Module 1: Introduction to Biostatistics and Data Description

What is Biostatistics?

Biostatistics deals with the application of statistical methods to biological problems.
Biostatistics = Statistics for Biology

In physics or chemistry:

• Variation is mostly due to experimental error. Recall the definition of variance and standard deviation.
• Averaging over repeated measurements on the same sample eliminates variance.

In biology:

• We study naturally varying populations (organisms, cells, patients, etc.).
• This biological variation is a meaningful phenomenon and not an error.
• We must go beyond repeated measurements to understand:
  • Genetic differences
  • Environmental effects
  • Random biological processes

Biostatistics helps us to do statistics while accounting for biological variation.

Classification of Data in Biostatistics

Note: Data structure appears first because it reflects how the data was collected before analyzing what type of data was recorded or how it was measured.

Data Structures

• Cross-sectional data

  • Data collected at a single time point; Multiple subjects, one measurement per variable
  • No tracking over time
  • Example: Blood pressure of 100 patients measured today

• Time series data

  • Repeated measurements of a single subject or system over time
  • Focus is on temporal trends, patterns, fluctuations
  • Time is a key variable
  • Example: Heart rate of a patient measured every hour for 24 hours

• Longitudinal data (Combines cross-sectional and time series elements)

  • Repeated measurements of multiple subjects over time
  • Tracks within-subject changes and between-subject variation
  • Example: Glucose levels of 50 patients measured weekly for 3 months

Types and Scales of Data

Based on types and scales, biological data (or variables) can be broadly classified into:

• Numerical (Quantitative) data: These are numeric values that can be measured or counted on interval or ratio scales.

  • Interval scale: Numeric scale with equal spacing but no true zero
    Example: Temperature in °C (40°C is not twice as hot as 20°C)

  • Ratio scale: Numeric scale with a true zero point
    Example: Height of a plant (40 cm is twice as tall as 20 cm)

• Categorical (Qualitative) data: These are non-numeric and describe categories or groups measured using nominal or ordinal scales.

  • Nominal scale: Categories without any intrinsic order
    Example: Blood group, species name

  • Ordinal scale: Categories with a meaningful order, but unequal spacing between categories
    Example: Abundance of a plant species as Dominant, Abundant, Frequent, Occasional, Rare (DAFOR)

Numerical (Quantitative) Data

Quantitative data are numeric values that can be measured or counted.

They allow arithmetic operations and are of two types:

• Discrete: Countable whole numbers (e.g., number of leaves)
• Continuous: Measurable quantities that can take any real value within a range (e.g., weight, height)

Quantitative data are measured on:

• Interval scale
• Ratio scale

Examples:

• Plant height (in cm)
• Body temperature (in °C)
• Enzyme activity levels

Interval Scale

Numerical values with equal intervals, but no true zero.

Properties:

• Addition and subtraction make sense

  • Example: The difference between 40°C and 30°C (10°C) is the same as between 20°C and 10°C — both represent a 10-degree change in temperature.

• Ratios do not make sense

  • Example: 40°C is not "twice as hot" as 20°C because 0°C does not represent the absence of temperature (it's not a true zero).

Examples:

• Temperature in Celsius or Fahrenheit
• IQ scores (in psychological studies)

Ratio Scale

Numerical values with equal intervals and a true zero point
(Zero means the absence of the quantity being measured).

Properties:

• All arithmetic operations are valid: addition, subtraction, multiplication, division
• Ratios are meaningful
  • Example: A plant that is 40 cm tall is twice as tall as one that is 20 cm.
  • Example: A mouse that weighs 30 g is 1.5× heavier than one that weighs 20 g.

Examples:

• Weight of a mouse
• Height of a plant
• Concentration of glucose in blood
• Cell count in a sample

Categorical (Qualitative) Data

Non-numeric data used to label categories or groups.

Measured using:

• Nominal scale
• Ordinal scale

Examples:

• Blood types (A, B, AB, O)
• Species name (Arabidopsis, Zea mays)
• Eye color

Nominal Scale

Categories with no intrinsic order.
They are labels used for naming or classification.

Operations allowed:

• Counting: How many samples belong to each category
  • Example: 12 samples are labeled as "neuron", 8 as "glial"
• Mode: Identify the most frequent category
  • Example: The most common blood group is "O"

Not allowed:

• Averaging or ranking
  • Example: You cannot compute an "average species"
  • Sorting genotypes alphabetically doesn't imply biological order

Examples:

• Genotype (AA, Aa, aa)
• Cell type (neuron, glial, epithelial)
• Blood group (A, B, AB, O)

Ordinal Scale

Categories with a meaningful order, but unequal spacing between levels.

Operations allowed:

• Ranking: You can sort or order the categories
  • Example: "Severe" disease is ranked higher than "Mild"
• Median: You can find the middle-ranked value in ordered data

Not allowed:

• Arithmetic operations
  • Example: You can’t say "Moderate" is the average of "Mild" and "Severe"
  • The difference between "Abundant" and "Frequent" is not equal to the difference between "Frequent" and "Occasional"

Examples:

• DAFOR scale: Dominant > Abundant > Frequent > Occasional > Rare
• Disease severity: Mild < Moderate < Severe
• Tumor grading: Grade I, II, III, IV (increasing severity)

Data Representation

Data can be represented in two main forms:

• Long Form Representation for the Raw Data

  • Collected as-is from observations or experiments
  • Typically stored in tables with rows = observations, columns = variables
  • Both categorical and numerical are presented as tables in raw form

• Compact Form Representation to Summarize the Raw Data

  • Useful for description, visualization, and comparison
  • Particular compact form depends on whether the variable is categorical or numerical

Long Form: Tables

Raw data is often recorded in tabular form:

This format is:

• Used for data entry and storage
• Directly imported into statistical tools (Excel, R, Python/pandas)
• The basis for further analysis and summarization

Compact Form: Categorical Data

Categorical variables are summarized using frequency tables.

Example: Abundance levels

Can be visualized as:

• Bar plots
• Pie charts

Compact Form: Numerical Data

Numerical data are summarized using descriptive statistics:

• Measures of central tendency:

  • Mean, Median, Mode

• Measures of spread:

  • Range, Variance, Standard Deviation, IQR

Example: Plant Height (cm)

• Mean = 42.3
• Median = 38.5
• SD = 12.1

Can be visualized as:

• Histograms
• Boxplots