Adv Corelat Methods Quiz 4 (Week 5)

Front 1

Observed variance in y can be broken down into 2 parts. What are they?

Back 1

1. Variance due to a linear relationship with x, which is equal to sy^(2) *r^(2)
2. Residual variance, or
s^(2)y

Front 2

What is the difference between r and rho?

Back 2

r is the correlation in a sample, while rho is associated with the same quanitiy in a population.

Front 3

What are the 3 basic hypotheses that we can test with regards to rho (p)?

Back 3

1. p = 0 in the population
2. p = a specific value in the population
3. p (sample 1) = p (sample 2), which would indicate that two samples came from the same population. Another way of expressing this hypothesis is that 2 populations have the same correlation, rho, between x and y.

Front 4

If r^2 = .00016, what does this mean?

(not sure if this should be r or R)

Back 4

If r^2 = .00016, then you can only explain .016% of the variance. This illustrates that what is statistically significant may not mean much if you can't explain much of the variance.

Front 5

When performing hypothesis testing with rho (p), which circumstances require that you convert p to a fisher's z?

Back 5

If rho equals a specific value in the population
OR
If you are testing the hypothesis that the rho from sample 1 is equal to the rho from sample 2.

Front 6

What are the steps associated with calculating confidence intervals for rho?

Back 6

1. Convert r to fisher's z
2. compute the standard deviation of z'
3. choose an alpha level and find the critical value of z that corresponds to that alpha level
4. construct a confidence interval around z'
5. transform confidence interval around z' back to r using table.

Front 7

A narrow CI is preferred if you want...

Back 7

a truly accurate estimate of the correlation.

(Conversely, wider CIs give you greater range w/in which to detect an effect).

Front 8

When calculating a CI for rho, why do we have to transform the CI around z' back to r at the end?

Back 8

Unless rho is zero, the distribution of the mean is not normal. The first 2 steps associated with calculating CIs allow us to use a normal distribution, necessitating a switch back at the end.

Front 9

When calculating CIs for rho, why do we initially convert r to fisher's z' using the r to z table?

Back 9

this transforms r to a normal distribution.

Front 10

What is Beta?

Back 10

population regression coeficient.

Front 11

What is rho? How is it represented?

Back 11

population correlation coeficient, looks like a p

Front 12

Distinguish between Beta and b.

Back 12

Beta = population regression coeficient

b = sample regression coeficient = slope

Front 13

CIs are written 1-alpha. If alpha = .05, then what % CI are we calculating?

Back 13

95%

Front 14

What does it mean to have a 95% CI?

Back 14

If you took many samples from the population and computed r and CI for each, 95% of the time, rho will be within the range specified by CI. In other words, 95% of the samples will contain rho.

Front 15

Describe the 4 assumptions of regression.

Back 15

LINH

Linear, Independence of residuals, Normal distribution of residuals, Homoscedasticity of jt distribution of residuals

1. There is a linear relationship between x and y

2. For every value of x, the residuals E = Y - Predicted Y are normally distributed with a mean of zero.

3. The joint distribution of residuals is homoscedastic. this means that the spread of the errors around the regression line is constant along the whole length of the line).

4. The residuals are independent of each other. (Error for one person isn't related to error for another person)

Front 16

The normal error regression model reads Y = alpha + BetaX +E, where E~N(0, sigma squared) IID. What does the IID mean?

Back 16

Errors are independent of each other and are identically distributed

Front 17

The normal error regression model reads Y = alpha + BetaX +E, where E~N(0, sigma squared) IID. What does the E~N(0, sigma squared) part mean?

Back 17

Errors are normally distributed with a mean of zero and a certain fized variance.

Front 18

One of the assumptions of regression is that for every x, residuals are normally distributed with a mean of zero. Define the term residual. How are residuals represented?

Back 18

residuals = errors

E = Y - predicted Y

(I think that this E might be an Epsilon).

Front 19

One of the assumptions of regression is that the joint distribution of residuals is homoskedastic. What does this mean?

Back 19

There will be equal variance for every value of x in terms of errors around that line.

Variance for each value of x is normally distributed.

Front 20

For this value of x, the errors will be normally distributed. There will be man points closer to the line and fewer farther out.
This statement reflects which of the assumptions of regression?

Back 20

For every x, residuals are normally distributed with a mean of zero.

Front 21

You don't need to meet this assumption of regression if you are just calculating a value, but you must meet this assumption if you are doing a hypothesis test.

Back 21

Assumption 4: Residuals are independent of each other; error for one person is not related to error for another person.

Front 22

If power = .37, what does this mean?

Back 22

If the null is false, we only have a 37% chance of finding that effect.

Front 23

If we know 3 of the following factors associated with power, the 4th can be determined. What are these 4 factors?

Back 23

PEAS

1. power of the test
2. effect size in the population
3. alpha level of the test
4. sample size

Front 24

Why might you do a power analysis on a study that you've already done?

Back 24

1. power analyses can help you revise plans for study
2. helps you understand the limits of your research (If I can't detect an effect with this sample size, then..)

Front 25

What are the two common and important types of questions about power that often arise in research.

Back 25

What is the power of our test?

What sample size do we need?

Front 26

What 4 things influence r?

Back 26

1. reliability of measures
2. restriction of range
3. combining samples
4. outliers

Front 27

Reliability is one of the things that influences r. If you have low reliability, how is r affected?

Back 27

low reliability, correlation is reduced.

Front 28

Restricted range is one of the things that wil affect r. If you restrict range, what happens to r?

Back 28

Restricted range typically lowers r, unless you have a curvilinear relationship (in which case restriction of range could increase r).

Front 29

Will combining samples reduce or elvate r?

Back 29

Either, depending on the range.

Front 30

Outliers can influence r in three different ways. What are these ways that outliers can influence r?

Back 30

Outliers might:
increase r, decrease r, or not affect it

Front 31

How do you determine the order of a matrix?

Back 31

list the number of rows (across) followed by number of columns (up and down).

Front 32

If you want to direct soeone to a single number inside of a matrix, tell them..

Back 32

the row and then the column

Front 33

What types of matrices are the most common in regression?

Back 33

1. square = have same number of rows and columns

2. vector = a column of numbers or a row of numbers

Front 34

What are the differences between square and vector matrices?

Back 34

1. square = have same number of rows and columns; you must have square matrices to divide.

2. vector = a column of numbers or a row of numbers

Front 35

Have same number of rows and columns

Back 35

square matrices

Front 36

Are needed for division of matrices.

Back 36

square matrices

Front 37

represent a single column of numbers or a row of numbers

Back 37

vector matrices
(row vector matrices, column vector matrices).

Front 38

In order to add/subtract matrices, what must be true?

Back 38

the natrices must be of the same order

Front 39

In order to multiply matrices, what must be true?

Back 39

The number of columns in the first matrix has to equal the number of rows in the second matrix. (ie, 2*3 and 3*4).

Front 40

In order to divide matrices, what must be true?

Back 40

Matrices must be square.

Front 41

What is a scalar?

Back 41

A scalar is a single number that is used when multiplying matrices.

Front 42

can you use the communicative property when multiplying matrices?

Back 42

no

Front 43

A is post multiplied by D. How is this represented?

Back 43

A*D

Front 44

D is premultiplied by A

Back 44

A*D

Front 45

Describe the process of transposing a matrix.

Back 45

When transposing a matrix, rows become columns and columns become rows.

Front 46

Taking any matrix and multiplying by the transpose gives us...

Back 46

a square matrix

Front 47

Matrices cannot be divided directly. How, then, does division occur?

Back 47

To divide matrices you must multiply the inverse of the divisor by the dividend.

Front 48

Division of matrices requires multiplication of the inverse of the divisor by the dividend. Distinguish between the divisor and the dividend.

Back 48

In 100/4, 4 is the divisor and 100 is the dividend.

Front 49

Division of matrices requires that you have:
1. a square matrix
and
2. the inverse of the divisor matrix.
How are each of these steps achieved?

Back 49

1. To get a square matrix, premultiply by transpose matrix.
2. We don't need to know how to compute the inverse of the divisor matrix

Front 50

Any square matrix that has ones on the diagonal and zeros everywhere else.

Back 50

identity matrix

Front 51

What is the inverse of a divisor matrix and why is it useful?

Back 51

Inverse matrix = the reciprocal of the original matrix.

Inverses are useful because if you multiply any matrix by it's inverse, you get an identity matrix. (An identity matrix is any square matrix that has ones on the diagonal and zeros everywhere else.

Front 52

If you multiply your matrix by this type of matrix, you get your original matrix.

Back 52

identity matrix

Front 53

What are 2 important properties of identity matrices?

Back 53

1. if you multiply any matrix by it's inverse, you get an identity matrix.
2. If you multiply your matrix by this type of matrix, you get your original matrix.

Front 54

What is the rank of a matrix?

Back 54

The rank of a matrix tells you the number of rows or columns that give us new info.

Redundant info will reduce rank. (One Example of redudant info includes one row being twice the value of another row).

The highest possible rank is 2.

Front 55

For square matrices, you can only find the inverse if the matrix is...

Back 55

full rank (ie, every row and column gives you new info).

Front 56

A square matrix that doesn't give you any redundant info, contains all independent info.

Back 56

full rank matrix

Front 57

What is the difference between full rank and singular matrices?

Back 57

Full rank: A square matrix in which all rows and columns contain independent info.

Singular matrix: a square matrix that is not of full rank. We cannot compute the inverse of a singular matrix and consequently cannot divide.

Front 58

How can we determine if a matrix is of full rank (and therefore has an inverse)?

Back 58

Find the determinant. If the determinant is zero, then the matrix is singular and has no inverse. If the determinant is any number other than zero (negative numbers are fine), then you have a full rank matrix.

Front 59

In this type of matrix, rows and calumns provide independent information

Back 59

full rank matrix

Front 60

In this type of matrix, you can compute an inverse.

Back 60

full rank matrix.

Front 61

If you can compute an inverse of a matrix, this means that...

Back 61

you can use the matrix to do division.

Front 62

Describe the things that are true of a full rank matrix.

Back 62

1. Rows and columns provide independent info.
2. You can compute an inverse, which means that you can use matrix to do division.

Front 63

Describe how to interpret the regression constant (i.e., y intercept).

Back 63

First, check the range of values for the x variable to see if it can truly go to zero.

*If x cannot be zero, then you need to say that the regression constant is a constant value that we need to add to the slope component in order to predict y more accurately.

If x can go to zero, plug in zero for x and make sure that the resulting value of y can fit into the range given for y.

Front 64

y predicted = 10.32 +2.41x
where x = social support score
y=depression

In the above equation, how would we interpret the regression coeficient?

Back 64

For every 1 point increase in social support (x), depression(y) increases by 2.41.

Front 65

Zy(depression) =
0.41 Zx(social support)

In the above equation, how would we interpret the standardized regression coeficient?

Back 65

For every one SD increase in social support, depression scores increase by .41 SDs, on average.

Front 66

Zy(depression) =
0.41 Zx(social support)

In the above equation, what is the correlation between x and y? Why?

Back 66

r = 0.41

For a single predictor, standardized b is equal to r. (This is not true for unstandardized b).