Factor Analysis pART 2 (WK 2)

Question 1

Name the 4 factor analysis diagnostics

Answer 1

1. Kaiser-Meyer-Olkin measure of sampling adequacy (KMO)
2. Bartlett’s test of sphericity
3. Determinant value
4. Percentage of non-redudant residuals <0.5

Question 2

What are the factor analysis diagnostics?

Answer 2

• provided in the EFA output, measuring the amount of correlation present between items
• can be helpful but not necessary!

KMO & factor analysis already do correlations for you - so no need to look at crrelations prior to testing (putting values in a correlation table & see how everything compares

Question 3

Are the FA diagnostics before or part of FA?

Answer 3

before factor analysis

Question 4

Describe the Kaiser-Meyer-Olkin (KMO) measure

Answer 4

• single value
  = computed as the ratio of the sum of squared correlations to the sum of squared correlations plus sum of squared partial correlations
  -provides an indicator of the proportion of variance in item responses that might be causes by underlying factors (summarises amount of correlational overlap between all items)
• small values (

Question 5

Describe Bartlett’s test of sphericity

Answer 5

= tests null hypothesis that correlation matrix is an identity matrix (a correlation matrix consisting of zero correlation between variables)

• Bartlett’s test is conservative, especially when sample sizes are large

Question 6

Significance is __________

what does this mean?

Answer 6

A: desirable

This indicates that the correlation matrix is significantly different from an identity matrix.

Question 7

What is an identity matrix?

Answer 7

a correlation matrix with zero correlation between variables

Question 8

What’s the difference between an approximate chi-square and a true chi-square value?

Answer 8

An approximate chi-square value = (~X^2)

A true chi-square value = (X^2)

either way:

• round off to 2dp
• unless significant values = then round off to 3dp

Question 9

Describe the determinant.

Answer 9

• a test of multicollinearity (correlational overlap) in the data
• we want determinant to be pretty small value (above .00001)
• provided as a table note, often in exponential notation = making it easier to miss!
• determinant is less important than other diagnostics

HOW TO DEAL WITH THE DETERMINANT:
> if it bad/different to what you want; comment “the determinant was not ideal”

> if there are not other issues, when looking at rest of FA; comment “this (determinant) did not appear to affect the data”

> if the determinant is exceeded enough to be an issue, the way we solve this is by looking for highly correlated items & deleting one out of its pair; i.e. if two items are very similair, they’re already messing up the FA (you can spot this easily)

> put it in your report and forget about it

Question 10

Describe non-redunant residuals

Answer 10

• the percentage of non-redundant residuals above .05 is provided in a table note under the reproduced correlation matrix (orthogonal rotation)
• measure of multicollinearity too!
• ideally want this percentage as low as possible, but up to 50% is still okay!

REMEMBER:
> it doesn’t have to highest/lowest but achieving a happy medium

Question 11

how do you run correlations between items and inspect them, on SPSS?

Answer 11

A: Analyze > Bivariate > Correlate (throw them in & think about your output)

• this step can be skipped as KMO & Bartlett’s test are already doing this
• e.g. maybe 2 items are so highly correlated, than 1 is redudant and should be deleted ?

Question 12

define reliability

Answer 12

= the term we use for stability and consistency in psychometric testing

• e.g. if I tested you this week, and you scored high on extraversion, I would expect you to score high on extraversion
• if you score low, then your test is NOT reliable

Question 13

what are the two types of reliability?

Answer 13

1) test-retest reliability

2) internal consistency

Question 14

describe test-retest reliability

Answer 14

• more to do with temporal consistency (consistency across time)
• ideal form of reliability
• however, not the most commonly used as it requires a bit of work to measure test-retest

> i.e. have to measure something twice within a certain time period; repeated measures

Question 15

describe split-half reliability

Answer 15

• internal consistency is measured through split-half reliability (degree to which items are forming a consistent construct)
• combine one half of a test with the other half; if we have items measuring the same thing, then they should roughly be correlated with another
• not used today!
• gold standard today = Cronbach’s alpha

Question 16

what is Cronbach’s alpha?

Answer 16

• statistical formula that provides the mean of all possible split-half correlations for a given set of items
• originally created by Cronbach to address the bias that people criticise split-half reliability for having (1950’s)
• commonly used today as ideal measure of internal consistency (the more reliable our test, the more internable)
• “you want Cronbach’s alpha to be above .6 at bare minimum, although .8 or ideally .9 is better”

Question 17

how do you conduct a reliability analysis, in SPSS?

Answer 17

A: Analyze > Scale > Reliability Analysis

• transfer the set of items you want to analyse into Items box
• ensure that Model is set to Alpha
• enter a scale label (good organising tip)

DESCRIPTIVES WINDOW
[- select item, scale, scale if item deleted
- continue back to the RELIABILITY ANALYSIS WINDOW
- hit ok to run the analysis]

Question 18

how many different levels of output are there?

Answer 18

three.
remember, whilst it has it’s own name (reliability analysis), don’t consider it an optional extra to FA - it is still part of FA.

(1) RELIABILITY STATISTICS
[= you’ll find the overall Cronbach’s alpha for the item set here]

(2) ITEM STATISTICS
[= useful to check out to see if there are any skewed items, or where most participants have made the same response]

(3) ITEM-TOTAL STATISTICS
[=table contains 2 important values for looking at how anitem relates to the set of items:
- the corrected item-total correlation
- the Cronbach’s alpha if item deleted]

Question 19

describe corrected item-total correlation

Answer 19

= this value is the correlation of the item with the sum of the rest of the item set
(item you want to look at + all the other items [redundancy variance = how well does this item fit in with the rest?])

• desirable to have corrected-item total correlations between .3 and .8 or so, as then the items fit well with other items without being redundant
• NOTE: lower is always worse than hight (.8 is not as bad as below .3) aim for happy medium!

Question 20

describe Cronbach’s alpha if item deleted

Answer 20

• more convienient = does exactly what it says
• what this metric does is asks: “what would that value be if what we’re looking at, wasn’t in the scale?” = that’s the reliability if you took the item out of the scale
• if removing the item increases reliability = then delete it ; but if keeping it improves the reliability (keep it) = but it’s all down to your interpretation!
• can’t use rule of thumbs & ignore practicality/common sense* you should aim to achieve middle ground/balance
• we have information from SPSS but it’s also our job to interpret it