Measures of Association for Nominal Variables 8-9
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What does a chi-square probability value of 0.003 indicate about the relationship between income and health?

  • There is a statistically significant relationship. (correct)
  • The null hypothesis is accepted.
  • The results cannot be interpreted.
  • There is a weak, non-significant relationship.

In the context of the provided analysis, which statement correctly describes the direction of the relationship between income and health among people in good health?

  • Lower income correlates with better health.
  • Higher income correlates with worse health.
  • Health status is irrelevant to income levels.
  • Higher income correlates with better health. (correct)

What maximum percentage point difference was observed in the relationship between income and health?

  • 9.1% (correct)
  • 20.0%
  • 5.1%
  • 15.2%

Which of the following is true regarding the relationship between volunteering and gender based on the previous demonstration?

<p>Volunteering behavior varies significantly by gender. (A)</p> Signup and view all the answers

Which statistical measures were requested when analyzing the relationship between volunteering and gender using SPSS?

<p>Chi-square, phi, Cramer's V, and lambda. (D)</p> Signup and view all the answers

What conclusion can be drawn when a statistically significant finding is observed in a large sample size?

<p>The result may lack practical significance despite statistical significance. (C)</p> Signup and view all the answers

What is a key aspect of conducting crosstab analysis in SPSS regarding the arrangement of variables?

<p>Dependent variables should be placed in the Rows box. (D)</p> Signup and view all the answers

How should results with significant chi-square values be interpreted?

<p>Suggests a relationship that should be further explored. (C)</p> Signup and view all the answers

What is the significance of clicking the 'Statistics' button when analyzing data?

<p>To request additional statistical outputs like chi-square. (C)</p> Signup and view all the answers

What type of relationship is indicated between income and health based on the data provided?

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

In the context of recoding variables, what does an increasing income code value indicate?

<p>An increase in income category amount. (A)</p> Signup and view all the answers

How can the maximum difference between income columns be calculated from the provided data?

<p>By subtracting the highest percentage from the lowest percentage in the same row. (B)</p> Signup and view all the answers

What does the term 'ordinal level' refer to in the context of the given relationship?

<p>Variables that can only be ranked without measurable differences. (C)</p> Signup and view all the answers

What is indicated by a negative association between two ordinal variables?

<p>High scores on one variable correspond to low scores on the other. (A)</p> Signup and view all the answers

What does the output of the crosstab analysis help determine regarding the relationship between two variables?

<p>The strength and direction of the relationship. (B)</p> Signup and view all the answers

Which of the following best describes the relationship coding system used for income and health in the analysis?

<p>Income is coded inversely to health. (A)</p> Signup and view all the answers

What does a lambda value of 0.000 indicate regarding the relationship between the variables?

<p>No relationship exists between the variables. (A)</p> Signup and view all the answers

Why should the lambda value be disregarded in this context?

<p>The conditional distributions change despite the false zero. (D)</p> Signup and view all the answers

What is the role of phi and Cramer’s V in the analysis?

<p>To measure the strength of the association between the variables. (A)</p> Signup and view all the answers

How is the significance of the chi square value interpreted in this analysis?

<p>It indicates that the relationship is statistically significant. (B)</p> Signup and view all the answers

Which of the following statements about the relationship between gender and volunteering behaviour is true?

<p>The relationship is weak but statistically significant. (B)</p> Signup and view all the answers

What does the term 'false zero' refer to in this analysis?

<p>A lambda value that incorrectly indicates no relationship. (B)</p> Signup and view all the answers

In crosstab analysis, what is the typical dependency of variables?

<p>Independent variable can be in either rows or columns. (B)</p> Signup and view all the answers

What should be considered when selecting which variable is dependent and which is independent?

<p>The variable that is hypothesized to cause a change is typically dependent. (B)</p> Signup and view all the answers

Which measure of association is appropriate for analyzing a 2 × 2 table?

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

What does lambda (λ) provide in terms of relationship interpretation?

<p>A proportional reduction in error (B)</p> Signup and view all the answers

What is the primary purpose of analyzing column percentages in association analysis?

<p>To maximize understanding of the relationship (D)</p> Signup and view all the answers

Which statistical measure is indicated as providing a direct interpretation of values between 0.00 and 1.00?

<p>Lambda (C)</p> Signup and view all the answers

Which statement accurately reflects the relationship between busy workers and job satisfaction?

<p>Busy workers are likely happier, making job satisfaction dependent. (B)</p> Signup and view all the answers

Which statistical measure is appropriate for tables larger than 2 × 2?

<p>Cramer’s V (A)</p> Signup and view all the answers

What type of analysis should accompany the measures of association to maximize insights?

<p>Analysis of column percentages (D)</p> Signup and view all the answers

What do Phi and Cramer’s V have in common?

<p>Both are chi-square based measures. (B)</p> Signup and view all the answers

What does a lambda value of 0.000 indicate about the relationship between the dependent and independent variables?

<p>There is no relationship between the variables. (D)</p> Signup and view all the answers

Which statistical measure indicates that the relationship between gender and volunteering behaviour is statistically significant?

<p>Chi-square (B)</p> Signup and view all the answers

What is the expected relationship between political ideology and support for same-sex marriage?

<p>Liberals are likely to support it more than conservatives. (A)</p> Signup and view all the answers

What characteristic of lambda should be noted when interpreting its value?

<p>It is asymmetric and depends on the dependent variable chosen. (B)</p> Signup and view all the answers

Which political ideology would most likely align with support for traditional gender roles?

<p>Conservatives who typically value traditional norms. (C)</p> Signup and view all the answers

What should be done with the value of lambda when observing a 'false' zero situation?

<p>It should be disregarded. (A)</p> Signup and view all the answers

When analyzing the relationship between political ideology and the death penalty, what might one expect?

<p>Conservatives typically favor the death penalty more than liberals. (B)</p> Signup and view all the answers

Which group is expected to strongly support the legalization of illicit drugs?

<p>Liberals who advocate for personal freedom and reform. (D)</p> Signup and view all the answers

What does a value of 0.097 for phi and Cramer’s V suggest about the relationship between the variables?

<p>The relationship is weak. (A)</p> Signup and view all the answers

What is the correct interpretation of statistical significance in the context of this analysis?

<p>It shows a reliable relationship exists. (A)</p> Signup and view all the answers

What statistical measures might be computed to analyze the relationship between political ideology and support for medical assistance in dying?

<p>Phi and lambda coefficients. (D)</p> Signup and view all the answers

Which statement best describes the correlation between political ideology and support for medical assistance in dying?

<p>Liberals generally advocate for this support more than conservatives. (B)</p> Signup and view all the answers

Which of the following pairs of variables was examined using the Crosstabs procedure?

<p>Recoded hm_01 and dh1ged (C)</p> Signup and view all the answers

What distinction is made when discussing phi and Cramer’s V in relation to the table structure?

<p>They are identical in value when the table has two columns. (C)</p> Signup and view all the answers

What is the role of analyzing column percentages in understanding bivariate relationships?

<p>To summarize the strength of relationship between variables. (D)</p> Signup and view all the answers

What conclusion can be drawn regarding predictions of political ideology and positions on issues?

<p>There is a consistent pattern of predictability based on ideology. (B)</p> Signup and view all the answers

What does a value of 0.00 indicate when measuring the strength of association using Gamma or Kendall’s tau?

<p>No association between the independent and dependent variable (D)</p> Signup and view all the answers

Which statistical measure is specifically referred to as the proportion of similar over dissimilar pairs excluding ties?

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

What is the purpose of requesting column percentages in crosstab analysis?

<p>To provide insight into relationships between variables (C)</p> Signup and view all the answers

If the value of a measure of association is greater than 0.30, what is the strength of the relationship?

<p>Strong (C)</p> Signup and view all the answers

Which statistical measure is used to determine the strength of association between two nominal variables?

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

What occurs to the value of measures like Gamma as the number of similar pairs increases relative to dissimilar pairs?

<p>It moves closer to 1.00 (B)</p> Signup and view all the answers

How is Cramer’s V calculated?

<p>By using the formula $V = \sqrt{\frac{\chi^2}{n[min(r - 1), (c - 1)]}}$ (D)</p> Signup and view all the answers

What does a significant lambda value indicate in analysis?

<p>The strength of the association increases or decreases (B)</p> Signup and view all the answers

What is the consequence when all pairs in a dataset are either similar or dissimilar according to the measures discussed?

<p>The value reflects a perfect relationship (D)</p> Signup and view all the answers

Which measure differs in how it treats tied pairs among Gamma, Kendall’s tau-b, and Somers’ d?

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

Which measures are appropriate for analyzing relationships involving ordinal-level variables?

<p>Gamma and Spearman’s rho (B)</p> Signup and view all the answers

What general guideline is indicated for the strength of association in values between 0.11 and 0.30?

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

What does the term 'logic of pairs' refer to in the context of association measurement?

<p>Evaluating relationships in pairs of variables (B)</p> Signup and view all the answers

What type of chart is suggested for assisting in the interpretation of column percentages in crosstab analysis?

<p>Panelled pie chart (C)</p> Signup and view all the answers

Which is true about the relationship between the number of similar and dissimilar pairs in assessing association strength?

<p>The difference in pairs affects the strength of association (B)</p> Signup and view all the answers

Why might one conduct a crosstab analysis with a dependent variable like 'fvisvolc'?

<p>To examine relationships between variables based on frequency distributions (B)</p> Signup and view all the answers

What can be inferred about the relationship between income and health based on the height of the bars in the analysis?

<p>Higher incomes correlate with better health outcomes. (B)</p> Signup and view all the answers

Which statistical result supports rejecting the null hypothesis in the context of income and health?

<p>$p$-value of 0.003 (B)</p> Signup and view all the answers

What does the maximum percentage point difference of 9.1% suggest about the significance of the findings?

<p>The findings are statistically significant but may lack practical importance. (B)</p> Signup and view all the answers

When examining the relationship between volunteering and gender, what was the result regarding gender differences?

<p>Females were more likely to have volunteered. (A)</p> Signup and view all the answers

What is the purpose of requesting measures like phi or Cramer’s V when analyzing data with SPSS?

<p>To assess the strength and direction of the association. (B)</p> Signup and view all the answers

What does a statistically significant finding imply in the context of a large sample size?

<p>There may be statistical significance without practical importance. (D)</p> Signup and view all the answers

Which step should be taken after moving variables into the Row(s) and Column(s) boxes in the SPSS Crosstabs procedure?

<p>Click the Cells button and request column percentages. (C)</p> Signup and view all the answers

How should one interpret the overall height of the bars representing good health in relation to poor health?

<p>More people reported good health across all income categories. (B)</p> Signup and view all the answers

Flashcards

Comparing bar heights

Comparing heights of bars on a graph, in a cross-tabulation, to see relationships between variables.

Column percentages

The percent of each group that falls into the various categories of another variable.

Cross-tabulation

A table showing the relationship between two categorical variables.

Statistically significant relationship

A relationship between variables that is unlikely due to chance.

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Null hypothesis

The assumption that there is no relationship between variables.

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Chi-square test

A statistical test used to assess if there's a relationship between categorical variables.

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Alpha (α)

A significance level; the threshold for considering a result statistically significant in a study.

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Measures of association

Statistical methods to quantify the strength and direction of a relationship between variables within a study.

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Crosstabs analysis

A statistical method to analyze the relationship between two categorical variables.

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Negative relationship

A relationship where high values of one variable are associated with low values of the other, and vice versa.

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Ordinal level of measurement

Data where categories have a meaningful order (e.g., low, medium, high; poor, fair, good, excellent).

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Relationship Strength (weak)

A relationship exists but the difference in percentages between categories isn't large.

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Relationship Direction

Describes whether the relationship is positive (higher values with higher values) or negative (higher values with lower values).

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Income and Health Codes

The relationship between income and health is determined by the assigned numerical codes for income categories (increasing values) and health categories (decreasing values, e.g., 1 = good health, 2 = poor health).

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Lambda

Asymmetric measure of association that changes value depending on which variable is dependent, showing the strength of association between two categorical variables.

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Symmetric lambda

A measure of association for two categorical variables where the direction of the relationship doesn't matter. It averages the two asymmetric lambda values.

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Goodman and Kruskal tau

A measure of association that, like lambda, is based on the logic of PRE (proportional reduction in error) and is asymmetric.

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Phi

A measure of association for two categorical variables when both variables have only two categories, demonstrating the strength of the relationship. It is symmetric.

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Cramer's V

A measure of association for two categorical variables, similar to phi but can be used with tables larger than 2x2. It is symmetric.

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False zero

When a measure of association (like lambda) indicates no relationship between variables, even when the conditional distributions suggest that there actually is a relationship.

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Association vs. Significance

Association describes the presence and strength of a relationship between variables, while statistical significance tests whether the relationship is unlikely to have occurred by chance.

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Causal Sequence

The order in which variables influence each other. It describes whether one variable causes another or vice versa.

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Phi (Ï•)

A measure of association for two categorical variables, used when both variables have only two categories. It quantifies the strength of the relationship.

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Lambda (λ)

A measure of association for two categorical variables, based on the proportional reduction in error (PRE). It provides a direct interpretation of the relationship strength.

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Conditional Distributions

The distribution of one variable within the categories of another variable. It reveals how one variable changes across different groups of the other variable.

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Negative Association

A relationship between two variables where higher values of one variable are associated with lower values of the other, and vice versa.

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Political Ideology & Same-Sex Marriage

Examining the relationship between a person's political ideology (liberal, moderate, conservative) and their support for same-sex marriage.

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Political Ideology & Death Penalty

Analyzing the connection between a person's political ideology and their stance on capital punishment.

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Political Ideology & Medical Assistance in Dying

Investigating the relationship between a person's political ideology and their support for the legal right to medical assistance in dying for individuals with incurable diseases.

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Political Ideology & Traditional Gender Roles

Exploring the connection between a person's political ideology and their support for traditional gender roles.

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Political Ideology & Legalization of Drugs

Examining the relationship between a person's political ideology and their stance on legalizing illicit drugs.

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Maximum Difference

The largest difference in column percentages between any two categories of the dependent variable within a cross-tabulation.

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Strength & Direction of Relationship

Describing the strength (how strong the association is) and direction (positive or negative) of the relationship between two variables, based on the analysis of column percentages.

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Comparing Column Percentages

In a cross-tabulation, comparing the percentages within each column to identify potential relationships between two variables. This is similar to comparing the heights of bars in a graph representing the same data.

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Alpha Level (α)

A predetermined threshold used to decide if a result is statistically significant. Commonly, α is set to 0.05, meaning there is a 5% chance of finding a statistically significant result when there is actually no relationship between the variables.

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Maximum Percentage Point Difference

The largest difference in percentages observed between any two categories of the dependent variable across different categories of the independent variable in a cross-tabulation.

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Interpreting Relationship Significance

A statistically significant finding does not guarantee that the relationship is important. The significance level only indicates the likelihood of chance occurrence. It is crucial to consider the context and the effect size to determine practical importance.

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Kendall's tau-b

Similar to Gamma, it measures the strength of association but considers tied pairs, making it more appropriate for data with many ties.

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Somers' d

A measure of association that focuses on the relationship between two variables, accounting for ties but prioritizing one variable as dependent.

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Similar Pairs

Two pairs of observations that both increase or decrease together in terms of the variables being measured.

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Dissimilar Pairs

Two pairs of observations where one pair increases while the other decreases in terms of the variables being measured.

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Tied Pairs

Two pairs of observations where at least one variable has the same value for both pairs.

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Strength of Association

The degree to which two variables are related, measured by the magnitude of the correlation coefficient.

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Interpreting Association Values

Understanding the meaning of the values of Gamma, Kendall's tau-b, and Somers' d, with values closer to 1 indicating a stronger relationship.

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Spearman's rho

A non-parametric measure of association for ordinal variables. It calculates the correlation coefficient of ranked data, measuring the relationship's strength and direction.

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Concordant Pairs

Pairs of observations where both variables move in the same direction. If one variable increases, the other also increases, or if one decreases, the other decreases.

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Discordant Pairs

Pairs of observations where the variables move in opposite directions. One variable increases while the other decreases, or vice versa.

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Study Notes

Measures of Association for Variables Measured at the Nominal Level

  • This chapter is about measures of association for nominal-level variables
  • Statistical significance tests are important in social science research but have limitations in analyzing the importance of relationships
  • Measures of association are used to describe and analyze the importance of relationships between variables, focusing on their direction, pattern, and strength.
  • Bivariate tables display values for two variables
  • Two variables are considered to be associated if the distribution of one variable changes under various conditions of the other.
  • The characteristics of a bivariate relationship are existence, strength, and direction or pattern.
  • By calculating percentages within columns and comparing across columns, you can investigate a bivariate association and properly interpret the results.
  • There are three common measures of nominal-level association: phi, Cramer's V, and lambda.

Learning Objectives

  • Explain how to use measures of association to describe and analyze the importance of relationships (versus their statistical significance)
  • Define association in the context of bivariate tables and in terms of changing conditional distributions
  • List and explain the three characteristics of a bivariate relationship: existence, strength, and pattern or direction
  • Investigate a bivariate association by properly calculating percentages for a bivariate table and interpreting the results
  • Compute and interpret three measures of association for variables measured at the nominal level: phi, Cramer's V, and lambda

Bivariate Tables and Associations

  • In bivariate tables, the independent variable is usually displayed in the columns and the dependent variable is displayed in the rows.
  • Row and column percentages can help to visually determine the strength and patterns of association visually.

Introduction to Measures of Association

  • Conditional distributions, column percentages, and the maximum difference
  • These methods provide useful information about bivariate associations but can be cumbersome for large tables.
  • Measures of association (e.g., phi, Cramer's V, lambda) provide a more compact way of describing the strength (and direction for some) of a relationship between variables.
  • Different measures of association are most appropriate depending on level of measurement of the variables. Nominal measures will use measures like phi or Cramer's V.

Chi Square-Based Measures of Association

  • While chi-square is used to test statistical significance, it can also be used to measure the strength between variables.
  • Phi is a simple chi-square-based measure used for 2x2 tables (with two rows and two columns).
  • Cramer's V is used for tables larger than 2x2
  • Calculating these can measure the strength of association between nominal variables.

Proportional Reduction in Error Measures of Association

  • Proportional reduction in error (PRE) measures provide a direct interpretation of how much prediction errors are reduced in the dependent variable when the independent variable is considered in the prediction.
  • The different types of errors in a prediction are accounted for by this measure, which calculates how much error is reduced when using the independent variable.

Lambda: A PRE Measure of Association

  • Lambda is a PRE measure for nominal variables.
  • Lambda is calculated by finding the number of prediction errors made when ignoring the independent variable and comparing this with the number of errors when the independent variable is taken into account.

Limitations of Phi and Cramer's V

  • Phi and Cramer's V provide general indicators of association strength.
  • They cannot prove a causal relationship between variables.

How Strong Is the Association?

  • Association can be determined through visual examination of percentage distributions and by calculation of the maximum difference.
  • A change in the percentage distribution shows that a relationship exists.
  • A larger maximum difference between columns indicates a stronger relationship.

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Statistics: Measures of Association (PDF)

Description

Explore the key measures of association relevant to nominal-level variables, including phi, Cramer's V, and lambda. Understand how bivariate tables can help in analyzing the strength and direction of relationships between variables. This quiz aims to clarify the statistical significance tests and their limitations in social science research.

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