Measures of Central Tendency
Peter Swanson, PhDGeorgia State University
Mode14 16 16 17 18 19 19 19 21 22
Median14 15 16 17 18 19 20 21 22
Mean1 2 3 4 5 6 7
Range
Shapes of Distributions
Positive Skew
Negative Skew
Measures of Variability
(a) 24, 24, 25, 25, 25, 26, 26 x̄= 175/7 = 25
(b) 16, 19, 22, 25, 28, 30, 35 x̄= 175/7 = 25
(c) is more homogeneous that those in (b).
Standard DeviationThe square root of the variance
What is the Standard Deviation?
Why care about the Standard Deviation?
A low standard deviation indicates that all of the data points are very close to the same value (the mean).
A high standard deviation indicates that the data are “spread out” over a large range of values.
Percentile Rank A score equals the percentage of scores in its
frequency distribution which are lower or equal to it.
Criterion-referenced tests
• Many criterion-referenced tests involve a cutscore, where students pass if their score exceeds the cutscore and fails if it does not (often called a mastery test).
• The criterion-referenced interpretation of a test score identifies the relationship to the subject matter.
• A criterion-referenced test will use questions which were correctly answered by students who know the specific material.
Norm-referenced tests• Yield an estimate of the position of the tested individual
in a predefined population, with respect to the trait being measured.
• Indicate whether the test-taker did better or worse than other people who took the test.
• Report primarily whether a student correctly answered more questions compared to other students in the group.
• Use questions which were correctly answered by the "best" students and not correctly answered by the "worst" students.
Advantages / Disadvantages
1. NRT cannot measure progress of the population of a whole, only where individuals fall within the whole.
2. The difficulty level of items themselves, as are the cut-scores to determine passing levels are also changed from year to year.
3. NRT have been criticized for bias against minorities.4. High Stakes testing- No Child Left Behind defines
failure if a school does not show improvement from year to year, even if the school is already successful.
Reliability and Validity
Reliability – the consistency of measurementValidity – Measuring what you purport to measure.