Instrumentation%20(cont.)

1
Instrumentation (cont.)

• February 28
• Note Measurement Plan Due Next Week

2
Unobtrusive Measures

• Many instruments require the cooperation of the
  respondent in one way or another.
• An intrusion into an ongoing activity could be
  involved which causes a form of negativity within
  the respondent.
• To eliminate this, researchers use unobtrusive
  measures, data collection procedure that involve
  no intrusion into the naturally occurring course
  of events.
• In most cases, no instrument is used, however,
  good record keeping is necessary.
• They are valuable as supplements to the use of
  interviews and questionnaires, often providing a
  useful way to corroborate what more traditional
  data sources reveal.

3
Types of Scores

• Quantitative data is reported in the form of
  scores
• Scores are reported as either raw or derived
  scores
• Raw score is the initial score obtained
• Taken by itself, a raw score is difficult to
  interpret, since it has little meaning
• Derived score are scores that have been taken
  from raw scores and standardized
• They enable researchers to say how well the
  individual performed compared to others taking
  the same test
• Examples include
• Age and Grade-level Equivalents
• Percentile Ranks
• Standard scores are mathematically derived scores
  having comparable meaning on different instruments

4
Four Types of Measurement Scales
5
Norm-Referenced vs. Criterion-Referenced
Instruments

• All derived scores give meaning to individual
  scores by comparing them to the scores of a
  group.
• The group used to determine derived scores is
  called the norm group and the instruments that
  provide such scores are referred to as
  norm-referenced instruments.
• An alternative to the use of achievement or
  performance instruments is to use a
  criterion-referenced test.
• This is based on a specific goal or target
  (criterion) for each learner to achieve.
• The difference between the two tests is that the
  criterion referenced tests focus more directly on
  instruction.

6
Descriptive Statistics
7
Statistics vs. Parameters

• A parameter is a characteristic of a population.
• It is a numerical or graphic way to summarize
  data obtained from the population
• A statistic is a characteristic of a sample.
• It is a numerical or graphic way to summarize
  data obtained from a sample

8
Types of Numerical Data

• There are two fundamental types of numerical
  data
• Categorical data obtained by determining the
  frequency of occurrences in each of several
  categories
• Quantitative data obtained by determining
  placement on a scale that indicates amount or
  degree

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Techniques for Summarizing and Presenting
Quantitative Data

• Visual
• Frequency Distributions
• Histograms
• Stem and Leaf Plots
• Distribution curves
• Numerical
• Central Tendency
• Variability

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Summary Measures
Summary Measures
Variation
Central Tendency
Arithmetic Mean
Median
Mode
Range
Variance
Standard Deviation
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Measures of Central Tendency
Central Tendency
Average (Mean)
Median
Mode
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Mean

• The most common measure of central tendency
• Affected by extreme values (outliers)

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
14
Mean 5
Mean 6
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Median

• Robust measure of central tendency
• Not affected by extreme values
• In an Ordered array, median is the middle
  number
• If n or N is odd, median is the middle number
• If n or N is even, median is the average of the
  two middle numbers

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
14
Median 5
Median 5
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Mode

• A measure of central tendency
• Value that occurs most often
• Not affected by extreme values
• Used for either numerical or categorical data
• There may may be no mode
• There may be several modes

0 1 2 3 4 5 6
0 1 2 3 4 5 6 7 8 9 10 11
12 13 14
No Mode
Mode 9
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Variability

• Refers to the extent to which the scores on a
  quantitative variable in a distribution are
  spread out.
• The range represents the difference between the
  highest and lowest scores in a distribution.
• A five number summary reports the lowest, the
  first quartile, the median, the third quartile,
  and highest score.
• Five number summaries are often portrayed
  graphically by the use of box plots.

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Variance

• The Variance, s2, represents the amount of
  variability of the data relative to their mean
• As shown below, the variance is the average of
  the squared deviations of the observations about
  their mean

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Standard Deviation

• Considered the most useful index of variability.
• It is a single number that represents the spread
  of a distribution.
• If a distribution is normal, then the mean plus
  or minus 3 SD will encompass about 99 of all
  scores in the distribution.

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Calculation of the Variance and Standard
Deviation of a Distribution (Definitional formula)
Raw Score Mean X X (X X)2
85 54 31 961 80 54 26 676 70 54 16 256 60 54 6 36
55 54 1 1 50 54 -4 16 45 54 -9 81 40 54 -14 196 30
54 -24 576 25 54 -29 841

404.44
Standard deviation (SD)
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Comparing Standard Deviations
Data A
Mean 15.5 S 3.338
11 12 13 14 15 16 17 18
19 20 21
Data B
Mean 15.5 S .9258
11 12 13 14 15 16 17 18
19 20 21
Data C
Mean 15.5 S 4.57
11 12 13 14 15 16 17 18
19 20 21
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Facts about the Normal Distribution

• 50 of all the observations fall on each side of
  the mean.
• 68 of scores fall within 1 SD of the mean in a
  normal distribution.
• 27 of the observations fall between 1 and 2 SD
  from the mean.
• 99.7 of all scores fall within 3 SD of the mean.
  
• This is often referred to as the 68-95-99.7 rule

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The Normal Curve
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Different Distributions Compared
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Fifty Percent of All Scores in a Normal Curve
Fall on Each Side of the Mean
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Probabilities Under the Normal Curve
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Correlation
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Correlation Coefficients

• Pearson product-moment correlation
• The relationship between two variables of degree.
• Positive As one variable increases (or
  decreases) so does the other.
• Negative As one variable increases the other
  decreases.
• Magnitude or strength of relationship
• -1.00 to 1.00
• Correlation does not equate to causation

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Positive Correlation
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Negative Correlation
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No Correlation
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Correlations

• Thickness of scatter plot determines strength of
  correlation, not slope of line.
• For example see
• http//noppa5.pc.helsinki.fi/koe/corr/cor7.html
• Remember correlation does not equate causation.

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Negative Correlation
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Validity and Reliability

• Chapters 8

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Validity and Reliability

• Validity is an important consideration in the
  choice of an instrument to be used in a research
  investigation
• It should measure what it is supposed to measure
• Researchers want instruments that will allow them
  to make warranted conclusions about the
  characteristics of the subjects they study
• Reliability is another important consideration,
  since researchers want consistent results from
  instrumentation
• Consistency gives researchers confidence that the
  results actually represent the achievement of the
  individuals involved

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Reliability

• Test-retest reliability
• Inter-rater reliability
• Parallel forms reliability
• Internal consistency (a.K.A. Cronbachs alpha)

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Validity

• Face
• Does it appear to measure what it purports to
  measure?
• Content
• Do the items cover the domain?
• Construct
• Does it measure the unobservable attribute that
  it purports to measure?

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Validity

• Criterion
• Predictive
• Concurrent
• Consequential

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Types of validity (cont.)
Here the instrument samples some and only of the
construct
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Types of validity
Here the instrument samples all and more of the
construct
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The construct
Here the instrument fails to sample ANY of the
construct
The instrument
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The construct
Here the instrument samples some but not all of
the construct
The instrument
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Perfection!
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Reliability and Validity