FA; Lec 1 & 2; Lab 1 & 2

Question 1

What is a very widely used form of data reduction?

Answer 1

Factor analysis

Question 2

Questions addressing similar issues are thought to address the same [X]?

Answer 2

Underlying construct

Question 3

Items/variables consistently responded to in similar manner by different respondents supposedly address the same [X]?

Answer 3

Underlying construct/Latent variable/Common factor (or just plain ‘factor’)

Question 4

What is a latent variable/underlying construct?

Answer 4

A hidden variable. For example, ‘health’ - there isn’t a single measurement of ‘health’ - it is an abstract concept. Instead we measure physical properties from our boy e.g. blood pressure, weight etc. These separate measurements can then be used by a trained person to judge your health. If we had a sensor for health we could measure and use that variable, but since we don’t we use other measurements which all contribute in some way to assessing health.

Question 5

When do you need FA?

Answer 5

1. To understand the structure of a set of variables (e.g. ‘intelligence’)
2. To formulate a questionnaire to measure a latent variable
3. To reduce a data set to a more manageable size while retaining as much of the original information as possible

Question 6

What is a common criticism of FA?

Answer 6

That it produces facile results. This is because it can always be used, resulting in erroneous application.

Question 7

What is a correlation matrix?

Answer 7

A grid organised such that the value of any cell represents the correlation between the variable assigned to the row and the variable assigned to the column, It is usual that the order of variables in the rows is the same as the columns so that the diagonal values of this grid represent the correlation of a given variable with itself.. This means that the diagonal values are all 1.

Question 8

What does a correlation matrix tell you?

Answer 8

It gives you a complete view of the bi-variate correlations that exist in whatever dataset you’re looking at.

Question 9

What is the symbol for Pearson’s Product-Moment Correlation Coefficient?

Answer 9

r

Question 10

What does Pearson’s correlation give an indication of?

Answer 10

It gives an indication of the extent to which a criterion variable (Y) varies in conjunction with the predictor variable (X)

Question 11

What is the 1. the verbal, and 2. the mathematical formula for Pearson’s Product-Moment Correlation Coefficient?

Answer 11

1. r= covariability of X and Y/Variability of X and Y separately
2. r= Sxy/√Sx².Sy²

Question 12

If you are eyeballing a correlation matrix how high must the correlation be to considered a correlation?

Answer 12

.3=<

Question 13

If you are asked to complete the cosine values for an anti-clockwise degree value, how do you work that out?

Answer 13

360-anticlockwise degree

e.g. 360-70=290

Question 14

If an item were at an angle of 360degrees to F1, what would be the correlation between the two of them?

Answer 14

Perfectly positive

Question 15

If an item were at an angle of 180degrees to F1, what would be the correlation between the two of them?

Answer 15

Perfectly negative

Question 16

Looking at correlation values, how would you determine if an item loaded onto a factor?

Answer 16

We usually require the correlation between an item and a factor to be equal to or greater than a magnitude of .3 before agreeing that it loads onto a factor.

Question 17

1. How would do you calculate communality for an item?
2. What does calculating the communality tell you?
3. When you have the communality, how do you determine how much of the variance of that item remains unexplained by the proposed factors?

Answer 17

1. The sum of the square of the correlations of that item across all the factors. E.g. (0.53)²+(0.14)²+(0.27)²= 0.37
2. This tells you how much of the variance for that item is explained by the three factors. In this example = 37%
3. 1 - (communality of item)
   e. g. 1 - 0.37 = 0.63 = 63% of variance for that item is unexplained by the three factors.

Question 18

How is FA represented through geometry?

Answer 18

Items of factors can be represented by straight lines of equal length. Lines are positioned such that the correlation between the items = cosine of the angle

Question 19

How do you calculate the cosine of the angle?

Answer 19

cosine of angle is = adjacent/hypotenuse

Question 20

If F1 is represented through geometry, and Item 1 is at a right angle to it - what is the correlation?

Answer 20

Item 1 has a zero correlation to F1

Question 21

What is an orthogonal solution?

Answer 21

When two common factors are extracted which are not themselves correlated (i.e. they are at right angles to each other). If the common factors are not correlated then they truly represent independent factors.

Question 22

What is an oblique solution?

Answer 22

When the common factors extracted may themselves be correlated. (more plausible for psychology)

Question 23

What is a ‘factor loading’?

Answer 23

The correlation between an item and a factor.

Question 24

What is a factor/structure matrix?

Answer 24

A table showing the correlations between all the items and the factors.

Question 25

what does b =?

Answer 25

factor loading

Factor loading is determined by the coordinate of that variable on the graph with respect to that factor.

Question 26

What 3 things does a factor matrix show?

Answer 26

1. Which items make up which common factor
2. The amount of overlap between an item/items and the potential factors - calculated through communality
3. The relative importance of each common factor (e.g. a factor that explains 40% of the overlap between the items will be more important than one that only explains 25%) - this is calculated through the eigenvalue.

Question 27

What is the communality of an item?

Answer 27

How much of the variability of an item is explained by the common factors.

Question 28

What is the most common way of calculating the communality of an item?

Answer 28

Squared multiple correlation

Question 29

Give 3 reasons why the communality for an item may be low?

Answer 29

1. Because it measures something conceptually different from all the other items
2. Because it has excessive measurement error
3. Because there are few individual differences in the way the item is responded to - it may be very easy or very difficult.

Question 30

How do you calculate the eigenvalue for a factor?

Answer 30

Square the factor loadings (items loading onto that factor) for a single factor, add them up = eigenvalue

Question 31

How do you calculate the proportion of variance explained by a factor?
2 steps

Answer 31

1. Square the factor loadings (all items) for a single factor, add them up = eigenvalue
2. Divide the eigenvalue by the number of items

Question 32

What are the two branches of FA?

Answer 32

1. Exploratory factor analysis - no prior assumptions about relationships among factors
2. Confirmatory factor analysis - tests a hypothesis that specific items are associated with specific factors (structural equation modelling)

Question 33

What are two types of exploratory factor analysis?

Answer 33

1. Principal components analysis

2. Factor analysis (principal axis factoring)

Question 34

What are two types of confirmatory factor analysis?

Answer 34

1. Path analysis

2. Latent variable analysis

Question 35

What does the sum of the square of all loadings, irrespective of magnitute, onto a particular factor give you?

Answer 35

The eigenvalue

Question 36

How do you calculate the percentage of variance explained by each factor?

Answer 36

The eigenvalue divided by the number of items