Assessment 1 Week 1

Steps for calculating variance in a sample

1. calculate the mean for each variable (X,Y)

2. for each variable, subtract the mean from each observation, then square the result. add all of those values together, then divide by N-1
   ∑((X-meanX)²) / N-1
   
   

Calculating standard deviation with variance

Standard deviation = √Variance

Steps to calculate covariance of two variables (x,y)

1. calculate mean and variance

2. for each observation, subtract the mean from each value of x and y, then multiple
   (x1-meanX) x (y1-meanY), (x2-meanX) x (y2-meanY)…

3. sum all of the products for each observation
   ∑(x1-meanX) x (y1-meanY) + (x2-meanX) x (y2-meanY)…

4. divide that sum by N-1 (same N as mean/variance, number of observations x=y)

How to calculate correlation (x,y)

covariance of (x,y) divided by (SDX times SDY)

What does 'σx' stand for and how do you calculate it?

Deviation (formula = x - μx)

What does 'μx' stand for and how do you calculate it?

Mean (formula = Σx/N)

What does 'Σ' stand for?

Summation

How do you calculate variance?

Σ(σx)^2/(N-1) OR deviations squared

What does (σx)^2 or V(x) stand for?

Variance

What is the square root of variance?

Standard deviation

What does 'σxy' or Cov(xy) stand for?

Covariance

How do you calculate covariance?

1/(N-1) * [Σ(σx)(σy)] OR 1/(N-1) * (sum of deviations)

What do 'ρxy' and 'rxy' stand for?

Correlation (spearman's rho and pearson's r)

How do you calculate correlation?

σx,y / [(sqrt. σx)*(sqrt.σy)] OR 1(N-1) * Σ(Zx Zy)

What is the relationship between mean and deviation?

Deviation is found by subtracting the mean of a dataset from a single data point (x - μx)

What is the relationship between deviation and variance?

Variance is the square of the sum of deviations [(σx)^2] 

What is the relationship between variance and standard deviation?

Standard deviation is the square root of variance [sqrt.(σx)^2]

What is the relationship between deviation and covariance?

Covariance is the average product of two deviations ( 1/(N-1)*[Σ(σx)(σy)] )

What is the relationship between covariance, correlation, and standard deviation?

Correlation is the standardized covariance (Cov(x,y)/ (sqrt.[σx^2] * sqrt.[σy^2])

How do you calculate a z-score?

Divided deviation by standard deviation (σx / [sqrt.(σx^2)])

What is psychometrics?

The science, theory, and techniques of measuring psychological attributes or constructs

What is measurement? What is the goal of measurement?

Measurement is the process of assigning a symbol (i.e., a number) to properties of an object. The goal is to faithfully represent the attribute or property. 

What is scaling?

Scaling is essentially assigning rules to your measure (e.g., fixed origin, distance between units is fixed, etc.)

What is a nominal value?

distinctive value (e.g., gender, race, etc.)

What is an ordinal value?

monotonically increasing value (e.g., 1st, 2nd, 3rd, education level, etc.)

What is an interval value?

value with equal spacing (and zero doesn't usually mean zero, e.g., celsius, IQ)

What is a ratio value?

value with an absolute zero (that really means zero, e.g., kelvin, money, etc.)

What are the 3 types of scaling Dr. Cirino reviewed? 

Person scaling (arrange by individuals)

Stimulus centered (arrange by stimulus)

Response centered (arrange by response; person and item are scaled together)

What is a test?

A test is a way of collecting a sample of behavior

Why is classical test theory important?

1) establishes measurement error as an explicit piece of observed measurement scores

2) provides a basic mathematical foundation for much of psychometrics

What are the 5 rules of CTT?

1. X = T + e OR observed score = true score + error

2. ε(X) = T OR expected score = true score

3. ρ (eT) = 0 OR correlation of T and e in a population equals zero

4. ρ (e1, e2) = 0 OR correlation of e on any 2 testings will equals zero

5. ρ (e1, T2) = 0 OR correlation of T of one test and e of another test equals zero

What is CTT trying to do?

CTT is trying to tell you how BAD a measure is, not how good it is 

What part of CTT (X, T, or e) is the construct?

NOTHING

What is the true score?

It is a constant value of the expected (ε) value that averages ALL observed scores possible obtained over an infinite repetitions of a test

What is an observed score?

It is a realization of random error

How can you calculate/find your true score?

You can't, it's unknowable

What does expected (ε) random error equal?

0, that's why CTT works. Random error has known statistical properties.

Does CTT account for systematic error (such as taking a test while tired)?

No, it can only account for random error. This makes it a (weak) true score theory.

What are parallel tests?

Two tests with CTT properties that have equal true scores and error variance (e.g., If two tests are parallel, someone with a true anxiety score of 50 on Test A would also have a true score of 50 on Test B, and the two tests would have equivalent amounts of measurement error)

What are tau-equivalent tests?

They have CTT properties, but relax some requirements from parallel tests (e.g., if the true score on test A is 50 and the true score on test B is 55, and this difference is constant across the population, it would be tau-equivalent)

What is assessment?

Use tests to understand behavior

What assumptions do assessments make?

Construct(s) exist and you can 1) measure them and 2) measure them in different ways

Assessment has multiple components and there is error with all components

Test ~ nontest behavior

Assessment classifies and drives decisions

Assessments should be fair and unbiased