Biostatistics: Dentistry Statistics 24-25

• The course is titled STATISTICS 24-25, which is designed for the Bachelor of Science Degree in Dentistry, and is taught by Francesc Montoro.
• Montoro can be contacted at [email protected]

Biostatistics

• Biostatistics uses statistical methods for scientific research in health fields like medicine, biology, and public health.

Statistics Defined

• Statistics involves data collection, analysis, interpretation, presentation, and organization.
• Statistics is a math branch and scientific method, used to understand large data, draw conclusions, make predictions, and inform decisions.
• Statistics involves systematization, collection, organization, and presentation of data related to a phenomenon, characterized by variability or uncertainty, for systematic study.
• The aim of statistics involves deducing laws governing these phenomena, and using it for forecasting, decision-making, and drawing conclusions (=information).
• Statistics is used to describe characteristics (variables) of a group and their relationships.
• It creates models for different phenomena (variables) and forecasts in uncertain situations and it allows statements about a population from a sample, with a certain probability level.

The Scientific Method

• Observation is the first step, followed by hypothesis formulation, then experiment design.
• Data collection and analysis follow experiment design, then conclusions are drawn.

Stages of a Statistical Study

• Problem statement is followed by data collection, then data organization, tabulation, and graphs.
• Description of characteristics known as descriptive statistics follows, then formal analysis.
• Data leads to information using descriptive statistics.

Course Outline

• The course covers descriptive statistics including introduction, 1 variable analysis, 2 variable analysis.
• Probability will be examined including basic concepts and random variables, and normal distribution.
• Inferential Statistics will be studied, including parameter estimation and hypothesis testing.

Descriptive Statistics Goals

• To condense and simplify dataset information using graphical methods and numerical measures.
• Descriptive statistics provides a foundation for data analysis and an initial understanding of the dataset's characteristics.

Population vs. Sample

• Population refers to the entire group of individuals, items, or data points of interest, used for drawing conclusions or making inferences.
• Populations tend to be too large for comprehensive study, making a complete survey impractical typically.
• A study of an entire population is called a census.
• A sample is a subset of the population accessed for gathering observations or measurements.
• Ideally, a sample should be representative of the population, reflecting its characteristics and diversity, usually chosen through systematic or random methods.

Basic Definitions

• Population is a set of elements on which a characteristic is studied.
• Sample is a representative subset of the population.
• Individual refers to each element of the population, which is a statistical unit.
• Variable is what is measured, representing a characteristic of the unit.

Steps in a Statistical Study

• Hypothesizing involves identifying a population, for example: smokers and non-smokers.
• Smokers have "lower" work performance than non-smokers in terms of frequency or average duration.
• Quantify confidence in inference, example: 95% confidence level.
• Decide what data to collect through experimental design.
• Samples include working-age smokers and non-smokers, consider exclusion criteria and chronic illnesses.
• Variables include number and duration of work absences, gender, occupational sector etc.
• Collect the data via sampling, decide whether to stratify or use systematic techniques.
• Describe (summarize) the data by calculating the average duration of absence in smokers and non-smokers, then the percentage of absences by smokers by gender using frequencies, graphs, etc.
• Make an inference about the population.
• Smokers are absent an average of at least 10 more days per year than non-smokers.

Experimental Design Practice

• Define population, sample and variables for studies wanting information from the population about weight control, environmental conservation, people who visit the physiotherapist, hábitos de consumo de alcohol, leisure habits during free time and physical activity practices.
• Decide what is to be measured, how often and to whom?

Variables Explained

• A variable is an observable characteristic that varies among different individuals in a population.
• Information known about each individual is summarized in variables.
• Defining and measuring variables accurately is crucial, as inaccuracies affect all subsequent statistics.
• Variables include blood type (Nominal Qualitative Variable), self-declared happiness level (Ordinal Qualitative Variable).
• Number of children (Discrete Quantitative Variable) and height (Continuous Numeric Variable).
• Some variables are hard to measure, for example: height, age, and blood glucose.
• Some variables, for example: marital status and gender may seem 'obvious' but are not necessarily straightforward.
• Some variables are complex to define and measure, for instance: social class, educational level, political ideology, and religiosity.

Types of Variables

• Qualitative is a variable in which their values cannot be naturally associated with numbers, meaning you cannot perform algebraic operations on them.
• Quantitative or Numeric is a variable that is or numeric.

Types of Qualitative Variables

• Nominal are qualities and cannot be ordered, examples: Sex, Blood Type, Religion, Nationality, Smoking (Yes/No).
• Ordinal are ordered, examples: Satisfaction Level, Pain Intensity, Preferences.

Types of Quantitative Variables

• Discrete takes on unique or integer values, examples, number of children, number of cigarettes, number of injuries.
• Continuous can have an infinite number of intermediate values between any two values, examples: Height, Intraocular Pressure, Dosage of administered medication, Age.

Measurement Scales

• Variables are categorized into nominal, ordinal, interval and ratio scales.
• Measurement scales categorize ways to measure and quantify variables.
• Each scale has properties and is statistically analyzed using different tests and measuring methods.

Nominal Scale

• Classifies or identifies elements into exhaustive and mutually exclusive categories.
• Establishing an order relationship between categories or mathematical operations is not possible.
• A category is not "greater or smaller" than another; they are different.
• Nominal scale is associated with qualitative variables and cannot perform arithmetic operations on its values.
• Sex and profession, pain location and place of residence, Apllied Technique and marital status, postal code and phone number are examples of nominal scales.

Ordinal Scale

• Allows for classifying or identifying elements into exhaustive and mutually exclusive categories.
• It is possible to establish an order relationship between the categories, being able to classify elements from higher to lower.
• Mathematical operations are not appropriate, as the values have a specific level, but arithmetic operations cannot be performed between them.
• Product Rating (Terrible – Bad - Average – Good – Excellent), Education Level (Primary – Secondary - Higher Education – Postgraduate), Likert Scales (Not Satisfied – Slightly Satisfied – Moderately Satisfied – Satisfied – Very Satisfied) are examples of ordinal scales.

Interval Scale

• Allow for addition and subtraction operations, includes the notion of order.
• The difference between values is in units with the same absolute and constant value across the scale.
• There is no natural zero value.
• There is an order among the values of the variable and a notion of distance, although complex operations are not performed.
• The zero or starting point is not natural and is more of a reference point.
• Temperatures and Personal Ratings, IQ Scores and Psychological Scales: are examples of interval scales.

Ratio Scale

• The most comprehensive measurement scale.
• Includes the notion of order and allows for all mathematical operations.
• It has a real zero point at its origin, therefore, it allows for comparison of values by ratio.
• Magnitude has a PHYSICAL MEANING; there is an absolute zero, there is an order, and you can determine how many times one value is greater than another.
• Number of, Weight, Height, Distance between, blood pressure and age examples of ratio scale.

Measurement Scale Importance

• The scale type is a fundamental criteria for selecting data analysis techniques.
• If a variable can be measured in various ways, use the level of measurement that allows more powerful tests.
• Achieve measuring the phenomenon with utmost precision.

Measurement Scale Examples

• The painful body area (e.g., back, neck, ...) is a Nominal Qualitative Variable, measured at the nominal level.
• The number of patients treated in a day is a Discrete Quantitative Variable, measured at the ratio level.
• The monthly salary is a Continuous Quantitative Variable, measured at the ratio level.
• The postal code of a locality is a Nominal Qualitative Variable, measured at the nominal level.
• The blood pressure of a patient is a Continuous Quantitative Variable, measured at the ratio level.
• The degrees offered at a university Qualitative Variable, measured at the nominal level.
• The order of preference for various products is an Ordinal Qualitative Variable, measured at the ordinal level.
• The severity status of a patient is an Ordinal Qualitative Variable, measured at the ordinal level.
• The body temperature of a patient is a Continuous Quantitative Variable, measured at the interval level.
• The anniversary date of an event is a Discrete Quantitative Variable, measured at the ratio level.