Psychometrics

Goals of statistics

• Describe what is happening now– DESCRIPTIVE STATISTICS

• Determine what is probably happening or what might happen in the future– INFERENTIAL STATISTICS

Measurement

• The process of assigning numbers or other symbols to the things in such a way that relationships of the numbers or symbols reflect relationships of the attribute being measured.

• A particular way of assigning numbers or symbols to measure something is called a scale of measurement.

Measurement

• Measurement theory helps us to avoid making meaningless statements.

Scales

Nominal Scales

• Nominal measurement consists of assigning items to groups or categories.

• No quantitative information is conveyed and no ordering of the items is implied.

• Nominal scales are therefore qualitative rather than quantitative.

• Religious preference, race, and sex are all examples of nominal scales.

Ordinal Scales

• Measurements with ordinal scales are ordered in the sense that higher numbers represent higher values.

• However, the intervals between the numbers are not necessarily equal.

• Gun control and attitudes

Ratio Scales

• One unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the scale.

• For example, if anxiety were measured on an interval scale, then a difference between a score

• Has a true 0 (zero)

Reliability

• The property of a test or measure having to do with its replicability

• Even when we use the same test and give the test under apparently identical circumstances, we will usually obtain somewhat different results.

• Influenced by factors that may or not be systematic– Behavior of the client– Procedure by which the measurement was obtained

• The more measures you take, the more the errors will cancel out. Therefore, longer tests are more reliable.

Describing reliability

• Agreement

• Stability

• Internal Consistency

Reliability and Agreement

• If the instrument uses a nominal scale for measurement aspects such as the presence or absence of a moment of stuttering, then the reliability of the measure is in the form of a measure of agreement

• See table 1.1

Reliability and Agreement

• Intrajudge agreement (within judge)

• Interjudge agreement (between judge)

Reliability and Stability

• If the instrument uses a ratio scale such as to measure fundamental frequency.

• Reliability measure should reflect the stability of the measure

• We can use test-retest reliability• See table 1.3• In statistics we use correlation coefficent such as

the Pearson Product Moment (r).• Some believe the .90 in test-retest reliability

coefficient should be the minimum.

Reliability and Internal Consistency

• Compare Scores obtained within the test

• Example – compare scores between the odd and the even numbered test items

• This is called split-half reliability

Validity

• Measures how accurately the measurement tool measures the characteristic in which we are interested.

• Provides us with what conclusions can be made from the measure

• It is concerned with the truthfulness of the measure• We need external standard of truth to compare our test

with• Types of external standards or validity indices

– Concurrent validity– Predictive validity– Construct validity

Concurrent validity

• A new or untested measure is compared with another measure that is widely as accurately measure the same property.

Predictive validity

• Used when the test is used to predict likely performance in some other place, time or task.

• Measure is compared to another situation.

Construct validity

• Used when test measure hypothetical traits or attributes that we believe underlies the person’s performance– Short term memory, anxiety, linguistic competence, things that

cannot be directly observed

• Examples of what we need– Theory– Predictions of how people may differ– Predict how it will be displayed– Develop tasks to measure this construct that differentiate people

due to the construct and not something else– Research to show consistency with theory and observations of

people with these behaviors and those without the behaviors

Diagnostic Accuracy

• Deals with correctness of clinical decision

• “Gold Standard” – the truth against which all clinical decisions are measured.

• Helps determine the false negatives from the true negatives

• See table 1.4

Measurement Interpretation

• Norm-referenced interpretation

• Criterion-referenced interpretation

• Client-referenced interpretation

Norm-referenced interpretation

• Compare client’s performance to some other group of individuals (normative group)

• We use– Standard Scores – Equivalent Scores

Standard Scores

http://ags.pearsonassessments.com/pdf/curverel1.pdf

Standard Scores

• Evaluates the client’s placement within the normative group

• Horizontal axis = range of scores• Vertical axis = number of people with that score• Dividing line is the mean, median, mode 50%

percentile, average• Standard deviation = the extent to which scores

deviate from the mean– 34.13% scores fall within 1 deviation below and

34.13% fall within 1 deviation above the mean

Percentile Scores

• Depends on how the person performs in relation to her or his comparison group.

Equivalent Scores

• Usually represent the group that has a median score equal to a given raw score.

• You can find age and grade equivalents

• Problems with these scores discourage their use.

Criterion-referenced interpretation

• Clinical standards that are identified by group of experts or evidence of desirable and undesirable behaviors

• Qualitative evaluation = good/bad, acceptable/unaccepatable

Client-referenced interpretation

• Comparing client’s performance– To his own performance in another area– To his own performance in another point in

time

• Most common form of clinical interpretation