Chapter 4 Measurement

Modified: 2005-10-25

• OPERATIONAL DEFINITIONS
• VARIABLES
  • Continuous
    • Variable that is theoretically infinitely divisible; for any two values, you can imagine an intermediate value
  • Discrete
    • Variable with a limited number of values; many intermediate values are not possible.
  • Dichotomous Variables
    • Variable that can have only two values.
  • Quantitative
    • A variable whose values indicate different numerical amounts.
  • Qualitative
    • Variable whose values differ in kind rather than in amount.
  • Category
    • Frequency count of observations in specified categories.
  • Ranked
    • Each observation is a rank score.
  • Scaled Data
    • Numerical measurements that are not ranks.
  • Scales of Measurement
    • Nominal Scale
      • Measurement scale in which numbers or names serve as labels and do not indicate a numerical relationship.
    • Ordinal Scale
      • Measurement scale in which numbers indicate rank order, but equal differences between numbers do not indicate equal differences between the thing measured.
    • Interval Scale
      • Scale in which equal differences between measurements indicate equal differences in the thing measured.
    • Ratio Scale
      • Measurement scale with the characteristics of an interval scale plus the characteristic of a true zero; zero means that none of the thing measured is present.
  • Using Scales of Measurement
• ERRORS IN MEASUREMENT
  • Systematic errors
    • Variation in a data set from causes that can be specified.
  • Random errors
    • Variation in a data set that comes from uncontrolled variables that cannot be specified.
• TRUSTWORTHY MEASURES
  • Reliability
    • The consistency or dependability of a measure.
  • Test-Retest Reliability
    • Determining reliability by administering a test a second time and correlating the two scores.
  • Split-Half Reliability
    • Determining reliability by dividing a test in half and correlating the two part scores.
  • Interobserver Reliability
    • Method of detecting inconsistent measuring by comparing observations of two independent observers
  • Other Assurances of Reliability
  • Validity
    • The extent to which a test measures what it claims to measure.
  • Content Validity
    • Determined by the degree to which the test items represent the characteristic tested.
  • Criterion-Related Validity
    • Determined by the degree to which the test correlates with other measures of the same variable.
  • Sensitivity
    • The ability of a test or measure to make distinctions.
    • Ceiling effect
      • Scores clustered near the maximum possible score prevent the detection of variables that raise scores.
    • Floor effect
      • Scores clustered near the minimum possible score prevent the detection of variables that lower scores.
• TESTS AND MEASUREMENTS
  • Published Tests
  • Custom-Made Tests
  • Item testing
  • Pilot statistics
    • Analysis of data from a pilot test.

In The Know--Perhaps the most important step you can take if you want to move from confusion to confidence about a scientific topic is to find out how the concepts are measured. Knowing how schizophrenia or intelligence or time is measured gives you a big boost toward understanding the topic.

In The Know--The question of how to use the information in Table 4.3 is one that has produced different answers at different times. When this scales of measurement catalog was first presented by Stevens (1946), it was promoted as a way to determine what NHST statistical tests were appropriate for a particular set of data. The idea was that different classes of NHST tests required a particular scale of measurement. Over the years (but with occasional resurgence), this idea has lost adherents. Our position is that the distinctions among scales of measurement are not helpful in deciding what statistical test to use. What is required is knowledge of the nature of the distributions of the numbers and not the scale of measurement.

In the Know--Magazines and the Internet are the source of many tests. People like to take tests. Using tests published in magazines, you can determine your score as a friend, lover, or intellectual. You can determine whether you are right-brained, depressed, or destined to become rich or lose weight. Unfortunately, most of these tests have not been checked for reliability or validity. Their purpose is entertainment, not measurement. Of course, now that you know the basics of reliability, you can check a test's reliability yourself.

GLOSSARY

• Category data
  • Frequency count of observations in specified categories.
• Ceiling effect
  • Scores clustered near the maximum possible score prevent the detection of variables that raise scores.
• Content validity
  • Determined by the degree to which the test items represent the characteristic tested.
• Continuous variable
  • Variable that is theoretically infinitely divisible; for any two values, you can imagine an intermediate value
• Criterion-related validity
  • Determined by the degree to which the test correlates with other measures of the same variable.
• Dichotomous variable
  • Variable that can have only two values.
• Discrete variable
  • Variable with a limited number of values; many intermediate values are not possible.
• Floor effect
  • Scores clustered near the minimum possible score prevent the detection of variables that lower scores.
• Interobserver reliability
  • Method of detecting inconsistent measuring by comparing observations of two independent observers
• Interval scale
  • Scale in which equal differences between measurements indicate equal differences in the thing measured.
• Nominal scale
  • Measurement scale in which numbers or names serve as labels and do not indicate a numerical relationship.
• Operational definition
  • Procedures or operations used to measure a variable or establish a condition.
• Ordinal scale
  • Measurement scale in which numbers indicate rank order, but equal differences between numbers do not indicate equal differences between the thing measured.
• Pilot statistics
  • Analysis of data from a pilot test.
• Qualitative variable
  • Variable whose values differ in kind rather than in amount.
• Quantitative variable
  • A variable whose values indicate different numerical amounts.
• Random error
  • Variation in a data set that comes from uncontrolled variables that cannot be specified.
• Ranked data
  • Each observation is a rank score.
• Ratio scale
  • Measurement scale with the characteristics of an interval scale plus the characteristic of a true zero; zero means that none of the thing measured is present.
• Reliability
  • The consistency or dependability of a measure.
• Scaled data
  • Numerical measurements that are not ranks.
• Sensitivity
  • The ability of a test or measure to make distinctions.
• Split-half reliability
  • Determining reliability by dividing a test in half and correlating the two part scores.
• Systematic error
  • Variation in a data set from causes that can be specified.
• Test-retest reliability
  • Determining reliability by administering a test a second time and correlating the two scores.
• Validity
  • The extent to which a test measures what it claims to measure.