Sampling (cont.)Instrumentation

Measurement Plan Due 3/7

Sampling Demonstration

In Small Groups

• Check each others literature review and hypothesis of choice.– Do literature review, rationale, and hypothesis go

together?– Offer constructive criticism-suggestions.

• Then,– Identify your

• Target population• Accessible population

– Sampling strategy• Strengths • Weaknesses

Instrumentation

Discuss Jared Diamond

Soft Sciences are Often Harder than Hard Sciences

Instrumentation

Instructions: Circle the choice that indicates your opinion.

1. Teachers’ unions should be abolished.Strongly Strongly

agree Agree Undecided Disagree disagree(5) (4) (3) (2) (1)

2. School administrators should be required by law to teach at least one class in a public school classroom every year.

Strongly Stronglyagree Agree Undecided Disagree disagree(5) (4) (3) (2) (1)

3. Classroom teachers should be able to choose the administrators in their schools.Strongly Strongly

agree Agree Undecided Disagree disagree(5) (4) (3) (2) (1)

What are Data?

• Data refers to the information researchers obtain on the subjects of their research.

• Demographic information or scores from a test are examples of data collected.

• The researcher has to determine what kind of data they need to collect.

• The device the researcher uses to collect data is called an instrument.

Key Questions

• The instruments and procedures used in collecting data is called instrumentation.

• Questions arise regarding the procedures and conditions under which the instruments will be administered:– Where will the data be collected?– When will the data be collected?– How often are the data to be collected?– Who is to collect the data?

• The most highly regarded types of instruments can provide useless data if administered incorrectly, by someone disliked by respondents, under noisy, inhospitable conditions, or when subjects are exhausted.

Validity, Reliability, and Objectivity

• 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

• Objectivity refers to the absence of subjective judgments

Usability

• An important consideration for any researcher in choosing or designing an instrument is how easy the instrument will actually be to use.

• Some of the questions asked which assess usability are:• How long will it take to administer?• Are the directions clear?• How easy is it to score?• Do equivalent forms exist?• Have any problems been reported by others who used it?

• Getting satisfactory answers can save a researcher a lot of time and energy.

Ways to Classify Instruments

• Who Provides the Information?– Themselves: Self-report data – Directly or indirectly: from the subjects of the study – From informants (people who are knowledgeable

about the subjects and provide this information)

Types of Researcher-completed Instruments

• Rating scales• Interview schedules• Tally sheets• Flowcharts

• Performance checklists

• Observation forms

Types of Subject-completed Instruments

• Questionnaires• Self-checklists• Attitude scales• Personality

inventories

• Achievement/aptitude tests

• Performance tests• Projective devices• Sociometric devices

Scientific America

Handwriting Analysis

Item Formats

• Questions used in a subject-completed instrument can take many forms but are classified as either selection or supply items.

• Examples of selection items are:• True-false items

• Matching items

• Multiple choice items

• Interpretive exercises

• Examples of supply items are:• Short answer items

• Essay questions

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.

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

Examples of Raw Scores and Percentile Ranks

95 1 25 100

93 1 24 96

88 2 23 92

85 3 21 84

79 1 18 72

75 4 17 68

70 6 13 52

65 2 7 28

62 1 5 20

58 1 4 16

54 2 3 12

50 1 1 4

N = 25

Raw Cumulative PercentileScore Frequency Frequency Rank

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.

Descriptive Statistics

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

Types of Numerical Data

• There are two fundamental types of numerical data:

1) Categorical data: obtained by determining the frequency of occurrences in each of several categories

2) Quantitative data: obtained by determining placement on a scale that indicates amount or degree

Techniques for Summarizing and Presenting Quantitative Data

• Visual– Frequency Distributions– Histograms– Stem and Leaf Plots– Distribution curves

• Numerical– Central Tendency– Variability

Summary Measures

Central Tendency

Arithmetic Mean

Median Mode

Summary Measures

Variation

Variance

Standard Deviation

Range

Measures of Central Tendency

Central Tendency

Average (Mean) Median Mode

1

1

n

ii

N

ii

XX

n

X

N

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

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

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 7 8 9 10 11 12 13 14

Mode = 9

0 1 2 3 4 5 6

No Mode

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.

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

1

)( 22

n

xxs i

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.

Calculation of the Variance and Standard Deviation of a Distribution (Definitional formula)

√

RawScore Mean X – X (X – X)

2

85 54 31 96180 54 26 67670 54 16 25660 54 6 3655 54 1 150 54 -4 1645 54 -9 8140 54 -14 19630 54 -24 57625 54 -29 841

Variance (SD2) =

Σ(X – X)2

N-1

= 3640

9 =404.44

Standard deviation (SD) = Σ(X – X)2

N-1

Comparing Standard Deviations

Mean = 15.5 S = 3.338 11 12 13 14 15 16 17 18 19 20 21

11 12 13 14 15 16 17 18 19 20 21

Data B

Data A

Mean = 15.5 S = .9258

11 12 13 14 15 16 17 18 19 20 21

Mean = 15.5 S = 4.57

Data C

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

The Normal Curve

Different Distributions Compared

Fifty Percent of All Scores in a Normal Curve Fall on Each Side of the Mean

Probabilities Under the Normal Curve

Standard Scores

• Standard scores use a common scale to indicate how an individual compares to other individuals in a group.

• The simplest form of a standard score is a Z score.• A Z score expresses how far a raw score is from the

mean in standard deviation units. • Standard scores provide a better basis for comparing

performance on different measures than do raw scores.• A Probability is a percent stated in decimal form and

refers to the likelihood of an event occurring.• T scores are z scores expressed in a different form (z

score x 10 + 50).