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Statistics - with some biostats series
JHSPH09
141
Other
Graduate
12/16/2009

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Term
What is theory of mind?
Definition
Theory of mind is conceptualized as a child's ability to recognize a causal relationship between mental states and actions and to recognize that beliefs can be false.
Term
Dimensionality is...
Definition
The homogeneity of items used to measure a construct
Term
Unidimensional is
Definition
Items underlie a single factor (construct).
Term
What do reliability and validity depend on?
Definition
Unidimensionality
Term
Multidimensional is
Definition
Items underlie more than one factor
Term
In terms of dimensionality if the partial correlation between two pairs of items is equal to zero that means...
Definition
It is likely unidimensional
Term
A set of items is unidimensional if..
Definition
Correlations among the items can be accounted for by a single factor
Term
An item is unidimensional if...
Definition
It is a measure of only a single construct
Term
3 Types of Correlations
Definition
1) Pearson
2) Polychoric
3) Tetrachoric
Term
Pearson correlation is used when...
Definition
The data are continuous or when variables are measured on at least interval scales.
Term
A correlation tells you?
Definition
The degree of linear relationship between X and Y, but it is affected by outliers
Term
Spearman is used when?
Definition
Data is skewed, there is an outlier bias, and data may be sparse. It then ranks the values and helps smooth a curve to a straight line
Term
Use tetrachoric correlation when
Definition
you have binary outcomes and you assume that both traits are normally distributed.
Term
What is the difference between a correlation and covariance?
Definition
Correlation is a scaled version of covariance. Covariance is a sum of variance between Xs and Ys
Term
Reliability is (two definitions)
Definition
1) The correlation between parallel measures
2) The ratio of TRUE score to TOTAL score
Term
What is Kappa?
Definition
Is an intraclass correlation coefficient, which corrects for chance and measures inter-rater agreement for categorical items.
Term
Kappa is calculated...
Definition
Po = Observed proportion of agreements
Pe = Expected proportion of agreements

Po - Pe / 1 - Pe
Term
What are Intraclass Correlation Coefficient
Definition
Assesses inter-rater reliability as variance in true score/variance in observed score
Term
What are the three research designs of ICCs
Definition
1) Unique
2) Random
3) Fixed
Term
ICCs can be either...
Definition
Average ratings or individual ratings
Term
Explain the difference in terms of raters (unique, random, fixed)
Definition
Unique: No overlap of raters
Random: Pool of raters, with random selected and then total overlap of raters.
Fixed: Total Overlap of Raters (but they are assigned raters, not random)
Term
Unique Rater Design would be...
Definition
Each of the i subjects are rated by a unique set of m raters, such that the total number of raters is m*i.
Term
Provide an example of the unique rater design
Definition
Each child in a survey is rated by two parents
Term
Random Rater Design is...
Definition
m raters are drawn from a larger pool of raters. Each of the subjects is rated by each of the m raters.
Term
Provide an example of a random rater design
Definition
Any psychiatrists' rating of subjects: questionnaire items drawn randomly from a large pool.
Term
What is a fixed rater design?
Definition
Each subject is rated by each of the same m raters, such that the total number of raters, R is m. These raters are the only raters of interest
Term
Can you provide an example of a fixed rater design?
Definition
Team of psychiatrist ratings of subjects in a clinical trial; a fixed set of questionnaire items.
Term
What is typically more reliable? Individual or averaged ratings?
Definition
Average (bigger n)
Term
Name three tests that give you internal consistency?
Definition
Cronbach's alpha
Kuder-Richardson
Split-half
Term
Split-half estimate steps
Definition
1) Arbitrarily divide the scale into two halves and create total score for the two halves
2) Correlate the two total scales
3) Adjust the correlation upwards with the Spearman-Brown prophecy formula
Term
What is the Spearman-Brown prophecy formula?
Definition
It is used to account for a scale having more or less items than it currently does. A required adjustment with split-half.
Term
How is the Spearman-Brown Prophecy formula calculated?
Definition
Calculate the old correlation = r
and phi = theoretical no. of items/observed no. of items= p

Rsb = pr / 1 + (p-1)r
Term
How is Cronbach's alpha a function of scale length?
Definition
As scale length increases, alpha increases, because the inter-item correlations go up.
Term
Cronbach's Alpha is equivalent to which ICC?
Definition
3,k
Term
Is Cronbach's alpha a measure of unidimensionality?
Definition
No, it is a measure of internal consistency after unidimensionality has been established
Term
What measure of reliability should be used for test-retest continuous variables?
Definition
R or ICC
Term
What measure of reliability should be used for test-retest categorical variables?
Definition
Kappa or ICC
Term
What measure of reliability should be used for inter-rater continuous variables?
Definition
R or ICC
Term
What measure of reliability should be used for inter-rater categorical variables?
Definition
Kappa or ICC
Term
What measure of reliability should be used for internal consistency continuous variables?
Definition
Cronbach's alpha or split-half or ICC
Term
What measure of reliability should be used for internal consistency categorical variables?
Definition
KR-20 or ICC
Term
Rank in order from weakest to strongest validity measures: construct, content, criterion, face
Definition
1) Face
2) Content
3 Criterion
4) Construct (weakest to strongest)
Term
Face validity is...
Definition
The extent to which an item appears to be valid
Term
Content validity is...
Definition
The extent to which there is representativeness across domain of meaning. Also the extent to which one can generalize from a particular collection of items to all possible items that would be representative of a specified domain of items
Term
Criterion Validity is...
Definition
The extent of correspondence of a measure with a criterion variable (gold standard)
Term
What are the two types of criterion validity?
Definition
Predictive and concurrent
Term
What is sensitivity?
Definition
How well the test picks up cases from true number of cases
Term
What is specificity?
Definition
How well the test picks up controls (non-cases) from true number of controls (non-cases)
Term
Increasing sensitivity increases what?
Definition
Type I errors (false positives)
Term
Increasing specificity increases...
Definition
Type II errors (false negatives)
Term
Kappa changes how with prevalence?
Definition
It goes down when a disease is rare
Term
Positive Predictive Value is...
Definition
The proportion of people who test positive who really have the disease
Term
Negative Predictive Value is...
Definition
The proportion of people who test negative who are really disease-free
Term
How do PPV and NPV relate to prevalence?
Definition
The higher the disease prevalence (the more common) the higher PPV and NPV
Term
What is a ROC curve?
Definition
Each point represents a 2x2 table and a probability cutoff used to distinguish people with and without disease (it's a measure of discrimination)
Term
What is the C Statistic?
Definition
The Area under the ROC curve
Term
What does the C statistic mean?
Definition
Probability that a sick person (case) will more likely test to be "sick" (a case) than well people (non-cases)
Term

What are on the axes of the ROC?

What does the ROC provide?

Definition

X = False-Positive Rate (1-Specificity)

Y = True-Positive Rate (Sensitivity)

 

It is a measure of diagnostic utility

Term
Where is the best cut-off point for the ROC curve?
Definition
Closest to the top left, maximize combination of sensitivity and specificity
Term
What is construct validity?
Definition
The degree to which a measure satisfies theoretical predictions about the construct, across a range of theories, and with a range of modalities of measurement
Term
Internal Construct Validity is...
Definition
The degree to which items in a measure are associated with each other in the theoretically predicted direction
Term
Convergent vs. Discriminant Internal Validity?
Definition
Convergent = similarity even with different modality
Discriminant = similar to similar, but distinct from others
Term
Convergent Internal Validity is...
Definition
The degree to which a scale is associated with measures of similar constructs even when they are measured with a different modality
Term
Discriminant Construct Validity...
Definition
Is the degree to which a scale is associated with measures of similar constructs and not associated with measures of distinct constructs
Term
What is the Multitrait Multimethod Matrix
Definition
A way of determining the internal construct validity by comparing the the same traits measured with different methods
Term
Describe the four measurements within the MTMM Matrix
Definition
MTMM= reliability diagonals
MTHM= validity diagonals, convergent validity, shouldn't be as high as reliability diagonals
HTMM>HTHM
Term
External Construct Validity is...
Definition
The degree to which the scale is associated with other constructs in the theoretically predicted direction (a generalization to other theories, not to populations -- nomological network)
Term
The relationship between reliability and validity?
Definition
Reliability sets a maximum for validity, which validity establishes reliability
Term
What is the point of correcting for attenuation?
Definition
it is possible that the measure you are using is not 100% reliable, therefore your correlation will be weaker then it should be. The formula will correct for that...
Term
What are the main uses of factor analysis?
Definition
1) Data reduction
2) Determine underlying variables among a set of observed variables
Term
What are the four assumptions of factor analysis?
Definition
1) Measurement error has constant variance and is on average = 0
2) There is no association between factor and measurement error
3) There is no association between errors
4) There is local conditional independence: given the factor, observed variables are independent of one another
Term
What is communality within a factor analysis model?
Definition
For standarized variables this is the of variability in X that can be explained by F (similar to the r-squared in regression analysis)
Term
What is the inverse of communality?
Definition
Uniqueness
Term
Is uniqueness good or bad?
Definition
It is bad if an items is not related to other items in the FA
Term
What do the loadings in a factor matrix tell you?
Definition
They represent the degree to which each of the variables is associated with each of the factors (range from 0 to 1)
Term
What does a high factor loading tell you?
Definition
They provide meaning and interpretation of the factors
Term
What are the steps to performing an EFA
Definition
1) Collect data, choose relevant variables
2) Extract initial factors (via PCA)
3) Choose number of factors to retain
4) Choose estimation method
5) Rotate and interpret
6) Construct scales for future use
Term
What questions need to be asked in a Principal components analysis?
Definition
1) How many factors to retain?
2) What type of factor analysis
3) Note: It makes the number of factors equal to the number of variables
Term
What are ways to determine how many factors to retain?
Definition
1) Eigenvalues (>1)
2) Scree plot (look for elbow)
3) Parallel analysis
4) Theory on what makes sense
Term
What are eigenvalues?
Definition
They are the number of variables represented by the factor, and help to explain the variance in the data. They do tend to overestimate the number of factors.
Term
What is the scree plot?
Definition
It shows the relative contribution of variables. You want to take above the elbow.
Term
What is a parallel analysis in PCA?
Definition
Generates several eigenvalues that would be expected from random data. It is the most accurate and becoming the standard
Term
Describe the two types of rotation in a factor analysis
Definition
Oblique (promax) = factors are correlated
Orthogonal (varimax) = factors are not correlated
Term
What the goal of factor rotation?
Definition
To distribute variance more evenly among factors and to make sharper distinctions among data - to make pattern matrix coefficents either very high or very low.
Term
Does rotation improve fit?
Definition
NO
Term
An oblique rotation will produce what that a orthogonal rotation does not?
Definition
A pattern matrix (loadings) and a structure matrix (correlations)

Note: pattern matrix=structure matrix for orthogonal rotation
Term
What are the key differences between CFA and EFA?
Definition
EFA is used to summarize data and describe the correlation structure between variables. CFAs on the other hand are used to test consistency with a preconceived theory, is a kind of SEM, and more useful when looking for associations between factors or between factors and other observed variables
Term
How is latent class probability defined?
Definition
n1= P(S1=1) and n2 = P(s1=2)
Term
What are the conditional probabilities in a latent class analysis/
Definition
pi11 - for probability within class 1 of endorsed symptom Y1
Term
How do you calculate pieces of data in an LCA?
Definition
2^M - 1, where m is the number of Ys
Term
What is the relationship between # of parameters and # of classes?
Definition
Parameters increase as the number of classes increase
Term
What is identifiability mean?
Definition
Can you uniquely identify what all the parameters mean (they all have unique formulas) It is an attribute of the model; do parameters have unique interpretations?
Term
How to determine if model is identifiable using latent class probability, conditional probability and pieces of data in a LCA?
Definition
Latent class probabilities (J-1) + Conditional probabilities (J*M) < Pieces of data (2^M - 1)
Term
Identifiability improves or worsens as you remove or fix parameters?
Definition
Improves!
Term
What is estimability?
Definition
It is an attribute of the data --- the question whether the sample is large enough to estimate the parameters, also speaks to the distribution of the data.
Term
What are the two assumptions of latent class modeling?
Definition
1) Independent Individuals
2) Conditional Independence
Term
What does entropy measure?
Definition
The level of misclassfication error, a high number is good. This is in a Latent Class Analysis
Term
Type I error (alpha) is
Definition
Rejecting the H0 when H0 is true
Term
Type II error (beta) is
Definition
A failure to reject the Ho when the Ha is true.
Term
What is a p-value?
Definition
P-value: The probability of obtaining a test statistic that is as extreme or more as the test statistic calculated from the current sample if H0 is true.
Term
What is Social Desirability Bias?
Definition
: the tendency of respondents to reply in a manner that will be viewed favorably by others
Term
What is Acquiescence Bias?
Definition
A tendency to agree with all the questions or to indicate a positive connotation
Term
What is Experimenter Bias?
Definition
bias towards a result expected by the human experimenter.
Term
What ICC is typical for inter-rater reliability and which is typical for internal consistency?
Definition
inter-rater = (2,1), or (2,k)
internal consistency = (3,k) - cronbach's
Term
What is Power (1-Beta)?
Definition
reject H0 when the H1 is true, power is a function of N, Δ and alpha, as these three increase so does power.
Term
What is measurement?
Definition
“the process of assigning a number to an attribute (or phenomenon) according to a rule or set of rules” or the result obtained from such a process.
Term
What is reliability?
Definition
extent to which the measurements remain consistent over repeated tests of the same subject under identical conditions.
Term
What is the relationship between bias and validity?
Definition
Smaller the bias, more valid the measure
Term
What is a latent variable?
Definition
A variable that is unobserved, or not measured directly.
Term
What is the difference between variance and covariance?
Definition
Variance: Measures variability in one variable, X. sum of (xi - xbar)

Covariance: Measures how two variables, X and Y, covary. sum of (xi - xbar)*(yi - ybar)
Term
What is the formula for a correlation?
Definition
Covariance of xy / square root (x2 variance)(y2 variance)
Term
What does internal consistency measure?
Definition
Degree of homogeneity of items within a scale
Term
A crap internal consistency could be the consequence of what two things?
Definition
1) More than one dimension
2) Bad items
Term
How to calculate cronbach's alpha?
Definition
1 - (sum of items variances / total score variance)
Term
What are examples of translational validity?
Definition
Content (theory driven)
Face (appearance driven)
Term
Sensitivity and Specificity are affected by the prevalence of what?
Definition
Sensitivity and Specificity are affected by the prevalence of positive test results
Term
Nomological Networks were proposed by whom?
Definition
Cronbach and Meehl (1955)
Term
Multitrait-Multimethod Matrix proposed by?
Definition
Campbell & Fiske, 1959
Term
What are the six steps to creating a scale?
Definition
1. See if a suitable scale exists already
2. Define the construct carefully
3. Choose a modality
4. Generate items
Choose a response format
Choose wording carefully
Avoid common biases
5. Conduct pilot tests
6. Evaluate results
Term
Give an example of some modalities for scales?
Definition
1) Clinical Rating
2) Examination
3) Self-report-- Structured Interview
4) Telephone Interview
5) Computer-assisted Interview
6) Paper and pencil
7) Informant Interview
Term
What are the assumptions of IRT?
Definition
1) Unidimensionality
2) Local Independence
3) Invariance
Term
What is the item characteristic curve?
Definition
plots the probability of responding correctly to an item as a function of the latent trait (denoted by θ)
Term
Three ways the item characteristic curve can be modified (and in way direction)?
Definition
1) Difficulty (left-right)
2) Discrimination (steepness)
3) Adjustment for guessing (up-down)
Term
What does the information function of the IRT tell you?
Definition
Information is a function of a, the discrimination parameter. It shows the responses
Term
What are three benefits to a large sample size?
Definition
1) minimize the probability of errors
2) maximize the accuracy of population estimates
3) increase the generalizability of the results
Term
Traits vs. states in terms of stability?
Definition
Traits are much stable over time as they described underlying personality traits, etc. States are reflections of the present moment, and are more likely to fluctuate over time. Think someone who has a melancholic personality (trait) vs. someone who is currently depressed (state)
Term
What are the potential consequences of using a pearson correlation when you had an ordinal variable in regards to FA? What should you have used?
Definition
A potential consequence is incorrect estimates of factor loadings and attenuation of the correlations. A polychoric correlation?
Term
How do you calculate class membership given a symptom profile type?
Definition
You need to use Bates Theorem here.

1) Calculate the conditional probability of a symptom profile for each class.
2) Multiple these symptom profile probabilities by the class probabilities to calculate an alpha
3) Divide the symptom profile and the class of interest by the alpha you just calculated.

This will tell you, give the profile type, what is the probability that they belong to class X.
Term
What is Bartlett's test?
Definition
It tests for equal variances across groups, with the null being that they are all equal, used in ANOVAs
Term
What is the null hypothesis in an ANOVA, what does the F-statistic tell you?
Definition
That mean value of Y differs in at least one of the groups compared to the others
Term
What does the Central Limit Theorem say?
Definition
The distribution of sample means (from all possible samples of the given sample size) is approximately normal
Term
A hazard at time t is approximately
Definition
The expected number of events per unit time at time t divided by the number at risk of an event at time t
Term
What is the coefficient of determination (r2)?
Definition
The proportion in the variability of Y explained by X
Term
What is the order of the mean, mode and median in a positive skew (right skew)?
Definition

You have skew towards lower values

 

Mean

Term
What is the order of the mean, mode and median in a negative skew (left skew)?
Definition

You have skew towards higher values

Mode

Term
What are the assumptions in linear regression models?
Definition
1. (L)inear relationship
2. (I)ndependent distribution
3. (N)ormally distributed
4. (E)rror terms ind. and normally distributed

Remember to Stay in LINE
Term
What is the addition rule?
Definition
P(A OR B)= P(A)+ P(B) - P(A and B)
Term
What is item-rest correlation?
Definition
The item vs. the remaining items in the subscale
Term
What is the item-test correlation?
Definition
The item vs. the entire scale, including that item
Term
How do you improve identifiability?
Definition
Remove parameters, thereby decreasing classes and indicators
Term
How do you improve estimability?
Definition
Increasing sample size, decrease classes, increase random starts
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