Correlation and Measurement Quiz

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Questions and Answers

What does a correlation coefficient (r) of 0 indicate?

  • A moderate positive correlation
  • A perfect negative correlation
  • A perfect positive correlation
  • No linear relationship between the variables (correct)

Low variability in data enhances the ability to detect correlations.

False (B)

If a correlation coefficient (r) is 0.60, what would be the value of the coefficient of determination (r²)?

0.36

The coefficient of determination, r², represents the proportion of ______ in one variable that is explained by the other variable.

<p>variance</p> Signup and view all the answers

Match the following terms related to correlation with their descriptions:

<p>Form = Linear or nonlinear relationship Degree = Strength and direction of the relationship r = Correlation Coefficient r² = Coefficient of determination</p> Signup and view all the answers

Which of the following scales of measurement involves ordered categories with equal intervals?

<p>Interval Scale (B)</p> Signup and view all the answers

Differential research involves comparing groups that are created by the researcher.

<p>False (B)</p> Signup and view all the answers

What is a crucial element of an experimental design that ensures the change in the dependent variable is due to the independent variable?

<p>control</p> Signup and view all the answers

In a time-series research, observations are compared from one time versus those made at ___________.

<p>another</p> Signup and view all the answers

Match the following scales of measurement with their descriptions:

<p>Nominal Scale = Data fall into different categories Ordinal Scale = Categories are organized in an ordered sequence Interval Scale = Ordered categories with equal intervals Ratio Scale = Interval scale with an absolute zero point</p> Signup and view all the answers

Which of the following is an example of a ratio scale?

<p>Length of an object (A)</p> Signup and view all the answers

Correlational designs can definitively establish causation between variables.

<p>False (B)</p> Signup and view all the answers

In experimental designs, what is the main purpose of randomisation to conditions?

<p>to reduce bias</p> Signup and view all the answers

A factor loading of +.35 is generally considered acceptable for inclusion in a factor.

<p>False (B)</p> Signup and view all the answers

What is the minimum number of items recommended for a factor to ensure adequate reliability?

<p>3 (D)</p> Signup and view all the answers

Describe two key considerations when deciding whether to eliminate an item from a factor analysis.

<p>Two key considerations are the size of the main factor loading and the size of cross-loadings. A large main loading and low cross-loadings are generally desirable.</p> Signup and view all the answers

The principle that suggests adding more items to a factor beyond a certain point provides diminishing returns is known as the ______ of diminishing returns.

<p>law</p> Signup and view all the answers

Which of the following factor loadings is considered 'very good' according to Comrey & Lee (1992)?

<blockquote> <p>.63 (D)</p> </blockquote> Signup and view all the answers

Match the following factor loading ranges with their corresponding descriptions:

<blockquote> <p>.70 = Excellent .63 = Very good .55 = Good .45 = Fair .32 = Poor</p> </blockquote> Signup and view all the answers

Factor analysis is a purely objective process that relies solely on mathematical calculations.

<p>False (B)</p> Signup and view all the answers

Why is it important to consider the interpretability of a factor structure?

<p>Interpretability is crucial because researchers need to understand and meaningfully explain the extracted factors. A well-interpreted factor structure allows for valid conclusions and meaningful insights.</p> Signup and view all the answers

What does ANOVA stand for?

<p>Analysis of Variance (C)</p> Signup and view all the answers

A t-test can only compare two means at a time.

<p>True (A)</p> Signup and view all the answers

What is the purpose of using a paired samples t-test?

<p>To compare means from the same group under different conditions.</p> Signup and view all the answers

In ANOVA, the __________ variable is referred to as a factor.

<p>independent</p> Signup and view all the answers

Match the following terms with their correct definitions:

<p>Null Hypothesis = Assumes no difference between means Experimental Hypothesis = Assumes a difference between means Independent Samples = Comparison between different groups Paired Samples = Comparison within the same group</p> Signup and view all the answers

What is the primary focus of a within-subjects experimental design?

<p>Measuring differences within the same group due to different conditions (A)</p> Signup and view all the answers

The F-value in ANOVA represents the ratio of within-group variance to between-group variance.

<p>False (B)</p> Signup and view all the answers

What is the difference between a single-factor design and a factorial design?

<p>A single-factor design has one independent variable, while a factorial design has two or more independent variables.</p> Signup and view all the answers

What is the recommended aim for the percentage of variance explained when conducting a factor analysis?

<p>50-75% (B)</p> Signup and view all the answers

The first factor extracted in factor analysis always explains the least amount of variance.

<p>False (B)</p> Signup and view all the answers

What should be done when factors no longer represent useful clusters or variables?

<p>Stop extracting factors.</p> Signup and view all the answers

A ______ plot is used to depict the amount of variance explained by each factor.

<p>Scree</p> Signup and view all the answers

What describes orthogonal rotation in factor analysis?

<p>Factors are uncorrelated. (A)</p> Signup and view all the answers

Name one type of rotation used in factor analysis.

<p>Orthogonal rotation or Oblique rotation.</p> Signup and view all the answers

Which statement is true regarding factor loadings?

<p>Some variables may not load highly on any factors. (D)</p> Signup and view all the answers

Match the type of rotation with its description:

<p>Orthogonal rotation = Factors are uncorrelated Oblique rotation = Factors have some degree of correlation</p> Signup and view all the answers

Which assumption of ANOVA pertains to the requirement that the variances of different groups are equal?

<p>Homogeneity of variance (A)</p> Signup and view all the answers

Exploratory Factor Analysis (EFA) is used to confirm existing hypotheses about factor structures.

<p>False (B)</p> Signup and view all the answers

What is the goal of conducting a factor analysis?

<p>To identify underlying factors that explain patterns in data.</p> Signup and view all the answers

The ______ test is a non-parametric alternative to ANOVA used when data does not meet the assumptions of normality.

<p>Kruskal-Wallis</p> Signup and view all the answers

Match the following regression analysis terms with their correct definitions:

<p>R² = Proportion of variance explained by predictors Mediator variable = Explains the relationship between two variables Moderator variable = Affects the strength of a relationship Linearity = Assumption of a straight-line relationship</p> Signup and view all the answers

Which of the following factors is not an assumption of a regression model?

<p>Redundancy (B)</p> Signup and view all the answers

Correlation implies causation between two variables.

<p>False (B)</p> Signup and view all the answers

What is a scree plot used for in factor analysis?

<p>To determine the number of factors to retain.</p> Signup and view all the answers

Flashcards

Quasi-Experimental Research

Research that resembles true experiments but lacks random assignment.

Differential Research

Study comparing pre-existing groups like gender or handedness.

Time-Series Research

Comparison of observations at different times, like before and after effects.

Nominal Scales

Measurement scale for categories without order, such as types of colors or groups.

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Ordinal Scales

Measurement scale that orders categories but does not measure the interval between them.

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Interval Scales

Ordered categories with exact intervals between them, e.g., temperature scales.

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Ratio Scales

Interval scales with a true zero point, such as weight or height.

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Parametric vs Non-parametric Tests

Parametric tests assume normal distribution; non-parametric do not.

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Random Variation

In large samples, random variation averages out, allowing detection of small correlations.

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% of Variance Explained

r² represents the percentage of variance in one variable explained by another variable.

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Correlation Coefficient (r)

r measures the direction and strength of a linear relationship between two variables.

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Coefficient of Determination (r²)

r² indicates the proportion of variance in one variable explained by another.

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Linear vs Nonlinear Relationships

Form describes whether the relationship between variables is linear or nonlinear.

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Meaningful Interpretation of Factors

Factors must be meaningfully interpreted and theoretically sound.

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Variance Explained

Aim for 50-75% explained variance with fewer factors than items.

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Scree Plot

A bar graph showing eigenvalues and explained variance by factors.

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Factor Loadings (FLs)

Indicate the importance of each item to its factor.

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First Factor Extraction

The first factor explains the maximum variance among items.

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Orthogonal Rotation

Keeps factors uncorrelated for simpler interpretation.

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Oblique Rotation

Allows correlation among factors for realistic analysis.

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Interpretation of Unrotated Factors

Unrotated factors often lack simplicity and clarity.

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T-test

A statistical method to compare means from 2 groups.

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Independent Samples T-test

Compares means from two different groups.

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Paired Samples T-test

Compares means from the same group under different conditions.

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ANOVA

Analysis of variance; compares means from 2 or more groups.

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Between-Subjects Design

Measures differences between two or more group conditions.

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Within-Subjects Design

Measures differences within the same group under different conditions.

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Factor in ANOVA

An independent variable in an experiment.

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F-value in ANOVA

Ratio of variance due to the independent variable to error variance.

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Assumptions of ANOVA

Normality, homogeneity of variance, and independence of observations are the three main assumptions.

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Non-parametric alternative to ANOVA

Use when data do not follow normal distribution or have unequal variances, such as the Kruskal-Wallis test.

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Goal of Factor Analysis

To identify underlying factors that explain patterns in data.

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Exploratory vs Confirmatory Factor Analysis

EFA uncovers unknown factor structures, while CFA tests if a hypothesized structure fits the data.

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Eigenvalue in Factor Analysis

Represents the variance explained by a factor in factor analysis.

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Mediator vs Moderator Variables

A mediator explains the relationship between two variables, while a moderator influences the strength of that relationship.

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Assumptions of Regression Model

Main assumptions include linearity, no multicollinearity, independence, homoscedasticity, and normality.

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Factor Loadings

Strength of a variable's relationship to a factor, often shown as a correlation coefficient.

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Cut-off for Loadings

Threshold value used to decide if a loading is significant or acceptable, typically around .40.

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Cross Loadings

Loadings of an item on multiple factors, preferably low to maintain clarity of factor structure.

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Interpretability

The ability to understand and make sense of the factors extracted from analysis.

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Reliability in Factors

Consistency of a factor's measure, improved with more items, ideally 4 to 10.

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Simple Factor Structure

Ideal condition where each variable loads strongly on one factor and most loadings are either high or low.

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Law of Diminishing Returns

Principle stating that beyond a certain point, adding more items yields lesser reliability improvements.

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Minimum Items per Factor

At least three items should be present in a factor for meaningful analysis.

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Study Notes

Introduction to Statistics

  • Statistics is a set of methods and rules for organizing, summarizing, and interpreting information.
  • Statistics can help condense large amounts of information into simpler figures or statements.
  • Researchers are often interested in specific groups of individuals or events (e.g., children, Americans, left-handed people).

Populations and Samples

  • A population includes every individual or event of interest.
  • A parameter is a characteristic of a population, such as the average age.
  • A sample is a subset of the population, intended to represent the population.
  • A statistic is a characteristic of a sample, such as the average age of people in a sample group.

Descriptive Statistics

  • Descriptive statistics simplify and summarize data using graphs, charts, and averages.

Inferential Statistics

  • Inferential statistics allow researchers to study samples and make generalizations about the population.
  • Techniques include Wilcoxon, chi-square, and correlations.
  • Researchers need to consider sampling error when making generalizations about populations from samples.

Research Methods

  • Correlational Research: Observes relationships between variables as they naturally exist (e.g., personality and executive performance). This method cannot determine cause-and-effect.
  • Experimental Research: Establishes cause-and-effect relationships by manipulating one variable (the independent variable) to observe its effect on another (the dependent variable). Researchers try to control extraneous factors.

Experimental Research in Detail

  • Independent Variable: The variable that is manipulated
  • Dependent Variable: The variable measured to assess the effect of the independent variable
  • Control Group: A group that does not receive the experimental treatment (often a placebo)
  • Confounding Variables: Uncontrolled variables that could affect results.
  • Quasi-Experimental Research: Similar to true experiments but lacks full experimental control. Useful when complete experiments are impossible or unethical.
  • Pre- and post-testing: Observing the dependent variable before and after the experimental manipulation to assess any change.

Scales of Measurement

  • Nominal: Data categorized into distinct groups (e.g., eye colour)
  • Ordinal: Categorized with an ordered sequence (e.g., ranks, ordinal ratings)
  • Interval: Ordered categories with equal intervals but no true zero point (e.g., temperature)
  • Ratio: Ordered categories with equal intervals and a true zero point (e.g., weight)

Recap of Questions

  • Identify parametric and non-parametric test types.
  • Understand differences between parametric and non-parametric tests.
  • Describe the function of correlations and when to use different correlation types.
  • Discuss when using t-tests, including the different types, and necessary assumptions.
  • Summarize important assumptions for using t-tests.

Correlation and Regression

  • Correlation: Measures the strength and direction of the relationship between two continuous variables (e.g., height and weight).
  • Regression: Predicts the value of one variable based on another. Linear regression predicts a single outcome based on a single predictor variable, while multiple regression uses multiple predictor variables.

Types of ANOVA

  • Between-Subjects ANOVA: Compares means from multiple independent groups
  • Within-Subjects ANOVA: Compares means from the same group under multiple conditions

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