Measures of Association 8-9
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Questions and Answers

What is a unique feature of measures like Gamma and Somers' d?

  • They require the data to be normally distributed.
  • They measure the strength of association based on ranks. (correct)
  • They can be used exclusively for nominal variables.
  • They only consider tied pairs.

    • In the context of the given data, how many unique pairs are derived from a sample size of 5?

  • 15
  • 5
  • 10 (correct)
  • 20

    • Which of the following accurately describes a 'Tied on the Dependent Variable' scenario?

  • Both variables are identical in value.
  • The independent variables are the same, but dependent variables differ.
  • The dependent variable values remain constant across different independent variable scores.
  • The pairs have identical scores for the dependent variable but differ on the independent variable. (correct)

    • Which of the following is NOT a characteristic of ordinal variables?

    <p>They can be added algebraically.</p> Signup and view all the answers

    What does the Phi coefficient measure?

    <p>The strength of association in nominal data.</p> Signup and view all the answers

    Which measure is best suited for evaluating the association between two nominal variables?

    <p>Cramer's V</p> Signup and view all the answers

    What does a high value of Cramer's V indicate?

    <p>Strong association between variables.</p> Signup and view all the answers

    In the analysis of pairs for strength of association, which type of pair does 'Similar Pair' refer to?

    <p>Pairs that share identical values on both variables.</p> Signup and view all the answers

    What kind of variables are described as having many scores that resemble interval-ratio level variables?

    <p>Continuous Ordinal Variables</p> Signup and view all the answers

    Which of the following measures of association is NOT applicable to collapsed ordinal variables?

    <p>Spearman's Rank Order</p> Signup and view all the answers

    When evaluating the strength of an association, which question is NOT typically asked?

    <p>What is the sample size?</p> Signup and view all the answers

    What defines a 'similar pair' of respondents in the context of measures of association?

    <p>The respondent with the larger value on the independent variable also has a larger value on the dependent variable</p> Signup and view all the answers

    Which of the following formulas is used to determine the total number of unique pairs?

    <p>Total pairs = n(n-1)/2</p> Signup and view all the answers

    Which measure is used to describe the strength of association for both continuous and ordinal variables?

    <p>Cramer's V</p> Signup and view all the answers

    Which type of ordinal variable has a limited number of categories, not exceeding six?

    <p>Collapsed Ordinal Variables</p> Signup and view all the answers

    Which of the following sub-group definitions describes a situation where two respondents have an equal score on the dependent variable?

    <p>Tied on DV (Y)</p> Signup and view all the answers

    What do measures of association primarily provide information about?

    <p>The strength and direction of relationships between variables</p> Signup and view all the answers

    In a bivariate analysis, what does it indicate if the distribution of one variable changes under different categories of another variable?

    <p>The variables are associated</p> Signup and view all the answers

    Which measure of association is appropriate for nominal variables?

    <p>Cramer's V</p> Signup and view all the answers

    What type of variables does a Chi-square test typically analyze?

    <p>Nominal and ordinal variables</p> Signup and view all the answers

    How can the strength of association between ordinal variables be interpreted?

    <p>Using Spearman's rank correlation</p> Signup and view all the answers

    What is a key characteristic of conditional distributions in bivariate association?

    <p>They display the distribution of scores on the dependent variable for each score on the independent variable</p> Signup and view all the answers

    What is the main purpose of using measures of association in research?

    <p>To document and analyze cause-and-effect relationships</p> Signup and view all the answers

    What does a high score in a measure of association indicate?

    <p>Strong relationship among variables</p> Signup and view all the answers

    What is one of the first steps to investigate the relationship between two variables?

    <p>Ask whether the variables are associated</p> Signup and view all the answers

    Which measure of association is commonly used for collapsed ordinal variables?

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

    What does the term 'dissimilar pair' refer to in the context of measures of association?

    <p>The respondent with a higher independent variable score has a lower dependent variable score.</p> Signup and view all the answers

    Which question is essential to determine when assessing the relationship between two ordinal variables?

    <p>Does association exist?</p> Signup and view all the answers

    In investigating pairs for strength of association, what characteristic defines a 'tied on the independent variable' scenario?

    <p>Both respondents have identical scores on the independent variable.</p> Signup and view all the answers

    Which of the following statements best summarizes the logic of pairs in measures of association?

    <p>Pairs analyze the rankings of respondents on both independent and dependent variables.</p> Signup and view all the answers

    What is the primary goal of using measures of association for ordinal level variables?

    <p>To evaluate the strength and direction of the relationship.</p> Signup and view all the answers

    How can the uniqueness of pairs be mathematically represented?

    <p>By a specific formula that counts the total unique pairs.</p> Signup and view all the answers

    What does it mean if two respondents are categorized as 'tied on the dependent variable'?

    <p>They share an identical score on the dependent variable.</p> Signup and view all the answers

    What does a chi-square score above 0.00 signify?

    <p>It suggests some level of association.</p> Signup and view all the answers

    What is the best method to look at conditional distributions of Y?

    <p>Calculate and compare column percentages.</p> Signup and view all the answers

    Which scenario exemplifies perfect non-association between variables?

    <p>Y maintains the same distribution regardless of changes in X.</p> Signup and view all the answers

    How is the strength of association defined?

    <p>By the variability of dependent variable Y across independent variable X.</p> Signup and view all the answers

    What does a perfect association indicate regarding the values of Y and X?

    <p>Each value of Y corresponds to one specific value of X.</p> Signup and view all the answers

    What does it mean if the conditional distributions of Y do not change across columns?

    <p>There is perfect non-association.</p> Signup and view all the answers

    Why are column percentages preferred over raw scores when detecting association?

    <p>They standardize totals and simplify detection.</p> Signup and view all the answers

    What does it indicate if changes in Y are observed under varying conditions of X?

    <p>There is likely an association.</p> Signup and view all the answers

    What is the range of Phi for assessing association strength?

    <p>0.00 to 1.00</p> Signup and view all the answers

    Which measure is appropriate for contingency tables larger than 2x2?

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

    What does a Cramer’s V score of 0.46 suggest about the strength of association?

    <p>Moderate association</p> Signup and view all the answers

    If the chi square value is zero, what does this indicate about the association between the variables?

    <p>No association exists</p> Signup and view all the answers

    What does a value of 0.00 indicate in the context of association measures?

    <p>No association between X and Y</p> Signup and view all the answers

    Which of the following statements accurately describes the relationship between statistical significance and strength of association?

    <p>Statistical significance indicates the presence of an association but not its strength.</p> Signup and view all the answers

    What occurs to the strength of association as the number of similar pairs increases relative to dissimilar pairs?

    <p>The strength of association increases</p> Signup and view all the answers

    In the context of measures of association, what is the purpose of conditional distributions?

    <p>To examine how one variable's distribution is influenced by another variable.</p> Signup and view all the answers

    What is the minimum value required from Cramer’s V formula?

    <p>Minimum of (r - 1) and (c - 1)</p> Signup and view all the answers

    In terms of directionality, how do ordinal level measures differ from nominal level measures?

    <p>Ordinal measures can indicate the direction of the relationship</p> Signup and view all the answers

    What does a Cramer’s V score of less than 0.10 indicate?

    <p>Weak association</p> Signup and view all the answers

    What does a negative value indicate in ordinal measures like Gamma?

    <p>Variables are moving in opposite directions</p> Signup and view all the answers

    How is a positive relationship in a tabular format represented?

    <p>Scores falling diagonally from upper left to lower right</p> Signup and view all the answers

    When using measures of association, which of the following is the lowest measurement level that dictates the choice of measure?

    <p>Nominal level</p> Signup and view all the answers

    What is the key characteristic of Gamma in relation to similar pairs?

    <p>It evaluates the number of similar pairs as a proportion of all pairs excluding ties</p> Signup and view all the answers

    In terms of value range, what does a Gamma score of +1.00 indicate?

    <p>A perfect positive relationship</p> Signup and view all the answers

    What is indicated by a score of -0.75 in the context of association strength?

    <p>A strong negative relationship</p> Signup and view all the answers

    When both values on X and Y increase together, what type of relationship is demonstrated?

    <p>Positive relationship</p> Signup and view all the answers

    When similar and dissimilar pairs are equal, how is the association value affected?

    <p>It remains at 0.00</p> Signup and view all the answers

    What is the primary limitation of Gamma when analyzing ordinal variables?

    <p>Gamma exaggerates the strength of association by ignoring tied pairs.</p> Signup and view all the answers

    Which measure includes only pairs tied on the dependent variable in its calculation?

    <p>Somers’ d</p> Signup and view all the answers

    Under what conditions can Kendall's Tau-b reach a value of ±1.00?

    <p>When the independent variable and dependent variable have the same number of categories.</p> Signup and view all the answers

    In the context of Kendall's Tau-b, what does X represent in the calculations?

    <p>The number of ties on the independent variable</p> Signup and view all the answers

    Why might Tau-b give unreliable results if the table does not have the same number of rows and columns?

    <p>Because it is designed only for symmetric tables.</p> Signup and view all the answers

    What is the maximum value that tau-c can reach?

    <p>1.00</p> Signup and view all the answers

    What does a tau-c value of 0.00 signify?

    <p>No relationship</p> Signup and view all the answers

    In the context of tau-c, what should be used if the number of categories on the independent variable is lower?

    <p>The minimum value of the categories</p> Signup and view all the answers

    What is a distinguishing feature of Somers' d compared to tau-c?

    <p>It considers ties on the dependent variable.</p> Signup and view all the answers

    What indicates a strong positive relationship in Somers' d?

    <p>A value close to +1.00</p> Signup and view all the answers

    How do the predictive powers of Somers' d change?

    <p>They differ based on which variable is treated as dependent or independent.</p> Signup and view all the answers

    Which scenario describes when tau-c is particularly useful?

    <p>When both variables have unequal categories.</p> Signup and view all the answers

    What is the range of values for Somers' d?

    <p>-1.00 to +1.00</p> Signup and view all the answers

    Study Notes

    Quantitative Research Methods in Political Science

    • This lecture covers measures of association for nominal and ordinal variables in political science research.
    • Measures of association quantify the strength and direction of relationships between variables.
    • They are crucial for assessing the importance of relationships and validating theories.
    • Cause-and-effect relationships are effectively documented with these measures.
    • Predictions can be formulated because if variables are related, a score on one variable can predict a score on another.

    Bivariate Association

    • Two variables are associated if the distribution of one changes under different categories or scores of the other.
    • A bivariate table (example provided) illustrates the relationship between job satisfaction (X) and productivity (Y) for 173 factory workers.
    • Examining columns in the table reveals the pattern of scores on Y for each score on X.
    • This example illustrates that 30 of 60 workers with low job satisfaction reported low productivity while 25 of 61 workers with moderate job satisfaction reported moderate productivity.
    • The relationship between these variables reveals the conditional distributions of Y (productivity), which are affected by X (job satisfaction).

    Questions to Ask

    • To fully analyze the relationship between two variables, one must ask:
      • Does association exist?
      • If association exists, how strong is it?
      • If association exists, what is the pattern and/or the direction of the association?

    Does Association Exist?

    • Chi-square testing can establish association.
    • Chi-square values above 0.00 represent association, however, this doesn't always indicate statistical significance.
    • To better understand the relationships, it is advisable to use column percentages to compute and compare.

    Does Association Exist? Cont'd

    • This is further illustrated by using percentages from a bivariate table as shown in the slides, to detect conditional distributions of Y (e.g., productivity).
    • This makes it clearer to see the relationship between job satisfaction and productivity.

    Does Association Exist? Cont'd

    • Another example of this using productivity and age group.
    • If an association did not exist the conditional distributions of Y across columns would be similar for each group.

    How Strong is Association?

    • Association strength ranges from perfect non-association to perfect association.
    • Perfect non-association is when the conditional distributions of Y do not change across columns.
    • Perfect association is when each value of Y corresponds to only one value of X.
    • The likelihood of perfect association is low, which makes measures of association essential to understand the strength of the relationship between variables.

    How Strong is Association? Cont'd

    • Perfect associations suggest a causal relationship – where variation in one variable causes variation in another.
    • This is important because a measure of association describes the strength of the relationship between two variables.

    What is the Pattern and/or Direction of Association?

    • Analyzing the direction and pattern of the association involves determining which values or categories of one variable are linked with those of another.
    • Examples show positive and negative associations. Positive associations occur when high scores on one variable are aligned with high scores on the other (or low with low), while negative ones indicate variation in opposite directions (high with low, or low with high).

    What is the Pattern and/or Direction of Association? Cont'd

    • Another example where an increase in education is related to a decrease in television viewership.

    Measures of Association

    • Measures of association detail the strength and direction of bivariate relationships, often displayed as a single numerical value.
    • The type of measure used depends on the level of measurement of the variables (e.g., nominal, ordinal, and interval/ratio).
    • Examples including Phi and Cramer's V apply to nominal level data.
    • Gamma, Somers' d, and Kendall's tau-b and tau-c apply to ordinal data.

    Chi Square-Based Measures of Association

    • Researchers use chi-square based measures of association to assess relationships between nominal level variables.
    • Chi-square values reflect the level of association; however, this does not indicate statistical significance.
    • The strength of association can be assessed using transformations of chi-square values.

    Phi

    • Phi (φ) is a measure of association used for 2x2 tables with nominal variables.
    • Its formula includes the chi-square value (χ2) and the sample size (n).
    • Phi values range from 0.00 (no association) to 1.00 (perfect association).

    Cramer's V

    • Cramer's V is a more general measure of association for nominal variables when the variable table is larger than 2x2.
    • Its formula considers the size of the table along with the chi-square value and sample size.

    Measures of Association for Ordinal Level Variables

    • These variables (e.g., collapsed ordinal variables with few categories), need different measures of association compared to nominal data.
    • The key measures are Gamma (G), Somers' d, Kendall's tau-b, and Kendall's tau-c, which also provide the direction of the relationship.

    The Logic of Pairs

    • Measures of association for ordinal variables, such as Gamma, Somers' d, and Kendall's Tau-b and Tau-c, work by comparing pairs of respondents.
    • Pairs are classified as similar, dissimilar, or tied based on their rankings on the independent and dependent variables.

    Analyzing Measures of Association for Ordinal Level Variables

    • Measures of association, like Gamma, Somers' d, tau-b, and tau-c, consider the number of "similar" versus "dissimilar" pairs when analyzing ordinal variables. These differ in how they handle tied pairs.
    • When similar and dissimilar pairs are equal, the statistic is 0.00 and no association exists.
    • As the number of similar pairs greatly exceeds dissimilar pairs, the value approaches 1.00 (perfect association).

    Interpreting Strength for Ordinal Level Measures

    • The strength of ordinal association is interpreted based on the value of these measures.
    • This interpretation is similar to what Phi and Cramer's V used, with a value between 0.00 and 0.10 indicating a weak relationship, 0.11 and 0.30 indicating a moderate relationship, and greater than 0.30 indicating a strong relationship.

    Direction of Relationship

    • Nominal variables (using phi or Cramer's V) only determine association strength; ordinal variables (using Gamma, Somers' d, Kendall's tau-b, tau-c) also identify directional trends (positive or negative).
    • A positive relationship indicates that both variables increase or decrease together, whereas a negative relationship indicates that as one variable increases, the other decreases.

    Positive Versus Negative Relationships

    Visualized

    • This provides a visualization of positive and negative relationships. This can be depicted as a positive relationship shows values increasing in the same direction (values on X increase and values on Y increase).
    • A negative relationship demonstrates an opposite trend (values on X increase as values on Y decrease).

    Gamma

    • Gamma (G) gauges association strength by counting similar pairs against dissimilar pairs as a proportion.

    Gamma Cont'd

    • Gamma measures the positive trend of a relationship (as opposed to Kendall's Tau that measures the strength of the relationship independent of direction).

    Limitations of Gamma

    • Gamma overlooks tied pairs (those with identical rankings), which might exaggerate the association strength. More sophisticated measures (Somers' d, Kendall's tau-b, Kendall's tau-c) address such ties by looking beyond the basic count approach.

    Kendall's Tau-b

    • Kendall's tau-b is a measure of the strength and direction of monotonic association between two ordinal variables.
    • Its calculation involves considering the frequency of similar and dissimilar pairs.
    • Tau-b is valid for a 2x2 tables but becomes more detailed with larger tables.

    Kendall's Tau-c

    • Tau-c is a measure of association similar to Kendall's tau-b, allowing for unequal categories.

    Somers' d

    • Somers' d is an asymmetric measure of ordinal association.
    • It measures the association between two variables where one is considered the independent variable (predictor) and the other the dependent variable (predicted).
    • It provides a more focused approach to assessing the predictiveness for every variable, and its result changes when each is treated as either the predictor or the predicted.

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    Quantitative Research Methods Lecture 8 PDF

    Description

    This quiz focuses on measures of association for nominal and ordinal variables within the scope of political science research. It delves into the significance of understanding relationships between variables and the implications of these associations for theory validation and predictions. Additionally, the provided bivariate example illustrates the practical application of these concepts.

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