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Intro to Stats
Statistics: Chapter 1
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Undergraduate 2
11/28/2024

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Term
Sample and population
Definition

  1. Population: The set of all individuals of interest in a study; this set must always be identified in research.
  2. Sample: A set of individuals selected from a population to represent that population (must also be identified).
  3. Relationship between population and sample: Sample is used to represent the population in a research study, but the findings from said study are generalized to the population. The same goes for population parameter and sample statistic.
Term
Descriptive & inferential statistics
Definition

  1. Descriptive statistics: statistical procedures used to summarize, organize, and simplify data via a table, graph., or computing an average (gives a single descriptive value for a data set).
  2. Inferential statistics: Methods that use sample data to make general statements about a population.

Term

 sampling error and how this concept creates the fundamental problem that inferential statistics must address

Definition

  1. Sampling error: the discrepancy (error) that exists between sample statistic and the corresponding population parameter (ex. Margin of error, sample proportion, chance). Does not mean it's wrong, just imprecise.
    1. If samples are smaller than populations, and therefore can lead to imprecisions, why do we use them at all? Because it's impossible to test all members of a population.
  2. What is the problem with inferential statistics?: A sample represents a population by testing a small part of the population, as such, results derived from testing the sample cannot fully apply to the entirety of the population. There's a risk factor in generalizing (sampling error)

Term
Variables & data
Definition

  • Variable: A characteristic or condition that changes or has different values for different individuals; must be measurable or observable.
  • Datum/score/raw score: a single measurement or observation that can be used to track changes in a variable or individual.
  • Data set/data: A collection of measurements or observations
  • Why can populations be referred to as sample of scores?: Because each individual in a study is measured by a score, and every sample (population) of individuals produces a corresponding sample of scores.

Term
Methods of research and the graphs that represent them
Definition

  1. Descriptive method: typically one variable of interest is observed/measured to allow us to make frequency claims (%, rate, average etc.)
  2. Correlational research/method: Observing the relationship between two (or more) variables on one group of individuals to see if they're related -> Scatter plots (graph) are commonly used.
    1. Limitations: does not provide an explanation or cause-and-effect relationship.
  3. Experimental method/research strategy
  4. Nonexperimental method

Term

Experimental method/research strategy

Definition

  1. Experimental method/research strategy: Demonstrates a cause-and-effect relationship between two variables (or more). Can make causal claims.
    1. Manipulation: Having an independent (not an experiment unless this is manipulated) and dependent variable.
    2. Control: Making sure no extraneous variables influence the relationship being examined, otherwise the study is confounded (impossible to reach an unambiguous conclusion due to multiple conclusions).
      1. Participant variables: characteristics such as age, gender etc. must be the same across a sample.
      2. Environmental variables: characteristics associated with the environment such as lighting, time of day, and weather conditions.
Term
Three basic techniques used to control participant and environmental variables
Definition

 

    1. Random assignment: each participant has an equal chance of being assigned to each of the treatment conditions.
    2. Matching: Making sure that every group has the same proportion of a characteristic.
    3. Holding them constant: Making sure each group has the same characteristics.

Term
Nonexperimental method
Definition

  1. Use the same kind of data found in an experiment (independent/dependent variables) but the variables are naturally occurring and the researcher just observes. Why are they not true?
    1. Nonequivalent groups: Researcher lacks control assignment over study; participant and environmental variables. (ex. Boys vs. Girls with no regard to age).
    2. Pre-post study: evaluation of a treatment's effect by comparing observations before and after the treatment.

Term

  1. Define independent, dependent, and quasi-independent variables

Definition
  1. Independent variable: the variable being manipulated or put through antecedent conditions.
  2. Dependent variable: the variable being measured/observed.
  3. Quasi-independent variable: a term used in nonexperimental studies that refers to an independent variable that isn't controlled; examined for their influence on a dependent variable. Also make association claims.
Term
How does an experimental study differ from a correlational study?
Definition

An experimental study measures the impact of one variable to another variable within a group (cause-and-effect) while a correlational study applies two variables on each individual and tests for a relationship (correlation).

Term
Why are correlational studies examples of nonexperimental research?
Definition

Because they feature nonequivalent groups (ex: Table 1.1).

Term
About Non-numerical variables
Definition

characteristics that have no numerical value (ex. Male or female). Proportions are used for inferential statistics (ex. 60% of males prefer texting).

Term
Constructs and operational definitions
Definition

  1. Constructs: internal attributes that cannot be directly observed but are useful for describing and explaining behavior.
  2. Operational definitions
    1. identifies a measurement procedure for measuring an external behavior and uses the result to measure a construct.
    2. Operational definitions are developed for constructs because what isn't tangible, and therefore cannot be directly observed, can still be an interest of, or important to, study.
Term
Discrete and continuous variables
Definition

  1. Discrete variables: separate, indivisible categories; can include decimals as long as they are distinct and can't be divisible.
  2. Continuous variables: variables that contain an infinite possibility of decimals numbers (can be represented as a continuous line on a graph).
    1. It should be rare to have two individuals have the exact same score due to the infinite possibility, otherwise something is wrong.
    2. Each continuous variable is an interval limited by boundaries (ex. If 2 ppl say they're 150, they are prob. not exactly 150 but around there; Figure 1.7).
      1. Real limits: Boundaries of intervals for continuous variables positioned halfway between adjacent scores.
        1. Upper real limit: Max of the interval; the limit (.5) belongs to a certain whole number based on your rounding rule (ex: nearest .5 -> 0.75, 1, 1.25).
        2. Lower real limit: min of the interval

Term
Nominal, ordinal, interval, and ratio scales of measurements
Definition

  1. Differentiate nominal, ordinal, interval and ratio scales of measurements
    1. Nominal scale: Classifying variables that are not related to each other (no better or worse category).
    2. Ordinal scale: Classifying variables in terms of size, order, magnitude etc. which shows there is a relationship between categories but they can't be assigned numerical scores (ex. Ranking).
    3. Interval and ratio scales: Ordered categories (like ordinal)
      1. Interval scale: ordered categories that are spaced the same size and where zero is arbitrary.
      2. Ratio scale: zero means something and there's a meaningful difference between scale points.

Term
Three types of operationalization
Definition

 

    • Self report: when participants provide info about themselves through surveys, questionnaires, or interviews. It's often used to gather data on subjective experiences, feelings, opinions, or past behaviors.
    • Observational: data is collected by observing participants in a natural or controlled setting without interference from the researchers. This method is useful for studying behaviors as they naturally occur.
    • Physiological: measuring biological data, which may include brain activity, hormone levels, heart rate, and other physical states. This type of data is often collected using medical equipment and can provide insights into the physiological underpinnings of behaviors and psychological states.

Term
Why do scales of measurement matter?
Definition

A construct isn't inherently a type of measurement, but it's a decision a researcher makes for sample, data analysis, conclusion, methodology.

Term
Scales of measurement
Definition

 

    • Categorical (qualitative): nominal and ordinal
    • Quantitative (numerical): Discrete and continuous (also ordinal to some extent)

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