Nominal and Ordinal Scales in Statistics
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Questions and Answers

What is the primary feature of nominal scales?

  • Classification based on one or more distinguishing characteristics (correct)
  • Rank ordering on some characteristic
  • Equal intervals between numbers
  • Absolute zero point

    • What is a key difference between ordinal and nominal scales?

  • Ordinal scales are used for classification
  • Ordinal scales have absolute zero points
  • Ordinal scales permit rank ordering (correct)
  • Nominal scales are used for intelligence tests

    • What is a characteristic of interval scales?

  • Classification based on one characteristic
  • Absolute zero point
  • Mutually exclusive and exhaustive categories
  • Equal intervals between numbers (correct)

    • What is not a feature of interval scales?

    <p>Absolute zero point</p> Signup and view all the answers

    What can be inferred about the difference in intellectual ability represented by IQs of 80 and 100?

    <p>It is similar to the difference between IQs of 100 and 120</p> Signup and view all the answers

    What is a presumption inherent in the use of interval scales?

    <p>No test taker possesses none of the ability or trait being measured</p> Signup and view all the answers

    What is Alfred Binet's view on the data derived from an intelligence test?

    <p>They are ordinal in nature</p> Signup and view all the answers

    What is the primary purpose of an intelligence test, according to Alfred Binet?

    <p>To classify and rank people on the basis of their performance</p> Signup and view all the answers

    What is the variance equal to?

    <p>The arithmetic mean of the squares of the differences between the scores in a distribution and their mean</p> Signup and view all the answers

    What does a positively skewed distribution indicate about a test?

    <p>The test was too difficult</p> Signup and view all the answers

    What is kurtosis?

    <p>The steepness of a distribution in its center</p> Signup and view all the answers

    Who is credited with first referring to the curve as the normal curve?

    <p>Karl Pearson</p> Signup and view all the answers

    What does a negatively skewed distribution indicate about a test?

    <p>The test was too easy</p> Signup and view all the answers

    What is the formula for the standard deviation based on?

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

    What does the term 'age norm' refer to in scholarly literature?

    <p>A particular variety of norm specified by age.</p> Signup and view all the answers

    What is the term used to describe the nature and extent to which symmetry is absent in a distribution?

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

    Who made substantial contributions to the development of the normal curve in the early nineteenth century?

    <p>Karl Friedrich Gauss</p> Signup and view all the answers

    What is the purpose of administering a test to a representative sample of test takers?

    <p>To establish norms.</p> Signup and view all the answers

    What is a normative sample?

    <p>A group of test takers whose performance is used as a reference.</p> Signup and view all the answers

    What is race norming?

    <p>The process of deriving norms based on race or ethnic background.</p> Signup and view all the answers

    Why do some test manuals provide user norms or program norms?

    <p>Because it is a cheaper alternative to norming with a nationally representative sample.</p> Signup and view all the answers

    What is test standardization?

    <p>The process of administering a test to a representative sample of test takers.</p> Signup and view all the answers

    In the process of developing a test, what does a test developer target?

    <p>A defined group as the population for which the test is designed.</p> Signup and view all the answers

    What is the plural form of 'norm'?

    <p>Norms.</p> Signup and view all the answers

    What is the influence of culture observed in the context of testing and assessment?

    <p>In aspects of test construction, scoring, interpretation, and validation</p> Signup and view all the answers

    What is criterion-related validity a judgment of?

    <p>How adequately a test score can be used to infer an individual’s most probable standing on some measure of interest</p> Signup and view all the answers

    What is concurrent validity an index of?

    <p>The degree to which a test score is related to some criterion measure obtained at the same time</p> Signup and view all the answers

    What is a characteristic of an adequate criterion?

    <p>It is pertinent or applicable to the matter at hand</p> Signup and view all the answers

    What is criterion contamination?

    <p>A criterion measure that is based on a predictor measure</p> Signup and view all the answers

    What type of validity is concerned with the degree to which a test score predicts some criterion measure?

    <p>Predictive validity</p> Signup and view all the answers

    What is an example of a criterion measure that is contaminated?

    <p>An 'Inmate Violence Potential Test' designed to predict a prisoner’s potential for violence in the cell block</p> Signup and view all the answers

    What is the purpose of establishing the validity of a criterion measure?

    <p>To ensure that the criterion measure is valid for the purpose for which it is being used</p> Signup and view all the answers

    What is the term referred to when a portion of the universe of people is deemed to be representative of the whole population?

    <p>Stratified sampling</p> Signup and view all the answers

    What type of sampling occurs when every member of the population has the same chance of being included in the sample?

    <p>Stratified-random sampling</p> Signup and view all the answers

    What is the term for the score at or below which a certain percentage of scores in a distribution fall?

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

    What is the purpose of administering a test to a sample of the population?

    <p>To obtain a distribution of test responses</p> Signup and view all the answers

    What type of sample is selected because it is convenient or available for use?

    <p>Convenience sample</p> Signup and view all the answers

    What is the term for the process of selecting a portion of the universe deemed to be representative of the whole population?

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

    What is the term for the distribution of scores obtained from a sample of test takers?

    <p>Standardization sample</p> Signup and view all the answers

    What is the term for the people in the normative sample when they are the same people on whom the test was standardized?

    <p>Standardization sample</p> Signup and view all the answers

    Study Notes

    Scales of Measurement

    • Nominal scales: simplest form of measurement, involve classification or categorization based on one or more distinguishing characteristics, mutually exclusive and exhaustive categories.
    • Ordinal scales: permit classification and rank ordering on some characteristic, data is ordinal in nature, no absolute zero point.
    • Interval scales: contain equal intervals between numbers, each unit on the scale is exactly equal to any other unit, no absolute zero point.

    Descriptive Statistics

    • Variance: equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean.
    • Formula for variance (s2): deviation scores.
    • Standard deviation: square root of the variance.
    • Skewness: nature and extent to which symmetry is absent in a distribution.
      • Positive skew: relatively few scores fall at the high end of the distribution, may indicate the test was too difficult.
      • Negative skew: relatively few scores fall at the low end of the distribution, may indicate the test was too easy.
    • Kurtosis: steepness of a distribution in its center, platykurtic (relatively flat), leptokurtic (relatively peaked), or mesokurtic.

    The Normal Curve

    • Development of the concept of a normal curve began in the 18th century with Abraham Demurer and the Marquis de Laplace.
    • Karl Friedrich Gauss made substantial contributions, referred to as the “Laplace-Gaussian curve”.
    • Karl Pearson coined the term “normal curve”, used to refer to behavior that is usual, average, normal, standard, expected, or typical.

    Norms

    • Norms: test performance data of a particular group of test takers, designed for use as a reference when evaluating or interpreting individual test scores.
    • Normative sample: group of people whose performance on a particular test is analyzed for reference.
    • Norming: process of deriving norms, can be modified to describe a particular type of norm derivation, e.g. race norming.
    • User norms or program norms: descriptive statistics based on a group of test takers in a given period of time, rather than norms obtained by formal sampling methods.

    Sampling to Develop Norms

    • Standardization or test standardization: process of administering a test to a representative sample of test takers to establish norms.
    • Population: complete universe or set of individuals with at least one common, observable characteristic.
    • Sampling: process of selecting a portion of the universe deemed to be representative of the whole population.
      • Stratified sampling: process of selecting a sample to prevent sampling bias.
      • Purposive sample: sample selected because it is believed to be representative of the population.
      • Incidental sample or convenience sample: sample that is convenient or available for use, generalization of findings must be made with caution.

    Types of Norms

    • Percentiles: dividing a distribution of scores into 100 equal parts.
      • Xth percentile is equal to the score at or below which x% of scores fall.

    Validity

    • Criterion-related validity: judgment of how adequately a test score can be used to infer an individual’s most probable standing on some measure of interest.
    • Concurrent validity: degree to which a test score is related to some criterion measure obtained at the same time.
    • Predictive validity: degree to which a test score predicts some criterion measure.
    • Criterion: standard against which a test or a test score is evaluated.
      • Characteristics of a criterion:
        • Relevance: pertinent or applicable to the matter at hand.
        • Validity: evidence exists that the criterion is valid for the purpose for which it is being used.
        • Lack of contamination: criterion measure is not based on predictor measures.

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    Description

    This quiz covers the basics of nominal and ordinal scales in statistics, including classification, categorization, and rank ordering.

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