Estatística Psicobio I 2026 #02 - Tipos de Variável e Medidas Descritivas I

Main ideas & lessons

1) Course framing: from measurement theory to operational statistics

• The instructor recalls that the previous class introduced measurement theory and now the course will become more “operational” (i.e., directly useful for doing statistics).
• Measurement theory’s central question: what does it mean to measure?
• Key philosophical point: in real-world phenomena you can decompose a phenomenon into attributes, but you generally cannot reconstruct the original phenomenon from attributes (the “return trip” is not counted in this course).
• This decomposition is enabled by rulers (i.e., measurement tools/instruments) that transform:
  • phenomena → attributes
• Each ruler must have:
  • Validity: measures what you intend to measure
  • Precision / granularity: discriminates between the groups/levels you need

2) Why this matters for psychology/psychobiology

• Measurement theory is described as closer to experimental psychology than typical undergraduate “statistics only” training.
• The instructor rejects the idea that tests reduce people to mere numbers. Instead:
  • statistics/measurement deal with attributes of phenomena, not “understanding the whole person.”
• They warn about “two-way/generalizing” thinking and emphasize building a bijection two-way approach across the curriculum, but gradually across semesters (course 1, 2, 3).

3) Probability rules connect to algebra and function/logic

• The instructor links probability rules:
  • AND corresponds to multiplication
  • OR corresponds to addition
• This is presented as a way to connect logic ↔ algebra ↔ functions (and mentions Cartesian “equals”/equivalence relations).

4) Variables and factors (research-question decomposition)

• A research question/phenomenon of interest is first broken down into:

  • Variables: directly observable quantifiable data points Examples: age, income, weight

  • Factors: groupings/constructs derived from the variables to represent what is not directly observed Examples: intelligence, satisfaction

5) Core instruction chain for statistics readiness

• Once you have variables/factors, you identify types of variables (what statistics classifies as continuous/discrete/categorical, etc.).
• Variable types determine:
  • the descriptive measures you use (e.g., mean, variance, SD)
  • the statistical tests later

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Detailed methodology / “how to proceed” (step-by-step)

Step 1: Build attributes from phenomena using valid, precise “rulers”

Ensure your measurement procedure has:

• Validity (measures the intended attribute)
• Precision/granularity (enough resolution for your comparisons)

Step 2: Decompose the research question into variables/factors

Convert the phenomenon into:

• Variables = observable, quantifiable points
• Factors = groupings derived to represent latent or non-directly observed constructs

Step 3: Choose variable types conceptually before running tests

Identify whether each variable is:

• Quantitative (numeric) or Qualitative (categorical) Then identify the finer categories within them (e.g., continuous, discrete, ordinal, nominal).

Step 4: Choose descriptive measures based on variable type

• For continuous/discrete variables: start with descriptives like:
  • Mean (expected value)
  • Variance
  • Standard deviation
• Later, categorical variables will use other descriptives (e.g., proportions).

Step 5: Use descriptive measure → test selection mapping

• Test choice depends on variable types, not vice versa.
• Examples:
  • Two continuous variables → correlation / linear regression
  • Both categorized (categorical vs categorical) → chi-square (Q² mentioned) / logistic regression alternatives
  • One continuous + one categorical → ANOVA or linear regression can apply

Step 6 (important data-collection tip): collect as “close to continuous” as possible

Practical recommendation:

• If unsure how to measure a variable, collect the most informative continuous version first.
• From continuous data you can down-convert to discrete/ordinal/nominal,
  • but you cannot accurately go back (information loss is irreversible).
• Example:
  • Instead of collecting only BMI category, collect height + weight, so you can compute BMI at whatever granularity you later need.

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Variable types: definitions + relationships

A) Quantitative variables

1) Continuous variable - Defined by many possible measurement levels. - Example: height - Emphasis: the “continuous” ideal contains more information than what finite tools can measure.

2) Discrete variable (counting) - Based on whole numbers (counting events). - Examples: - number of cigarettes per day - number of accidents - Mentioned also: BMI is continuous in nature but becomes discrete when measured/rounded.

B) Qualitative variables

1) Ordinal variable - Categories with an explicit order. - Example: nutritional status - eutrophic < overweight < obese - Example transformation: BMI (continuous) → categorical ranges → ordinal nutritional status categories.

2) Nominal variable - Categories with no order. - Examples: - sex (man/woman) - soccer team / football team - city of birth - Example transformation: - ordinal/nutritional categories can be reduced to unordered labels (e.g., “adequate vs inadequate”).

3) “DAME” variable (binary/presence-absence) - Presented as a special qualitative variable with: - only one meaningful category: presence vs absence - Example: hypertension - has hypertension vs does not - Conceptual distinction: - binary nominal with two categories (e.g., male vs female) is different from “dame,” where “absence” groups everyone not in the presence category. - Also clarified: - “dame” is generally used more in regression later in the course (not heavily now).

C) The “chain/continuum of information” among variable types

• Overall rule:
  • Variable types form a continuum of information
• You can go down:
  • continuous → discrete → ordinal → nominal → dame (presence/absence)
• You cannot go back up to recover lost information.

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Descriptive measures: what they are and why they matter

1) Mean (Average) = expected value

• Calculation for a set:
  • average = (sum of observations) / n
• Conceptual point:
  • the average is not the “exact true value” of any single hidden individual.
  • it is an expected value that reduces uncertainty compared to saying “I don’t know.”
• Motivation (psychology/social-judgment framing):
  • People often default to attribution (guessing based on self-related biases) when they lack information.
  • A scientific approach uses methods (like average) to reduce uncertainty.

2) Attribution vs Judgment (psychology tie-in)

• Judgment: estimating based on what you can perceive/observe.
• Attribution: estimating when you lack relevant information, producing explanations more about the person/respondent than about the target.
• Attribution is framed as a basis for prejudice and magical thinking.

3) Variance: three definitions explained

Core meaning:

• Variance measures how much data fluctuate around the mean (oscillation).

Definitions provided:

1. How much the data deviate from the mean on average (conceptual)
2. Variance formula: average of the squared deviations
   • squaring prevents positive/negative deviations from canceling out
3. Reliability of the mean’s expected-value guess
   • small variance → mean is a good representative guess
   • large variance → mean is less reliable because data spread widely

Formula shown:

• variance = ( Σ (xi − mean)² ) / n
• Note: the instructor says n−1 will be addressed later.

4) Standard deviation: variance’s square root

• Defined as:
  • standard deviation = √variance
• Same conceptual role as variance, but:
  • it’s in the same unit as the original data (more convenient to interpret)
• Repeated conclusion:
  • Use mean + standard deviation to interpret data properly.
  • Average alone is often misleading in media/news.

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Confidence intervals and statistical comparison (planned next)

• The instructor foreshadows:
  • mean/variance/SD are descriptive for your sample
  • to infer about the population, you use confidence intervals
• Statistical differences are framed as:
  • not just one-point differences,
  • but differences that consider intervals and variability (confidence intervals), i.e., an “interval overlap/touching” logic.

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Speakers / sources featured

• Unnamed instructor (main speaker; appears to be the course teacher)
• Rafael
• Marcelo
• Gilmara (asks about factors vs attributes)
• Maira (asks/mentioned in context of learning evaluation)
• Lucas (commenter; relates ordinal/nominal confusion correction)
• Renan (asks about acceptable standard deviation)
• Tatiana (mentions about advertisement/configuration)
• Júlio (participates in the height/guessing example)
• Miranda (comment referenced in the attribution/judgment discussion)
• Fritz Heider (author related to attribution concepts)
• Piaget (children saying “I don’t know” and chance)
• Gödel (incompleteness theorem framing)
• Descartes (origin of the equals sign / Cartesian graph reference)
• “Blue Archer” (referenced participant/questioner; identity not clarified)
• John (mentioned during variance comparison discussion)