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.