# LECTURE 9.

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LECTURE 9

MEASUREMENT Procedure for assigning symbols, letters, or numbers to empirical properties of variables according to rules.

Difficulty in measuring concepts directly (e.g., academic achievement)
Usually measure indicators of concepts (e.g., CGPA) Level of measurement determines the type of statistical analysis. The level of measurement you use depends on how you want to measure an outcome.

Levels of Measurement Nominal Ordinal Interval Ratio

Nominal Latin word nomin (name) Variable categorical in nature
Differ in quality not quantity (numbers have no meaning only label) Characterizes observation into one (and only one) category  mutually exclusive Solely qualitative No obsolute zero (0) Matematical operation not possible.

Ordinal Describes variables that can be ordered along some type of continuum. Not only categories, order as well. Ranking according to various outcomes, e.g., big & little. No obsolute ‘0’, only relative position; e.g., Zul is taller than Sheereen and Sheereen is taller than Rozumah (no information on how much taller). Matematical operation not possible.

Interval Latin word intervalum (spaces between walls).
Describes variables that have equal intervals btw them. Allow us to determine the difference btw points along the same type of continuum (e.g., the difference btw 300 and 400 is the same as the difference btw 700 and 800; i.e., 100). 0 is arbitrary (subjective, temporary). Simple matematical operation. More precise & convey > info than nominal & ordinal; but must be cautious in interpreting.

Ratio Latin word ratio (calculation).
Describes variables that have equal intervals btw them & have absolute 0. Most precise. Complex matematical operation. Highest level of measurement.

QUIZ: Matching questions
Nominal Ordinal Ratio Interval Have a true zero (highest level). Categorical in nature (lowest level) Have equidistant points along some underlying continuum. Are ranked.

QUIZ: Matching questions
TYPES OF MEASUREMENT ON HEIGHT A is 5 inches taller than B (know precise difference). Precise height measured on a scale with true zero. Categorize people into A and B (people different in height). d. Tall and Short (have some meaning, but nature of difference is not known). Nominal Ordinal Ratio Interval

Summary Nominal level variables are categorical in nature (lowest level) Ordinal -- are ranked. Interval -- have equidistant points along some underlying continuum. Ratio -- have a true zero (highest level).

RELIABILITY & VALIDITY OF MEASUREMENT
Reliability and validity are the hallmarks of good measurement. Assessments tools must be reliable and valid, otherwise the research hypothesis may be incorrectly rejected.

Reliability is a practical measure of how consistent and stable a measurement instrument or a test might be. Reliability is often measured using the correlation coefficient.

Synonyms for Reliability
Dependency Consistency Stablility Trustworthiness Predictability Faithfulness

Types of Reliability Test-retest Parallel forms Inter-rater
Internal consistency

1. Test-retest: A measure of stability.
Examines consistency over time. Administer the same test/measure at two different times to the same group of participants. Coefficient: rtest1.test2

2. Parallel Forms A measure of equivalence.
Examines consistency between forms. Administer different forms of the same test to the same group of participants. Coefficient: rform1.form2

3. Inter-rater A measure of agreement.
Examines consistency across raters. Have two raters, rate behaviors and determine the amount of agreement between them. Coefficient: % of agreement.

4. Internal consistency A measure of consistently each item measures the same underlying construct. Examines reliability within a particular set of item. Correlate performance on each item with overall performance across participants. Coefficient: Chronbach’s alpha

Validity Is the quality of a test doing what it is designed to do.
The test or instrument you are using actually measures what you need to have measured.

Synonyms for Validity Truthfulness, Accuracy Authenticity Genuineness
soundness

Types of Validity Content Criterion Concurrent Predictive Construct

Content Validity A measure of how well the items represent the entire universe of items Established by asking expert if the items assess what you want them to. History test = test items ask questions on history not Science.

Criterion Validity A measure of how well a test estimates a criterion.
Concurrent validity A measure of how well a test estimates a criterion. Established by selecting a criterion and correlate scores on the test with scores on ther criterion in the present. Good student = test result + reports by lecturers.

ii. Predictive Validity
A measure of how well a test predicts a criterion. Select a criterion and correlates scores on the test with scores on the criterion in the future. High merit on STPM/Diploma = Score high CGPA. Pass driving test = Good driver.

Construct Validity A measure of how well a test assesses some underlying construct. Assess the underlying construct on which the test is based and correlate these scores with the scores. Theoretically and practically sound. Intelligence test actually measures intelligence.

Relationship between Reliability and Validity
A test can be reliable without being valid but the reverse is not true. A test can be reliable, but not valid, but a test cannot be valid without first being reliable. Reliablity is a necessary, but not sufficient, condition of validity. You are answering questions on simple addition, but we called it spelling test! Obviously it is not a test on spelling  lack of validity, does not affect reliability.