In survey design, mutually exclusive categories refer to response options that do not overlap with one another. When assessing categorical variables, it is crucial that the provided categories are mutually exclusive so that a respondent's answer unambiguously falls into only one category.

Mutually Exclusive Categories

Exhaustive categories in a survey item provide enough options to cover all possible responses a participant might make. Since it is often impossible to list every potential answer for a categorical variable, researchers frequently include an 'Other' option with a blank space to ensure the categories remain exhaustive.

Exhaustive Categories

Categorical variables represent qualities that are measured by assigning a descriptive label or category to each individual rather than a numerical amount. Common illustrations of categorical variables include a student's chosen university major (such as Psychology, English, or Nursing), a person's nationality, their current occupation, and whether or not they are receiving psychotherapy.

Examples of Categorical Variables

A dummy variable, or indicator variable, is created to numerically represent categorical data. When a categorical feature has multiple possible discrete values, it is converted into a series of separate binary columns. For a given record, the column corresponding to its correct category is assigned a value of $$1$$, while all other dummy columns are set to $$0$$.

Dummy Variable

Which statement best describes a categorical variable in psychological research?

A categorical variable is a type of variable that represents a characteristic or quality, typically assessed by assigning a descriptive category label to each individual rather than a number. Examples include a person's chosen major, nationality, occupation, or whether they are receiving psychotherapy.

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Syracuse University

University of Michigan - Ann Arbor

Multiple regression model looks like the polynomial model which was introduced before but we will dive into it, and use this method to figure out "correlation". 
Multiple regression have more independent varialbles, or explanatory variables, to determine the output (the dependent variable)

Multiple Regression Model 

A variable is any quantity, quality, or characteristic that can change or vary across different individuals, situations, or over time. In psychological research, some variables are straightforward and simple to measure, such as age or height, while others are more complex and require careful operational definition to be studied empirically.

Variable

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

McElreath, R. (2016). Statistical rethinking: A Bayesian course with examples in R and Stan. Page 152 


Multiple Regression Model

1. Reveal spurious correlation
2. Uncover hidden association

Benefits of Multiple Regression

1. Possible to cause spurious correlation
2. Hide real associations

Shortcomings of Multiple Regression

Q: Does marriage cause divorce?
What are the variables that cause divorce?

Example: Marriage and Divorce

1. Nominate the predictor variables 
2. Make a parameter that will measure the association with the outcome for each predictor 
3. Multiply the parameter with variable and add them together

Steps of Applying Multiple Regression Model

Three good interpretative plot models:
1) Predictor residual plots. These plots show the outcome against residual predictor values. They are useful for understanding the statistical model, but not much else.
2) Posterior prediction plots. These show model-based predictions against raw data, or otherwise display the error in prediction. They are tools for checking fit and assessing predictions. They are not causal tools. 
3) Counterfactual plots. These show the implied predictions for imaginary experiments. These plots allow you to explore the causal implications of manipulating one or more variables.


Plotting multivariate posteriors.

Categorical Variable

A constant is a property or quantity that does not vary across individuals or situations, such as the speed of light. Because constants do not change, they are not the focus of psychological research questions, which instead seek to understand phenomena that vary.

Constant

A quantitative variable is a type of variable that represents a measurable quantity, typically assessed by assigning a numerical value to each individual. Common examples in psychological research include a person's height, level of talkativeness, number of siblings, or score on a depression scale.

Quantitative Variable

An abstract construct, also referred to as an intangible variable, is a psychological characteristic or internal state that cannot be directly observed, such as self-esteem, mood, or a behavioral intention. Because psychological research relies on empirical data, researchers must develop specific methods to transform these intangible concepts into quantifiable variables so they can be measured and studied.

Abstract Construct

In experimental research, an independent variable is the presumed cause in a cause-and-effect relationship. It is the specific factor that a researcher systematically manipulates or varies to observe its impact on another variable. While experiments require manipulation, in some non-experimental or factorial designs, an independent variable may simply be measured.

Independent Variable

A dependent variable is the factor in an experiment that represents the presumed effect within a causal relationship. It is the variable that researchers measure to evaluate if it changes as a direct result of the manipulation of the independent variable.

Dependent Variable

In research, a population is the entire group of individuals that the researchers seek to draw conclusions about based on their findings from the sample. 

Population

In research, a population is the entire, often very large, group of individuals that researchers are interested in studying and drawing conclusions about. Depending on the researcher's goals, a population could be as broad as all human beings or as specific as all American teenagers, children with autism, or professional athletes.

To illustrate how quantities and qualities can vary across individuals or situations, consider the students enrolled in a university course. The physical height of these students serves as a clear example of a variable because it differs from one individual to another. Similarly, their chosen major is also a variable, provided that the class consists of students who have declared different fields of study. These illustrations demonstrate how commonly variations occur in the world.

Example of a Variable: Height and Chosen Major

Non-experimental research is a broad category of research methodologies defined by the lack of manipulation of an independent variable. Instead of controlling factors, researchers simply measure variables as they naturally occur in real-world or laboratory settings. Although experimental research can provide strong evidence that changes in an independent variable cause differences in a dependent variable, non-experimental research generally cannot. Despite this inability to draw causal conclusions, non-experimental research is still considered extremely important and is utilized in cases where experimental research cannot be carried out.

Non-Experimental Research

The distribution of a variable describes how individual scores or values are spread across the different levels or categories of that specific variable within a dataset.

Variable Distribution

In psychology, a construct is a complex variable that defies direct observation or straightforward measurement—such as an attitude, ability, personality trait, or emotional state. These variables cannot be seen directly because they represent broad behavioral tendencies rather than isolated actions, and they involve hidden internal processes like specific feelings, thoughts, and nervous system activities. Ultimately, a construct acts as a theoretical summary that encapsulates these intricate sets of internal and external processes.

Psychological Construct

Measurement is the process of systematically assigning scores to individuals or objects so that these scores accurately represent a specific characteristic of interest. Crucially, this broad concept does not limit measurement to the use of specific physical instruments or tools; rather, it requires any methodical procedure that yields a representative score.

Measurement

An operational definition defines a psychological variable in terms of the exact procedures used to measure or observe it. Because most variables are abstract constructs that cannot be directly observed (e.g., stress), researchers must transform these conceptual definitions into concrete, quantifiable forms. For instance, stress could be operationally defined as a score on a standardized questionnaire, the concentration of cortisol in saliva, or the number of recent stressful life events experienced.

Operational Definition

A participant variable, also known as an individual difference, is a type of extraneous variable derived from the pre-existing characteristics of the individuals involved in an experiment. Examples of these variables include demographic factors such as gender, as well as personal attributes or habits like diet and writing ability. Because these individual differences are likely to have their own independent effect on the dependent variable, they must be controlled to prevent them from obscuring the effect of the experimental manipulation.

Participant Variable

Psychological measurement is the systematic empirical process of quantifying abstract variables and constructs—such as moods, self-esteem, or behavioral intentions—to facilitate scientific analysis. By utilizing standardized tools and methodologies, researchers can translate intangible psychological characteristics into objective, numerical data that can be rigorously evaluated and studied.

Psychological Measurement

The distribution of a variable describes how scores or values are spread out across the different levels or categories of that specific variable.

Distribution of a Variable

Which of the following best describes a variable in psychological research?

A researcher wants to study 'self-esteem' in a psychology experiment. Because self-esteem is an internal psychological state that cannot be directly observed or physically measured like height, it cannot be considered a variable in empirical research.

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