Study Guide: Basic Concepts in Measurement Flashcards
Measurement
Assigning numbers to persons in such a way that some attributes of the persons being measured are faithfully reflected by some property of the numbers.
Traits of Measurement
- Traits need to be quantifiable.
* Not all traits are easily identifiable
Scales of Measurement
- Nominal
- Ordinal
- Interval
- Ratio
Nominal Scale
- Numbers receive verbal label, but don’t signify any particular amount of a trait.
- “least valuable”, but useful for labeling
- Example: Coding Male vs. Female as 1 and 2
Ordinal
- Numbers denote order/ranking, but not the amount of a trait, and there is no consistent distance between numbers.
- Example: List of contestants’ race times–there is an order/rank, but the time between scores has no consistency.
Interval
- Numerical differences in scores represent equal differences in the trait being measured.
- Does not have a true zero
- Example: Temperature–there are set and standard differences between numbers, but “0” does not mean the lack of temperature!
Ratio
- Has a true zero point that represents the absence of a trait.
- Can make proportional statements (twice the score = twice the attribute)
Example: Income, GPA, Years of Experience
What scale meets the minimum criteria for statistical measurement?
Interval scale
Measures of Central Tendency
- Mean
- Median
- Mode
In a normal distribution…
mean=median=mode
What measure of central tendency is most often utilized?
Mean!
*Takes all data points into account
- Highlights importance of outliers
- Larger sample sizes can absorb more of a difference between data points
What is the normal curve and why is it important?
- A theoretical distribution of human traits in nature.
- More abnormal=less precise scores become.
- it gives a standard to compare against
Variability
- Everyone differs…and we can measure it!
* Measures the degree of variance (like outliers), deviation from average score.
How to calculate Variability
- The sum of squared deviations from the mean, divided by number of scores
- Also, the square of standard deviation
sigma^2 = [ E(X-u)^2 ] // N
Z-score
Returns the squared measure of variability to the original metric (how many deviations from the mean)
How to calculate Z-score
z= x-u // standard deviation
Standard Deviation
- The understanding of the percentage of people that fell above and below the mean
- Measures the amount of variation or dispersion from the average
- Calculated: Square root of the variance. (square root of the above calculation)
Benefits of Z-score
- Normalizes distribution
* Able to compare tests with different metrics
Correlation
- How is one score on one measure associated with a score on another measure
- Ranges from -1 to +1
Prediction
- Can often be on different scales of measurement
* Linear regression: Allows for an adjustment for different scales of measurement.
Intercorrelation
Factor Analysis: identifies the underlying variables that account for correlations between test scores
Types of Norms
- Equivalency
* Reference
Equivalency
The group with which the individual’s score is most consistent (grade equivalence, age equivalence)
Reference
How the individual performed compared to those from the norm group (percentile)
Cautions of Norms
- Beware of over-interpreting equivalency scores
- Be sure to use the norm group most appropriate and representative
- It is all relative info!
