PUBH 8500 MEASUREMENT STUDY GUIDE
MIDTERM 2024
Levels of Measurement
Data are collected and coded into numbers
Levels define what the numbers assigned to variables represent
There are 4 levels or scales
o Nominal: numbers represent assigned or named categories (e.g., 1 = male, 2 =
female)
o Ordinal: numbers represent ranked or ordered categories that are not necessarily
equal in size (e.g., 1 = low, 2 = medium, 3 = high)
o Interval: numbers represent values of equal units (e.g., temperature, age in years).
Note: temperature of 0°C is not the same as 0°F and 0° on both scales does not mean there is
no temperature; age in years is not ratio because 0 years old is anywhere between birth and
the day before the first year.
o Ratio: numbers represent values of equal units and there is a set zero point
(height, weight, blood pressure)
Note: with ratio data ONLY, values can be compared as ratios
(e.g., a risk factor doubled the odds of disease, a diet supplement resulted in a 5% weight
loss)
Rules:
Higher level data can be converted to a lower level
Examples:
o ratio data for weight loss can be arranged in 5 lb. interval groups;
o interval age in years can be converted to ordinal age groups such as 5-17, 18-44,
45-64, >65 years;
o ordinal ranks can be combined in nominal categories as in 1 = agree and strongly
agree, 2 = disagree and strongly disagree, 3 = no opinion, (where there is no
specific order)
Lower level data cannot be converted to a higher level
Data types:
There are 3 data types
o Categorical: nominal and ordinal data; numbers represent categories
(examples: gender, race/ethnicity)
o Ordinal: categorical data that are ranked; not everyone makes this distinction
(examples: low, medium, high)
o Continuous: interval and ratio data; numbers represent numerical values
(examples: age, height, weight)
Rules (extension of the rules for levels of measurement):
o Continuous data can be transformed to categorical data
o Categorical data cannot be transformed to continuous data
, Descriptive Statistics
Descriptive statistics describe the data
Types of descriptive statistics
o Frequency data
▪ How often (or frequent) a measurement occurs in the sample or population
▪ Used primarily with categorical data
▪ Often presented as numbers (sample “n” or population “N”) and
percentages (%) of observations
Examples: n (%) male, n (%) female in a cohort;
N (%) age <18, N (%) age 18-44, N (%) age 45-64, N (%) age ≥65 in a
population
▪ Can describe relationships between two variables
Examples: a study showing n (%) females with BMI ≥30 and n (%) males
with BMI ≥30;
N (%) <18 years who have smoked, N (%) <18 years who never smoked
▪ Usually presented in tables (tabular format)
o Measures of central tendency
▪ Show where the bulk of the data lie; where most of the data are centered.
▪ Includes the Mean, Median, and Mode
▪ The level of measurement can determine which descriptive statistic can be
used
Mean
Sum of measurement values divided by the number of observations
Should only be used with continuous data
Is affected by extreme values
Median
The midpoint or the center of all data in a variable level
Can be used with continuous and ordinal data, but NOT nominal data
There are equal numbers of observed values above and below the
median
Is not summed
Not affected by extreme values; always remains in the center
Mode
The most frequently occurring value
Can be used with ALL data types – categorical, ordinal AND
continuous
o Measures of variability or dispersion
▪ Includes Range and Percentiles, Variance and Standard Deviation
MIDTERM 2024
Levels of Measurement
Data are collected and coded into numbers
Levels define what the numbers assigned to variables represent
There are 4 levels or scales
o Nominal: numbers represent assigned or named categories (e.g., 1 = male, 2 =
female)
o Ordinal: numbers represent ranked or ordered categories that are not necessarily
equal in size (e.g., 1 = low, 2 = medium, 3 = high)
o Interval: numbers represent values of equal units (e.g., temperature, age in years).
Note: temperature of 0°C is not the same as 0°F and 0° on both scales does not mean there is
no temperature; age in years is not ratio because 0 years old is anywhere between birth and
the day before the first year.
o Ratio: numbers represent values of equal units and there is a set zero point
(height, weight, blood pressure)
Note: with ratio data ONLY, values can be compared as ratios
(e.g., a risk factor doubled the odds of disease, a diet supplement resulted in a 5% weight
loss)
Rules:
Higher level data can be converted to a lower level
Examples:
o ratio data for weight loss can be arranged in 5 lb. interval groups;
o interval age in years can be converted to ordinal age groups such as 5-17, 18-44,
45-64, >65 years;
o ordinal ranks can be combined in nominal categories as in 1 = agree and strongly
agree, 2 = disagree and strongly disagree, 3 = no opinion, (where there is no
specific order)
Lower level data cannot be converted to a higher level
Data types:
There are 3 data types
o Categorical: nominal and ordinal data; numbers represent categories
(examples: gender, race/ethnicity)
o Ordinal: categorical data that are ranked; not everyone makes this distinction
(examples: low, medium, high)
o Continuous: interval and ratio data; numbers represent numerical values
(examples: age, height, weight)
Rules (extension of the rules for levels of measurement):
o Continuous data can be transformed to categorical data
o Categorical data cannot be transformed to continuous data
, Descriptive Statistics
Descriptive statistics describe the data
Types of descriptive statistics
o Frequency data
▪ How often (or frequent) a measurement occurs in the sample or population
▪ Used primarily with categorical data
▪ Often presented as numbers (sample “n” or population “N”) and
percentages (%) of observations
Examples: n (%) male, n (%) female in a cohort;
N (%) age <18, N (%) age 18-44, N (%) age 45-64, N (%) age ≥65 in a
population
▪ Can describe relationships between two variables
Examples: a study showing n (%) females with BMI ≥30 and n (%) males
with BMI ≥30;
N (%) <18 years who have smoked, N (%) <18 years who never smoked
▪ Usually presented in tables (tabular format)
o Measures of central tendency
▪ Show where the bulk of the data lie; where most of the data are centered.
▪ Includes the Mean, Median, and Mode
▪ The level of measurement can determine which descriptive statistic can be
used
Mean
Sum of measurement values divided by the number of observations
Should only be used with continuous data
Is affected by extreme values
Median
The midpoint or the center of all data in a variable level
Can be used with continuous and ordinal data, but NOT nominal data
There are equal numbers of observed values above and below the
median
Is not summed
Not affected by extreme values; always remains in the center
Mode
The most frequently occurring value
Can be used with ALL data types – categorical, ordinal AND
continuous
o Measures of variability or dispersion
▪ Includes Range and Percentiles, Variance and Standard Deviation
