CDIS 455 CH. 4Measurement Study Notes

Chapter 4: Measurement

Charis Powell, M.S., CCC-SLP
Fall 2021

Purpose of Measurement

  • The purpose of measurement is to specify differences in the degree to which objects, persons, and events possess the characteristic being measured.

  • To measure effectively, researchers collect and organize information in the form of data.

  • Statistics, a branch of mathematics, analyzes and interprets this data.

4 Scales of Measurement / Types of Data

  • There are four primary scales of measurement:

    • Ordinal

    • Nominal

    • Interval

    • Ratio

  • These scales are divided into two categories: Categorical Data Types (Nominal and Ordinal) and Numerical Data Types (Interval and Ratio).

Ordinal Measurement

  • Ordinal data is ordered from one category to another:

    • From highest to lowest

    • From best to worst

    • From least to greatest

  • Examples of ordinal data include:

    • Height (shortest to tallest)

    • Grading scales (A, B, C, D, F)

    • Likert scales (1: strongly agree, 2: disagree, 3: undecided, 4: agree, etc.)

  • Ordinal scales are not very precise in their measurements.

Nominal Measurement

  • Nominal data does not measure anything but is used to label individuals, objects, behaviors, events, or other entities.

  • The numbers or labels assigned are arbitrary and possess no numerical value.

  • Examples include:

    • Numbers on sports jerseys

    • Gender categories

    • Socioeconomic status classifications

Interval Measurement

  • Interval data possesses the arithmetic properties of both unequal and equal intervals.

  • It allows for the computation of differences in data but does not permit multiplication or division.

  • For example, the difference between scores of 100 and 70 on a test is 30, but this does not mean that the person with a score of 100 is 30% smarter than the person with a score of 70.

  • Interval data lacks a true zero.

  • Examples include:

    • Temperature measured in Celsius or Fahrenheit

Ratio Measurement

  • Ratio data is similar to interval data but includes a true zero point.

  • A true zero indicates the absence of the property being measured, for example, a weight cannot be -10 pounds, whereas temperature can be -10 degrees (interval scale).

  • Ratio data is also referred to as continuous data.

  • Comparison: Nominal data is considered very weak, whereas ratio data is viewed as very strong.

  • Examples include:

    • Weight

    • Height

    • Time (seconds, hours, etc.)

Data Transformation

  • Data transformation involves modifications that simplify the structure of data values.

  • The main goals include making the distribution of the data more symmetrical and ensuring constant variability, which usually improves the normality of the data.

  • Common types of data transformations include:

    • Logarithms

    • Simple powers

    • Square roots

    • Inverse transformation

Descriptive Statistics

  • Descriptive statistics arrange data in a meaningful way.

  • Types of descriptive statistics include:

    • Measures of Location: These are single values that describe an entire set of data, including:

    • Mean (average): The sum of values divided by the number of values.

      • Example data set: 2, 4, 6, 8, 9 → Mean = 5.8

    • Median: Midpoint of data; the middle number or average of two middle numbers when no two values are alike.

      • Example data set: 2, 4, 6, 8, 9 → Median = 6

    • Mode: Most frequently occurring value used primarily with nominal data.

      • Example data set: 2, 4, 4, 6, 8 → Mode = 4

    • Measures of Individual Location: Specify the location of one participant in relation to the group, including:

    • Ranks: Orders of participants based on performance

    • Percentiles (fractionals): Divide data into 100 equal parts (e.g., a 60th percentile indicates performance above 60% and below 40% of the group).

    • Standard scores (z-scores): Raw scores converted into standard deviation units. In a system where the mean is 100 and the standard deviation is 25, a score of 75 is one standard deviation below the mean and a score of 125 is one standard deviation above the mean. The formula for calculating the standard score is as follows:

      • SS = \frac{\text{Raw Score} - \text{Mean}}{\text{SD}}

      • Example calculation: Score = 75, Mean = 70, SD = 10, then SS = \frac{75 - 70}{10} = 0.5

    • Measures of Variability: Measure the degree of dispersion in a set of data, including:

    • Number of categories

    • Range: Largest value minus lowest value.

      • Example: Sample range: 10-90 → Range = 80.

    • Variance: Dispersion of individual values around the mean, suitable for interval or ratio data.

Standard Deviation

  • The standard deviation (SD) indicates the spread of values around the mean.

  • If the SD is small, the values are closely spread around the mean.

  • If the SD is large, the values are widely spread from the mean.

  • The formula for standard deviation is:

    • SD = \sqrt{\text{Variance}}

Univariate Statistical Graphs

  • Types of univariate statistical graphs:

    • Histograms

    • Stem-and-leaf plots

    • Bar graphs

    • Box plots (box-and-whiskers)

    • Examples illustrated on the respective graphs

Bivariate Statistical Graphs

  • Bivariate statistical graphs effectively display relationships between two variables.

  • Types include:

    • Scatterplots: Show positive, negative, or no relationship between two variables.

References

  • Meline, T. (2010). A research primer for communication sciences and disorders. Pearson.