EDCI 6312 Educational Measurement

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EDCI 6312 - Educational Measurement

• Dr. Reynaldo Ramirez, Jr
• Associate Professor for Secondary and Science
  Education

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Course Content
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Know the Math

• Measurement and Scales
• Frequency Distributions
• Measures of Central Tendency
• Percentiles and Norms
• Measures of Variability
• Correlation
• Evaluation and Interpretation of Tests

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Measurement and Scales

• Nominal Scale Numbers are assigned for the sole
  purpose of differentiating one object from
  another. Example We are having class in Room
  2.222 UTBs address is 80 Fort Brown to get to
  class most people drove down US 77-83, and so on.
• Give me an example.

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Measurement and Scales

• Ordinal Scale A number has the property of
  order. The numbers imply direction. They,
  however, do not imply the difference between two
  objects or events. Example the rank in height of
  a basketball team, the order in which runners
  cross the finish line, the order in which you
  walked in to class tonight, and so on.
• Give me an example.

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Measurement and Scales

• Interval Scale Numbers representing equal
  distances between observation points on the
  scale. For example measures of height, test
  scores, measured in terms of number of items
  correct, and so on.
• Give me an example.

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Measurement and Scales

• Ratio Scale Numbers representing equal
  distances between observation points on the scale
  from an absolute zero. For example something
  twice as long, or half as short, and so on.
• Give me an example.

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Frequency Distribution

• Achievement Scores on an English Examination
• 69, 71, 71, 82, 66, 89, 81, 68, 95, 88, 70, 85,
  61, 81, 88, 94, 79, 81, 75, 97, 72, 72, 85, 74,
  82, 86, 93, 64, 84, 86, 62, 73, 82, 79, 86, 76,
  76, 87, 90, 68, 78, 91, 82, 90, 83, 75, 80, 80,
  92, 67.

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Frequency Distribution

• Which is the highest and lowest score?
• 69, 71, 71, 82, 66, 89, 81, 68, 95, 88, 70, 85,
  61, 81, 88, 94, 79, 81, 75, 97, 72, 72, 85, 74,
  82, 86, 93, 64, 84, 86, 62, 73, 82, 79, 86, 76,
  76, 87, 90, 68, 78, 91, 82, 90, 83, 75, 80, 80,
  92, 67.

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Highest to Lowest Distribution

• Highest Score 97
• Lowest Score 61
• What else do we know?

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What Can the Data Tell Us?

• Which is the highest and lowest score?
• Which score comes up most often?
• Which score is in the middle?
• Which score comes up the least?
• What is the normal distribution of the scores?

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Grouped Frequency Distributions

• Group data into intervals (5 or 10)
• Note the highest and lowest scores
• Include the high and low scores within the
  interval

Interval Tally Frequency 90-99
//// /// 8 80-89 //// //// ////
//// 20 70-79 //// ////
//// 14 60-69 //// /// 8
N 50
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Grouped Frequency Distributions

• Group data into intervals of 5

Interval Tally Frequency 95-99
// 2 90-94 //// / 6 85-89
//// /// 8 80-84 //// //// //
12 75-79 //// //
7 70-74 //// // 7 65-69 ////
5 60-64 /// 3 N 50
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Simple Frequency Distribution

• Group data into intervals of 1

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Histogram of English Scores

• Lay out an area on a piece of graph paper that
  corresponds to a three-fourths ratio of height to
  width.
• Draw a horizontal line. Label it, the x-axis,
  Scores.
• At the left end of the x-axis draw a vertical
  line, y-axis, calling it Frequency.
• Complete the histogram by drawing lines parallel
  to the height represented by the frequency for
  each interval.

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Frequency Polygon of English Scores

• Label the frequency polygon as you did the
  Histogram.
• Place a dot at the midpoint of each interval.
• Connect the extremes at the midpoint of the
  adjacent interval.

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Practice Items on Blackboard
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Measures of Central Tendency

• Arithmetic Mean or Mean The sum of all scores
  divided by the number of scores.
• Mode The most frequent score.
• Median The score (point) that denotes the
  separation between the upper half of the
  distribution from the lower half.

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Calculation of the Mean

• Individual X
• A 2
• B 7
• C 8
• D 6
• E 3
• F 6
• G 2
• H 3
• I 8
• J 5
• N10 SX 50

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Calculation of the Individual Deviation

• Individual Score X
• Individual Deviation Score x
• Calculation for x
• x X - M

For Individual A x X M x 2 5 x -3
For Individual B x X M x 7 5 x 2
and so on
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Calculation of the Mode

• X
• 24
• 23
• 22
• 21
• 21
• 21
• 21
• 20
• 19
• 19
• 19
• 18
• 17
• 16

Principal Mode 21 Secondary Mode 19
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Calculation of the Median (N is odd)

• X
• 16
• 15
• 15
• 14
• 14
• 13
• 12
• 10
• 9
• N 9

5th score from the bottom

5th score is 14
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Calculation of the Median (N is Even)

• X
• 15
• 14
• 14
• 13
• 12
• 10
• 9
• 8
• 6
• 3
• N 10

5.5th score from the bottom

Median 11
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Which measure of Central Tendancy is the best to
use?

• Mode is not very useful.
• Mean is most often used.
• Median helps during situations when extreme
  scores exaggerate the mean.

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Grouped Data TechniquesA BETTER ILLUSTRATION OF
THE GROUPED FREQUENCY DISTRIBUTION FOR THE
ENGLISH ACHIEVEMENT SCORES
N No. of observations f The frequency i
Size of the interval L exact lower limit of
any interval Mp the midpoint of any interval
Interval Frequency (f) 95-99 2 90-94
6 85-89 8 80-84 12 75-79
7 70-74 7 65-69 5 60-64 3 N 50
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Grouped Data TechniquesCALCULATIONS OF THE MEAN
FOR BIOLOGY SCORES, GROUPED DATA
Scores f d fd 85-89 1 3 3 80-84
3 2 6 75-79 6 1 6 15 70-74
15 0 65-69 12 -1 -12 60-64 8 -2 -16 55-59
3 -3 -9 50-54 2 -4 -8 -45 N
50 Sfd 30
Sfd N
Formula for the mean M Mp i
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Grouped Data TechniquesCALCULATIONS OF THE MEAN
FOR BIOLOGY SCORES, GROUPED DATA
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Grouped Data TechniquesCALCULATIONS OF THE
MEDIAN FOR GEOGRAPHY QUIZ SCORES, GROUPED DATA
Scores f Calculations 75-79 2 (a) 50 of
54 27 70-74 4 65-69 8 (b) 2 3 6
15 26 60-64 14 55-59 15 (c)
R 27 26 1 50-54 6 45-49 3 (d) F50
14 40-44 2 N 54 (e) L 59.5
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Grouped Data TechniquesCALCULATIONS OF THE
MEDIAN FOR GEOGRAPHY QUIZ SCORES, GROUPED DATA
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Next Week

• Percentiles and Norms
• Chapter 1 Educational Testing and Assessment
  Context, Issues, and Trends
• Maybe Measures of Variability