Chapter 2-norms & basic stats Flashcards
Measurement def
Process of obtaining a NUMERICAL description of the degree to which an individual possesses a particular characteristic
-> Assigning numbers to obj
Outcome of measurement
Assign an individual/obj to a category (number)
A measurement scale determines the kinds of: (2)
(1) STATISTICAL procedures that can be applied to the scores produced by the measure
(2) COMPARISONS we can make among individuals using that scale
Nominal scale def
Numbers are assigned to represent labels or categories of data only
Appropriate Statistics for Nominal scale (2)
Frequency, mode
Ordinal scale def
Numbers are assigned to rank-ordered data. The distances between numbers are NOT equal
Appropriate stats for Ordinal scale (5)
Frequency, mode, median, percentile, rank-order correlation
Interval scale def
(1) Numbers are assigned to rank-ordered data, and (2) the DISTANCE between numbers is EQUAL. There is NO absolute zero point (i.e., a number indicating the complete absence of what is measured).
Appropriate stats for Interval scale (6)
Frequency, mean, mode, median, percentile, Pearson correlation, t test
Ratio scale def
(1) Numbers are assigned to rank- ordered data, (2) the distance between numbers is EQUAL, and (3) there IS an absolute zero point.
Appropriate stats for Ratio scale (7)
Frequency, mean, mode, median, percentile, Pearson correlation, proportion, t test
Norm def
Test scores achieved by a defined group of individuals (i.e., norm sample).
Norm-based interpretation
Compare an individual’s score to the norm group
Types of Norms (3)
(1) DEVELOPMENTAL Norms
(2) WITHIN-GROUP Norms
Norms without a Norm Sample
(3) CRITERION-REFERENCED Norms
Developmental Norms def
Typical level of performance in each of the AGE group or grade levels that the test’s target population comprises.
-> Age-equivalent or grade-equivalent scores are assigned based on the MEDIAN RAW SCORE for that chronological age or grade level.
-> Median = TYPICAL score = norm
Within-Group Norms (3)
(1) Percentiles
(2) Z-scores
(3) Transformed standard scores
Percentiles def
Percentage of individuals falling below a test score
Standard Deviation def
A measure of the average distance of scores from the mean.
Transformed Standard Score formula
Bz + A
B = desired SD
A = desired Mean
Percentiles advantages (3)
(1) Easy to grasp
(2) Easy to compute
(3) Interpretation doesn’t change with the shape of the distribution
Percentiles disadvantages (2)
(1) Magnifies differences near mean; minimizes differences at extremes
(2) Some common statistical analyses are NOT possible with percentiles
Standard scores advantages (2)
(1) Gives a sense of distance from the mean
(2) Can be used in most common statistical analyses
Standard score disadvantages (2)
(1) Unfamiliar to many non-specialists
(2) Interpretation difficult when distribution not normal
Criterion-Referenced Norms def
Evaluate performance relative to an absolute criterion or standard rather than performance of other individuals.
-> An absolute vs relative evaluation
Within-Group Norms: Criticisms (2)
(1) Only meaningful if the standardization (norm) sample is representative
(2) Within-group comparisons encourage competition
Requirement for Criterion-Referenced Norms
Define content of domain narrowly and specifically.
E.g. Driving skills, 8th grade math curriculum
Criterion-Referenced Norms: Issues (3)
(1) Can elements of performance be specifically defined?
-> Hard to clearly define what “good” or “bad” performance looks like.
-> Criterion-referenced norms require a clear standard (e.g., scoring 80% on a test to pass), but creating these standards can be challenging because it’s hard to decide what knowledge or skills are essential.
(2) Focus on minimum standards
-> e.g., “Did you pass?”
-> Ignore how much better one person is compared to others.
(3) Absence of relative knowledge
-> You don’t know how someone performs compared to others.
Developmental norms cons
Often interpreted inappropriately
-> Overgeneralization, misinterpreting median…
Developmental & within-groups norms are dependent on _______________
the quality of norm sample
Criterion-referenced norms have limited ___________
applicability
Norm-referenced testing convert raw score to ___________ score
standardized
What is an elevated score?
2 z-scores
Characteristics of a GOOD norm sample (3)
(1) Sufficiently LARGE (avoid sampling error)
(2) Representative of the largest population
(3) Contemporary
Properties of scales (3)
(1) Magnitude
(2) Equal Intervals
(3) Absolute 0
Propriety of Magnitude def
A scale has the property of magnitude if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance.
Propriety of Equal Intervals def
A scale has the property of equal intervals if the difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units.
Propriety of Absolute 0
An absolute 0 is obtained when nothing of the property being measured exists.
Frequency distribution def
Displays scores on a variable/measure to reflect how frequently each value was obtained.
The greater the percentile, the more ______________
la personne est bonne!!!
McCall’s T
Same as standard scores (Z scores), except that the M=50 and SD=10.
Standardization vs normalization
McCall’s T, z-scores (…) - Do not change the characteristics of the distributions.
If a distribution of scores is skewed before the transformation is applied, it will also be skewed after the transformation has been used.
Transformations _________ but do not _______.
standardize; normalize
Interquartile range
Interval of scores bounded by the 25th and 75th percentiles.
-> bounded by the range of scores that represents the middle 50% of the distribution.
Deciles
Use points that mark 10%.
-> Thus, the top decile, or D9, is the point below which 90% of the cases fall. The next decile (D8) marks the 80th percentile, and so forth.
Stanine system
Converts any set of scores into a transformed scale, which ranges from 1 to 9.
M = 5, SD = 2
Overselection
Selecting a higher percentage from a particular group than would be expected on the basis of the representation of that group in the applicant pool.
Overselection is a problem with ______
Within-Group Norms
Tracking (developmental norms)
Tendency to stay at about the same level relative to one’s peers.
Big Data
Revolution in social science research.
= Data sets with sizes beyond the ability of commonly used software tools to capture, curate, manage, and process the data within a tolerable elapsed time.
