Biostats – Community Dentistry · FCPS Part 1

💡Reminders

Think of parametric tests as the "normal-data family":

t-test → ANOVA → Pearson

And their common non-parametric counterparts:

Mann–Whitney → Wilcoxon → Kruskal–Wallis → Spearman

💡Types of scales

Scale	What the respondent does	Example	Key idea
Likert scale	Indicates degree of agreement	Strongly agree → Agree → Neutral → Disagree → Strongly disagree	Agreement
Guttman scale	Responds to items arranged in increasing order of intensity	Would you accept dental checkup? → treatment? → extraction?	Cumulative
Semantic differential / adjective scale	Rates something between two opposite adjectives	Good ⟵ 1 2 3 4 5 6 7 ⟶ Bad	Opposite adjectives
Visual Analogue Scale (VAS)	Marks a point on a continuous line	No pain ───────── Worst pain	Continuous intensity
Rating scale	Gives a numerical rating	Satisfaction: 1–5	Degree/rating
Nominal scale	Chooses a category	Blood group: A/B/AB/O	Names only
Ordinal scale	Chooses an ordered category	Mild/Moderate/Severe	Rank/order
Numerical rating scale	Gives a number to describe intensity	Pain = 0–10	Numeric intensity

💡Null Hypothesis Error

Reality	Study says: No difference (H₀ accepted/not rejected)	Study says: Difference (H₀ rejected)
Actually NO difference	✅ Correct	❌ Type I error
Actually a DIFFERENCE	❌ Type II error	✅ Correct

Type I = False Positive

You say there is a difference, but there actually isn't.

Type II = False Negative

You say there is no difference, but there actually is.

💡Formulas

💡Graphs

Graph	Use it when…	Example
Bar chart	Categorical data	Number of patients by blood group
Histogram ⭐	Continuous numerical data grouped into intervals	Age distribution of patients
Line graph ⭐	Showing change/trend over time	Incidence of caries from 2015–2025
Pie chart	Showing proportions/percentages of a whole	% of patients by smoking status
Scatter plot ⭐	Relationship/correlation between 2 numerical variables	Age vs number of missing teeth
Frequency polygon	Comparing frequency distributions	Age distribution of males vs females
Box-and-whisker plot	Showing distribution, median, spread & outliers	DMFT scores in different groups
Stem-and-leaf plot	Displaying numerical data while retaining individual values	Distribution of ages in a small sample
Pictogram	Simple presentation using symbols/pictures	Number of children receiving dental screening

💡Validity / prerequisites of common statistical tests

Test	Use when	Important prerequisites / conditions
Z test – mean	Compare mean with reference / another mean	Continuous data; approximately normal or large sample; population SD usually known
One-sample t-test	1 sample mean vs known value	Continuous data; observations independent; data approximately normal; population SD unknown
Independent t-test ⭐	Compare means of 2 independent groups	Continuous outcome; independent observations; approximately normal within groups; groups independent; equal variance for the classical pooled version
Paired t-test ⭐	Compare means before vs after in same subjects	Paired observations; continuous outcome; differences between pairs approximately normal
ANOVA ⭐	Compare means of ≥3 independent groups	Continuous outcome; independent observations; approximately normal within groups; similar/equal variances
Chi-square test ⭐⭐⭐	Association between categorical variables	Categories mutually exclusive; observations independent; adequate expected frequencies
Fisher's exact test	Categorical data with small expected frequencies	Independent categorical observations; particularly useful when Chi-square expected counts are too small
Pearson correlation ⭐	Relationship between 2 continuous variables	Continuous variables; approximately linear relationship; independent observations; approximately normal/bivariate normal data for usual significance testing; no major outliers
Spearman correlation	Relationship between ranked/non-normal variables	Ordinal or continuous data; independent observations; monotonic relationship
Mann–Whitney U	2 independent groups, non-parametric	Independent observations; ordinal/continuous outcome; distributions suitable for comparison
Wilcoxon signed-rank	Paired data, non-parametric	Paired observations; differences can be ranked; approximately symmetric differences for the usual interpretation
Kruskal–Wallis	≥3 independent groups, non-parametric	Independent observations; ordinal/continuous outcome
McNemar test	Paired categorical data, usually before/after	Paired/dichotomous data; same subjects measured twice

💡Association vs Correlation

	Association	Correlation
Meaning	Whether two variables are related	How strongly and in what direction two variables move together
Usually used for	Categorical variables	Numerical variables
Example	Smoking ↔ periodontal disease	Age ↔ number of missing teeth
Common test	Chi-square	Pearson / Spearman correlation
Result	χ², p-value, etc.	r from −1 to +1
Tells direction?	Usually not	Yes
Tells strength?	Not usually with basic Chi-square	Yes

💡Sampling

Methods

Sampling = selecting a subset of people from a population.

Method	How it works	Example
Simple random	Everyone has equal chance	Randomly select 100 patients
Systematic	Select every kth person	Every 10th patient
Stratified	Divide into strata, sample from each	Sample males and females separately
Cluster	Randomly select entire groups/clusters	Select 5 schools and survey all students
Multistage	Sampling done in several stages	Province → district → school → students
Convenience	Select whoever is easily available	Patients currently in your clinic
Purposive	Researcher deliberately selects specific subjects	Select experts in dental public health
Snowball	Existing participants recruit others	Useful for hard-to-reach populations

💡Ages

Age group	Age
Neonate / Neonatal period ⭐	Birth–<28 days
Infant ⭐	<1 year
Early infancy	Birth–<6 months
Late infancy	6 months–<1 year
Toddler	1–3 years
Preschool child	3–5 years
Child	<10 years (context-dependent)
Adolescent ⭐	10–19 years
Teenager	13–19 years
Young adult	20–24 years (often used in public health)
Adult	≥18 years legally; epidemiological definitions vary
Older adult / Elderly ⭐	≥60 years in many WHO/public-health contexts
Very old / Oldest old	≥80 years

💡MEAN, MEDIAN AND MODE

Measure	Definition	Example
Mean	Sum of observations divided by the number of observations	Average DMFT score
Median	Middle observation after arranging values in order	Middle patient age
Mode	Most frequently occurring observation	Most common type of restoration

Example: Data = 2, 3, 3, 4, 18

Mean = (2 + 3 + 3 + 4 + 18) / 5 = 6

Median = 3

Mode = 3

The extreme value of 18 pulls the mean upward, while the median remains 3.

💡NORMAL DISTRIBUTION AND SKEWNESS

Normal distribution

A normal distribution is symmetrical and bell-shaped.

Characteristics:

Mean = Median = Mode.
The curve is symmetrical around the mean.
Most observations lie close to the mean.
Fewer observations occur as we move farther from the mean.
Many parametric statistical tests assume normally distributed data or normally distributed model residuals.

Positive skew (right-skewed distribution)

Definition: A distribution with a long tail toward the right.

Characteristics:

Mean > Median > Mode.
High values pull the mean toward the right tail.
Examples: Income, waiting times, hospital length of stay.
A few very high values may substantially increase the mean and SD.

Negative skew (left-skewed distribution)

Definition: A distribution with a long tail toward the left.

Characteristics:

Mean < Median < Mode.
Low values pull the mean toward the left tail.
Example: An easy examination in which most candidates score highly but a few score very poorly.

Effect of skewness on mean, median, mode and standard deviation

Distribution	Relationship of Mean, Median and Mode	Effect on SD
Normal/symmetrical	Mean = Median = Mode	SD reflects spread around the mean
Positive/right skew	Usually Mean > Median > Mode	High values in the right tail may increase SD
Negative/left skew	Usually Mean < Median < Mode	Low values in the left tail may increase SD
Distribution with extreme outliers	Mean may be pulled toward the outliers	SD may increase substantially

Skewness does not determine standard deviation by itself. SD measures the spread of observations around the mean, not the direction of skewness.

A skewed dataset can have either a small or a large SD.
Two datasets can have the same SD but different distribution shapes.
Extreme outliers often increase SD because deviations from the mean are squared.
For markedly skewed data, median and interquartile range (IQR) are often more appropriate than mean and SD.

MEASURES OF DISPERSION

Measure	Definition	Important Point
Range	Maximum − minimum	Simple but very sensitive to extreme values
Variance	Average squared deviation from the mean, with different formulas for samples and populations	Expressed in squared units
Standard deviation (SD)	Square root of variance	Measures spread around the mean
Interquartile range (IQR)	Q3 − Q1	Spread of the middle 50%; relatively resistant to outliers
Standard error (SE)	Standard deviation of a statistic's sampling distribution	Measures precision of an estimate, not variation among individuals

For a sample mean:

SE = SD / √n

Where:

SD = Sample standard deviation
n = Sample size

Difference between SD and SE:

SD describes variability among individual observations.
SE describes the uncertainty or precision of an estimated statistic.
Increasing sample size reduces the SE of the mean, all else equal.
Increasing sample size does not necessarily reduce the population's SD.