Part 2: Quantitative Methods

October 2, 2006

A Scientific Process

Research Question

Defining the Problem

ReviewLiterature

ArticulateTheory

DefineHypothesis

Testing the Hypothesis

Subject sampling Instrumentation Research design Piloting

Collecting Data Choosing analyses Conducting analyses

Conclusions

Results or Findings

Sampling

Target vs. Accessible Population

• High School Sports Officials

• Students enrolled in 5th grade in NM schools

• Albuquerque Residents

• The U.S. Electorate

• National Association of Sports Officials Membership

• New Mexico 5th graders

• Albuquerque Phone Book

• Registered Voters

PopulationValidity

size of sample

RandomProcesses

Prosand

Cons

Sampling Procedures

Simple Random Sampling

Systematic Sampling

Cluster Sampling

Convenience Sampling

Stratified Sampling

Biased Sampling

Sampling Error

The Inferential

Leap

volunteers

Selection and

Assignment

The Inferential Leap

???

???

Target Population

Accessible or Operational Population

Sample

Sampling Unit

Sampling Unit

Sampling Unit

Sampling Unit

Simple Random Sampling1 092725 012157 827052 297980 625608 9641342 104460 007903 484595 868313 274221 3671813 676071 388003 266711 323324 044463 7628034 881878 862385 203886 261061 096674 8115485 534500 336348 086585 241740 581286 0084356 094276 615776 242112 985859 075388 082003

1. Andrea2. Tina3. Paul4. Wilbur5. Sandra

6. Kathy7. Jim8. George9. Emir10. Becky

11. Sharon12. Gladys13. Jose14. Bill15. Sue

16. Erica17. Aaron18. Fred19. Pam20. Roger

Stratified Random Sampling1 092725 012157 827052 297980 625608 9641342 104460 007903 484595 868313 274221 3671813 676071 388003 266711 323324 044405 7628034 881878 862308 203886 261061 096674 8115485 534500 336348 086585 241740 581286 0084356 094276 615776 242112 985859 075388 082003

1. Andrea2. Tina3. Kathy4. Sandra5. Becky

6. Paul7. Wilbur8. Jim9. George10. Emir

6. Sharon7. Gladys8. Sue9. Erica10. Pam

1. Jose2. Bill3. Aaron4. Fred5. Roger

Systematic Sampling

• Say you have a target population that has a 100,000 members.– And:

• A list is available.• You need 1,000 cases for your sample.

• 100,000/1000 = 100.– Select a random number from table.

• Then select every 100th case.

Cluster Sampling

• Naturally occurring groups.– State, district, school, classroom, student.– Randomly sample from one level then survey,

interview, etc. • Multistage sampling.

– Randomly select from one level.– Then randomly select within that level.

Convenience Sampling

• Why convenient?– Sample that is located near the researcher– Connections with administrator or staff– Researcher is familiar with the setting– Data is already available

• Shortcomings of convenience samples?

Volunteers in Sampling• How might volunteers differ?• Children having parental permission

– More academically competent– More popular with peers– More physically attractive– Less likely to smoke or use drugs– More likely to be white– More likely to come from two-parent household– More likely to be involved in extracurricular activities– Less likely to be socially withdrawn– Less likely to be aggressive

Size of the Sample

• Bigger is (usually) better.– Unless?

• How big is big? Power analysis.• Practical issues.• Attrition.• Reliability.• Cost/ benefit.

Correlation& Instrumentation

Reliability and Validity

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

Positive Correlation

Negative Correlation

No Correlation

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 to causation.

Negative Correlation

Operationism vs. Essentialism

• According to Stanovich– What are they?– How do they differ?

• Essentialist – Like to argue about the meaning of our terms

• “What does the theoretical concept really mean?”– Must have a complete and unambiguous

understanding of the language involved.• Operationism

– Link concepts to observable events that can be measured.

– Concepts in science related to a set of operations.• Several slightly different tasks and behavioral events are

used to converge on a concept.

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

Reliability

• Test-retest reliability• Inter-rater reliability• Parallel forms reliability• Internal consistency (a.k.a. Cronbach’s

alpha)

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?

Validity

• Criterion– Predictive – Concurrent

• Consequential

Types of validity (cont.)

The construct

The instrument

Here the instrument samples some and only of the construct

Types of validity

The instrument

The construct

Here the instrument samples all and more of the construct

The construct

The instrument

Here the instrument fails to sample ANY of the construct

The construct

The instrument

Here the instrument samples some but not all of the construct

Perfection!

The construct and the instrument!

Reliability and Validity

In groups of 3 to 4

• Sampling– What is the target population?– What sampling procedure was used?– Do you think the sample is representative?

• Why or why not?

• Measurement– What types of reliability and validity evidence

are provided?– What else would you like to know?

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

Excerpt from a Behavior Rating Scale for Teachers

Instructions: For each of the behaviors listedbelow, circle the appropriate number, using the following key: 5 = Excellent, 4 = Above Average, 3 = Average, 2 = Below Average,1 = Poor.

A. Explains course material clearly.1 2 3 4 5

B. Establishes rapport with students.1 2 3 4 5

C. Asks high-level questions.1 2 3 4 5

D. Varies class activities.1 2 3 4 5

Excerpt from a Graphic Rating Scale

Instructions: Indicate the quality of the student’s participationin the following class activities by placing an X anywhere alongeach line.

AlwaysFrequently Occasionally Seldom Never

1. Listens to teacher’s instructions.

Always Frequently Occasionally Seldom Never

2. Listens to the opinions of other students.

Always Frequently Occasionally Seldom Never

3. Offers own opinions in class discussions.

Sample Observation Form

Discussion Analysis Tally Sheet

Performance Checklist Noting Student Actions

Types of Subject-completed Instruments

• Questionnaires• Self-checklists• Attitude scales• Personality

inventories

• Achievement/aptitude tests

• Performance tests• Projective devices

Example of a Self-Checklist

Example of Items from a Likert Scale

Example of the Semantic Differential

Pictorial Attitude Scale for Use with Young Children

Sample Items from a Personality Inventory

Sample Items from an Achievement Test

Sample Item from an Aptitude Test

Sample Items from an Intelligence Test

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.

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.