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Basic Concepts of Elementary Education
Research Terminology PowerPoint
EDEL 600 Online
The Mean The mean is the arithmetic average of the scores
and is the most frequently used measure of central tendency.
It is calculated by adding up all of the scores and dividing that total by the number of scores.
Example - IQ scores: 96, 96, 97, 99, 100, 110, 115, 120, 130. Mean = 96+96+97+99+100+110+115+120+130/9 = 107 (arithmetic average)
Gay & Airasian (2000)
The Mode The mode is the score that occurs most
frequently. The mode is determined by looking at a set of
scores or at a graph of scores
Example - IQ scores: 96, 96, 97, 99, 100, 110, 115, 120,
130. Mode = 96 (it occurs twice.)
Gay & Airasian (p.439)
The Median The median is the midpoint. Odd number of scores – the median is the middle
score. Even number of scores – the median is the point
halfway between the two middle scores. Example - IQ scores: 96, 96, 97, 99, 100, 110, 115, 120,
130. Median = 100 (middle point) - Scores: 50, 55, 60, 65, 70, 75 Median = 62.5 (average of two middle scores)
Gay & Airasian (p.439)
Mode / Median / Mean
N Score
1 50
2 60
3 60
4 70
5 80
Mode: 60
Median: 60
Mean: 64
The Standard Deviation A measure of the variability of the scores in a set of
scores equivalent to the average distance of the scores from the mean.
Example:The mean for the following set of five scores is 11 and the standard deviation is 2:9, 10, 10, 12, 14.
The scores vary on average about two points from the mean.
For the following set of five scores, the mean is 10 and the standard deviation is 0:10, 10, 10, 10, 10. There is no variation among the scores.
Primer on Educational Research 2004
The Range The range is the difference between the highest
and lowest score once the scores are arranged in order and is determined by subtraction.
It gives a quick, rough estimate of variability
Example: Score 60, 70, 80, 90 Range: 90-60= 30
Gay & Airasian (p.441)
The Normal Distribution
It is bell-shaped score distribution and quite symmetrical.
The normal distribution has a range of about three SD above the mean and three SD below the mean
About 68 percent of the scores in a normal distribution will fall within one standard deviation above and below the mean; about 95 percent of the scores will fall within two standard deviations above and below the mean, and almost 98 percent of the scores will fall within three standard deviations above and below the mean.
DiagramGay & Airasian (p.443)
The Normal Distribution• The diagram shows normal distribution.
Marzano, Pickering, and Pollock (2001)
Effect Size
When conducting a meta-analysis, a researcher translates the results of a given study into a unit of measurement referred to as an effect size.
Effect size expresses the increase or decrease in achievement of the experimental group in standard deviation units.
Effect size can be translated into a percentile gain.
Example Conversion table for effect size/ Percentile gain
Effect Size Examples
Instructional Practice
Ave. Effect Size (ES)
Percentile Gain
Identifying similarities and
differences
1.61 45
Summarizing and note taking
1.00 34
Reinforcing effort and providing recognition
.80 29
Homework and practice
.77 28 (Marzano, Pickering, and Pollock p.7) Conversion Table
Conversion TableEffect Size
Percentile gain
Effect Size
Percentile gain
Effect Size
Percentile gain
0.00 0 0.33 13 0.71 26
0.02 1 0.36 14 0.74 27
0.05 2 0.39 15 0.77 28
0.08 3 0.41 16 0.81 29
0.10 4 0.44 17 0.84 30
0.13 5 0.47 18 0.88 31
0.15 6 0.50 19 0.92 32
0.18 7 0.52 20 0.95 33
0.20 8 0.55 21 1.00 34
0.23 9 0.58 22
0.25 10 0.61 23 Note this
Table is not
0.28 11 0.64 24 complete
but is
0.31 12 0.67 25 sufficient
for the exam
References Marzano, R.J., Pickering, D.J., Pollock, J.
E. (2001). Classroom Instruction that works. Alexandria, VA.
Primer on Educational Research (2004) http://www.ecs.org/html/educationIssues/Research/primer/glossary.asp
Gay, L.R., Airasian, P. (2000). Educational Research. Prentice-Hall, Inc. NJ.
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