proportion of individuals testing negative who are actually free of disease: $\frac{TN}{TN + FN}$.