Multivariate Statistics Exam 1

Knowledge Construction

largely dependent on the ability to measure attributes of interest

Measurement

the process of assigning numbers that reflect the amount or nature of an attribute possessed by a person, object, or event

Rules

codes or methods that tell us what to do

What is the first step in measurement?

See if someone else has already done the work

Who introduced a framework that defined four “levels of measurement”?

S.S. Stevens

Nominal

\#’s are just labels

Ordinal

\#’s can be used to determine order of things but not how far they are apart

Interval

\#’s can be used to determine order of things and how far apart they are, but have no natural zero point

Ratio

Same as interval, except that a “natural” zero exists

Balanced Scales

equal number of favorable and unfavorable (left/right) categories

Multi-Item Scales

use more than one item to measure the same concept

Reliability

the degree tn which measure is free from random error; does not imply that a measure is unbiased (free from systematic error)

Stability

measurements are stable across time, locations, and instruments

Internal Consistency

components of a measure are consistent with each other

What are the two aspects of reliability?

Stability and Internal Consistency

How do you assess stability?

Test-retest stability

How do you assess internal consistency?

Cronbach’s alpha

How to quantify test-retest reliability?

1. Compute the degree of association between the scores (e.g. correlation)
2. The association should be positive and strong

Interpretations of Cronbach’s Alpha

1. Alpha=1, indicates that all the variability in the test scores is due to true score differences (i.e. zero measurement error)


1. Alpha= 0, indicates that no reliable variance is present and only measurement error exists in the items

Rule of Thumb for Internal Consistency

internal consistency is acceptable if alpha is between .70 and .95

Validity

are we measuring what we think we are measuring

Face Validity

subjective, intuitive assessment of whether the wording/meaning of a measure of a construct reflects


1. all the facets of the construct


1. 2. only the facets of the construct

Construct Validity

using theory, determine whether the measure shows expected correlations and expected non-correlations with measure of previously validated constructs

Convergent Validity

measures of constructs that ought to be related to each other are in fact related

Discriminant Validity

measures of a construct that ought to not be related are in fact nor related

Leading/ Loaded Questions

may push the respondent toward a particular response

Double Barreled Question

when multiple questions are embedded within a single item

Inapplicable Questions

Questions may not apply to the respondent

Explicit Alternatives

we bias memory retrieval when we only ask people to think about one option or alternative

Jargon

use language that respondents can not expect or understand

Malformed Categorical/Ordinal Lists

Categories should be collectively exhaustive, mutually exclusive, and meaningfully clustered

Over-demanding Recall

People find it very difficult to accurately estimate behavioral frequencies for extended time frames or frequently performed behaviors

Social Desirability

portraying the self in a favorable light by claiming empathy or good citizenship

Prestige Seeking

Portraying the self in a favorable light by claiming superiority or status

Auspices

when respondents know in advance who is sponsoring the study, feelings toward the sponsor may bias their responses (positively or negatively)

Serial Position: Primacy

tendency to select the first or early options at a higher rate than other options had they appeared in some other position in the list

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Satificing

only paying attention to early information or settling for a good-enough answer

Alertness

energy/interest is higher in the beginning than the end of the list

Rehearsal

thinking about the list as it unfolds means that the early items get repeated more in memory

Serial Position: Recency

tendency of people to select the last or later options at a higher rate than those option would have been selected had they appeared in some other position in the list

Omission

people think you have omitted the best option

Frequency as information about the “norm”

people assume the distribution of response options is a clue from the researcher regarding the “norm”

Unstated Criteria

criteria for judging must be clearly stated

Ambiguity

when multiple interpretations of the same questions are reasonable

Telescoping

misperceptions of time

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Forward Telescoping

we tend to think events occurred more recently

Backward Telescoping

we tend to think events occurred more distantly that they actually did

Averaging

tendency to report “the usual'“ or “norm” instead of actual memory

Uninformed Response Error

People sometimes try too hard to be helpful or appear informed

2 Techniques to Ask Sensitive Questions

1. Randomized Response Techniques
2. Unmatched Count Test

Chi-Square Test of Goodness of Fit

Only considers a single variable . Tests whether frequencies for the variable follow a specified pattern

Residuals

Observed - Expected

Pearson Residual

benchmarking the “raw” residuals against expectations

Why do we square the Pearson residual?

Squaring the Pearson residual emphasizes (gives more weight) to larger differences. It tells us how much each category is contributing to the overall difference between the observed and expected value

If the P value is small (.001 < .05)

Reject the null hypothesis

Chi Square

1. If the Null is true, there is a correlation between the 2 variables
2. If the null is untrue, there is no correlation between the 2 variables

Chi-square Test of Independces

Involves two variable. Tests whether the variable are independent or dependent

What do large value Chi squares mean?

Indicate that the null hypothesis are not true

P Value

how likely that your data could have occurred under the null hypothesis

Z-Value

Equal to 1.96. Compare the residual. It is two variables. Chi square test of independence

Logistic Regression Approach

addresses weaknesses of the linear regression. Stays in the range (0,1) and is symmetric

B^0

Shifts the curve up and down

b1

adjusts the slope positive, flat, or negative

(Naive) Probability

ratio of category frequencies to the total

Odds

ratio of category frequencies to each other

Jittering

involves adding small random numbers to each value. This randomly shifts each dot up/down, which can help avoid misinterpretations when overlapping points are “hiding” information about density

Deviance

compares our model’s fit to a hypothetical model that perfectly fits the data

What does a smaller deviance mean?

Smaller deviance means a better fit

AIC (Akaike’s Information Criterion)

adds “penalty” to the deviance of models that use more predictors

What does a small AIC mean?

A smaller AIC means a better fit

What does deviance and AIC do?

Deviance and AIC allow us to compare models fit to the same data

X^2

reflects how much lower our model’s deviance is compared to the deviance of a model that has no predictors

What does a large x^2 mean?

A large x^2 means a better fit

McFadden’s R^2

considers how much our model deviate not only from the perfect model but all the naïve model

What does a large McFadden R^2 mean?

A large or increasing McFadden R^2 means that the data fits the model

Steps for Predicted Probability Equations

1. Odd’s equation
2. Natural Log of Previous Answer
3. Natural Log Answer / (1 + Natural Log Answer)