BIOSTATISTICS | ZOOL-600-601 LECTURE 4
Instructor: Dr. Waheed Ali Panhwar | University of Sindh BS Zoology — Final Year
Categorical & Non-Categorical Data
Connection to Lecture 3: In Lecture 3, you learned that variables are either qualitative or
quantitative. Lecture 4 applies the same logic to data. Categorical data comes from
qualitative variables. Non-categorical data comes from quantitative variables. The new
content in this lecture is the two subtypes of each: Nominal and Ordinal (for categorical),
and Discrete and Continuous (for non-categorical).
DATA
CATEGORICAL DATA NON-CATEGORICAL DATA
Qualities, labels, categories. Cannot be Actual numbers with mathematical meaning. Can
averaged. be averaged and calculated.
NOMINAL ORDINAL DISCRETE CONTINUOUS
No order between Has order, but unequal Counted. Whole Measured. Any value,
categories gaps numbers only. incl. decimals.
Blood group, species Disease severity, No. of eggs, teeth, Weight, height, length,
name, sex, ID number, education level, parasites, students temperature, age, time
habitat type satisfaction, aggression
level
1. Categorical Data
Definition:
Categorical data represents qualities, labels, or group memberships rather than actual
numbers. It tells you what type or which category something belongs to. Even when
numbers appear as labels (like ID #47 or jersey numbers), they carry no mathematical
meaning — you cannot add, subtract, or average them meaningfully.
Key Characteristics: Data is placed into named groups or classes. Arithmetic operations are not
meaningful. Analysis uses frequencies (counts) and percentages. The most common category can be
found (the mode).
Subtype 1 — Nominal Data
Definition:
Nominal data is categorical data where the categories have absolutely no natural order or
ranking. The groups are simply different labels — none is higher, lower, better, or worse
than another. The word 'nominal' comes from the Latin word for name, which is a helpful
reminder.
Key test for nominal: Can you logically say one category is 'more than' or 'ranked above' another? If
no — it is nominal.
• Zoology Examples: Species names (Apis mellifera vs Apis cerana — neither is ranked above
the other), sex of an animal (male/female), habitat type (forest/wetland/desert), blood group (A,
B, AB, O), river system (Indus or Hub), animal ID numbers.
Common Mistake: ID numbers and jersey numbers look like quantitative data because
they are written as numbers, but they are nominal categorical data. ID #47 is not
mathematically greater than ID #23 — it is just a different label. Any time a number is used
, purely as a name tag, it is nominal.
Subtype 2 — Ordinal Data
Definition:
Ordinal data is categorical data where the categories have a meaningful natural order or
ranking, but the gaps between the ranks are NOT equal or measurable. You know which
category is higher, but you cannot say by exactly how much.
Key test for ordinal: Can you rank the categories in a logical order? If yes — are the gaps between
ranks measurable and equal? If no to the second question — it is ordinal.
• Zoology Examples: Disease severity (Mild → Moderate → Severe), aggression level (Low →
Medium → High), body condition score (Poor → Fair → Good → Excellent), education level
(Primary → Secondary → Higher).
Key Point: The crucial difference between nominal and ordinal: in nominal data, the
categories are just different. In ordinal data, the categories are different AND they have a
ranking. But neither type allows you to measure the exact distance between categories —
that only becomes possible in Lecture 5 with interval and ratio scales.
Nominal Data Ordinal Data
Categories with NO natural order Categories WITH a natural order/ranking
Cannot say one is 'more than' another Can say one is higher or lower than another
Cannot rank the categories Can rank, but gaps between ranks are
unequal
Examples: species name, sex, blood group Examples: disease severity, aggression
level
Blood group A is not 'more' than group O Severe IS worse than Moderate — by how
much? Unknown
2. Non-Categorical Data
Definition:
Non-categorical data consists of actual numbers that represent genuine measurable or
countable quantities. The numbers have real mathematical meaning — you can add them,
subtract them, multiply them, divide them, and calculate averages. This is the type of data
used in most statistical calculations.
Key Characteristics: Numbers carry real mathematical meaning. All arithmetic operations are valid.
Mean, standard deviation, and most other statistical measures can be calculated. Analysis is much
richer than categorical data.
Subtype 1 — Discrete Data
Definition:
Discrete data is obtained by COUNTING. It can only take whole number values — fractions
and decimals are not possible because you are counting individual, indivisible units.
• Zoology Examples: Number of eggs in a nest (3, 5, 8 — never 3.7), number of parasites on a
fish body, number of teeth in a crocodile's jaw, number of students in a class, number of insect
species found in a habitat survey.
Common Mistake: Age in years is a very common trap. Students often say 'age is
discrete because we count years.' But age is CONTINUOUS — a crocodile can be 7.5
years old, or 12.3 years old. We report age as whole numbers in everyday speech, but the
Instructor: Dr. Waheed Ali Panhwar | University of Sindh BS Zoology — Final Year
Categorical & Non-Categorical Data
Connection to Lecture 3: In Lecture 3, you learned that variables are either qualitative or
quantitative. Lecture 4 applies the same logic to data. Categorical data comes from
qualitative variables. Non-categorical data comes from quantitative variables. The new
content in this lecture is the two subtypes of each: Nominal and Ordinal (for categorical),
and Discrete and Continuous (for non-categorical).
DATA
CATEGORICAL DATA NON-CATEGORICAL DATA
Qualities, labels, categories. Cannot be Actual numbers with mathematical meaning. Can
averaged. be averaged and calculated.
NOMINAL ORDINAL DISCRETE CONTINUOUS
No order between Has order, but unequal Counted. Whole Measured. Any value,
categories gaps numbers only. incl. decimals.
Blood group, species Disease severity, No. of eggs, teeth, Weight, height, length,
name, sex, ID number, education level, parasites, students temperature, age, time
habitat type satisfaction, aggression
level
1. Categorical Data
Definition:
Categorical data represents qualities, labels, or group memberships rather than actual
numbers. It tells you what type or which category something belongs to. Even when
numbers appear as labels (like ID #47 or jersey numbers), they carry no mathematical
meaning — you cannot add, subtract, or average them meaningfully.
Key Characteristics: Data is placed into named groups or classes. Arithmetic operations are not
meaningful. Analysis uses frequencies (counts) and percentages. The most common category can be
found (the mode).
Subtype 1 — Nominal Data
Definition:
Nominal data is categorical data where the categories have absolutely no natural order or
ranking. The groups are simply different labels — none is higher, lower, better, or worse
than another. The word 'nominal' comes from the Latin word for name, which is a helpful
reminder.
Key test for nominal: Can you logically say one category is 'more than' or 'ranked above' another? If
no — it is nominal.
• Zoology Examples: Species names (Apis mellifera vs Apis cerana — neither is ranked above
the other), sex of an animal (male/female), habitat type (forest/wetland/desert), blood group (A,
B, AB, O), river system (Indus or Hub), animal ID numbers.
Common Mistake: ID numbers and jersey numbers look like quantitative data because
they are written as numbers, but they are nominal categorical data. ID #47 is not
mathematically greater than ID #23 — it is just a different label. Any time a number is used
, purely as a name tag, it is nominal.
Subtype 2 — Ordinal Data
Definition:
Ordinal data is categorical data where the categories have a meaningful natural order or
ranking, but the gaps between the ranks are NOT equal or measurable. You know which
category is higher, but you cannot say by exactly how much.
Key test for ordinal: Can you rank the categories in a logical order? If yes — are the gaps between
ranks measurable and equal? If no to the second question — it is ordinal.
• Zoology Examples: Disease severity (Mild → Moderate → Severe), aggression level (Low →
Medium → High), body condition score (Poor → Fair → Good → Excellent), education level
(Primary → Secondary → Higher).
Key Point: The crucial difference between nominal and ordinal: in nominal data, the
categories are just different. In ordinal data, the categories are different AND they have a
ranking. But neither type allows you to measure the exact distance between categories —
that only becomes possible in Lecture 5 with interval and ratio scales.
Nominal Data Ordinal Data
Categories with NO natural order Categories WITH a natural order/ranking
Cannot say one is 'more than' another Can say one is higher or lower than another
Cannot rank the categories Can rank, but gaps between ranks are
unequal
Examples: species name, sex, blood group Examples: disease severity, aggression
level
Blood group A is not 'more' than group O Severe IS worse than Moderate — by how
much? Unknown
2. Non-Categorical Data
Definition:
Non-categorical data consists of actual numbers that represent genuine measurable or
countable quantities. The numbers have real mathematical meaning — you can add them,
subtract them, multiply them, divide them, and calculate averages. This is the type of data
used in most statistical calculations.
Key Characteristics: Numbers carry real mathematical meaning. All arithmetic operations are valid.
Mean, standard deviation, and most other statistical measures can be calculated. Analysis is much
richer than categorical data.
Subtype 1 — Discrete Data
Definition:
Discrete data is obtained by COUNTING. It can only take whole number values — fractions
and decimals are not possible because you are counting individual, indivisible units.
• Zoology Examples: Number of eggs in a nest (3, 5, 8 — never 3.7), number of parasites on a
fish body, number of teeth in a crocodile's jaw, number of students in a class, number of insect
species found in a habitat survey.
Common Mistake: Age in years is a very common trap. Students often say 'age is
discrete because we count years.' But age is CONTINUOUS — a crocodile can be 7.5
years old, or 12.3 years old. We report age as whole numbers in everyday speech, but the
