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.