2021
Short summary CMA
lectures
MASTER MARKETING 2021-2022
VRIJE UNIVERSITEIT
, 1
CMA
Lecture 3 Measurement + scaling: reliability, validity, and dimensionality
Chi square → Nominal
Pearsons correlation → Interval / ratio
Linear regression → DV interval / ratio
Logistic regression DV is nominal
Comparative scaling
- Paired comparison scaling: apple or pear
- Rank order: pear, apple, banana
- Constant sum scaling: apple 50, banana 30, pear 20
Non-comparative scaling
- Likert scale
- Semantic differential scale: pepsi is: sweet…………sour
Reliability: is it stable?
Validity: measures what is supposed to?
Assessing scale reliability: internal consistency
→ Cronbach’s α
- Fundamental research: ok α >.70, good α > .80
- Practical application: α > .90
→ Improve by deleting items with low correlation with total and other items.
Scale validity:
- Content validity: do the items cover all aspects of the complex construct
- Criterion validity: scale performs as expected in relation to other variables
- Construct validity: measure what it should measure according to the theory.
Factor analysis
Key objective: capture as much info (variables) in the original variables as possible with as few factors as
possible.
- Reduce large number of variables
- Minimize loss of information
- Data reduction, summarization
Factor analysis design
- Min observations: 50
- 3-5 variables per factor
Factor analysis step by step
1. Inspect correlation matrix: is FA appropriate?
2. Choose method of extraction. (principle component analysis)
3. Determine number of factors underlying the data (A-priori determination, eigenvalue > 1, scree test)
4. Rotate the initial solution for proper interpretation (varimax)
5. Interpret the rotated solution and name the factors.
6. Calculate Cronbach for each factor found.
7. Create summated scales or factor scores for further analysis
Correlation matrix: is FA appropriate?
- Bartlett’s test of sphericity provides statistical significance that the correlation matrix
o H0: all possible correlations between variables = 0
o Significant? p <0.05
- Kaiser-meyer-Olkin (KMO measure of sample adequacy (MSA)
degree of inter-correlations among variables
o MSA must exceed .50
, 2
Correlation matrix: is FA appropriate?
- KMO MSA = >.50
- Barlett’s: p < .05
How many factors?
Eigenvalue > 1 = amount of variance explained by factor
- Sum eigen values = amount of variables.
How many factors? “Elbow” rule:
▪ Look for the “elbow” (break, sudden flattening in
eigenvalues) (e.g., k)
▪ Take the number of factors before the elbow (k-1)
Communalities extracted
All communalities are very high, so no variable should be eliminated.
, 3
Communalities extracted
- How much of the variance of each variables is captured by the extracted factors.
- Of communality is very low (say <.30), the item is “quite unique” since it correlates weakly with other
variables. Such variable should be removed, as it is definitely measuring “something else”.\
Interpretation of the rotated solution
Naming the factors
- Factor 1 (planning
- Factor 2 (participation with staff)
- Factor 3 (handling stress/ efficiency)
Calculate Cronbach’s for each factor.
After a factor analysis, select high loading variables on each factor and conduct reliability analysis.
- Recode items with negative factor loading
- Calculate resulting Cronbach’s
- To increase reliability, look at item-total correlations and
Cronbach’s if item is deleted.
Create summated scales or factor scores for further
analysis
- Next, we can compute summated scales or factor scores
for subsequent analysis
- Three factor solution suggests three summated scales
(or three factor scores) should be constructed.
- These three new variables (replacing the original set of
variables) are used for further analysis.
Summated scales: compute mean scores on
dimensions
→ compute mean of the high loading variables in each
dimension.
Factor scores
Score of the individual respondent on the factor
(incorporate all variables)
Conclusion
- The 11 managerial skills can be grouped into 3 super-
variables (dimensions): Planning, participation with staff, handling stress/ efficiency.
- The scale is reliable: Cronbach’s for each dimension >.70.
- We can use the resulting 3 summated scales for subsequent analyses.
o On average, how does the company X do on employee’s managerial skills?
o How do employee’s managerial skills at company X and company Y compare?
o To reduce high correlation among predictors in a regression. E.g., how do managerial skills predict
organizational performance?
Lecture 4: Creating perceptual maps: using factor analysis
Perceptual map: representation of how the market sees a set of products or competing products in some
memory-like or cognitive sense. Percpeiton of them
Short summary CMA
lectures
MASTER MARKETING 2021-2022
VRIJE UNIVERSITEIT
, 1
CMA
Lecture 3 Measurement + scaling: reliability, validity, and dimensionality
Chi square → Nominal
Pearsons correlation → Interval / ratio
Linear regression → DV interval / ratio
Logistic regression DV is nominal
Comparative scaling
- Paired comparison scaling: apple or pear
- Rank order: pear, apple, banana
- Constant sum scaling: apple 50, banana 30, pear 20
Non-comparative scaling
- Likert scale
- Semantic differential scale: pepsi is: sweet…………sour
Reliability: is it stable?
Validity: measures what is supposed to?
Assessing scale reliability: internal consistency
→ Cronbach’s α
- Fundamental research: ok α >.70, good α > .80
- Practical application: α > .90
→ Improve by deleting items with low correlation with total and other items.
Scale validity:
- Content validity: do the items cover all aspects of the complex construct
- Criterion validity: scale performs as expected in relation to other variables
- Construct validity: measure what it should measure according to the theory.
Factor analysis
Key objective: capture as much info (variables) in the original variables as possible with as few factors as
possible.
- Reduce large number of variables
- Minimize loss of information
- Data reduction, summarization
Factor analysis design
- Min observations: 50
- 3-5 variables per factor
Factor analysis step by step
1. Inspect correlation matrix: is FA appropriate?
2. Choose method of extraction. (principle component analysis)
3. Determine number of factors underlying the data (A-priori determination, eigenvalue > 1, scree test)
4. Rotate the initial solution for proper interpretation (varimax)
5. Interpret the rotated solution and name the factors.
6. Calculate Cronbach for each factor found.
7. Create summated scales or factor scores for further analysis
Correlation matrix: is FA appropriate?
- Bartlett’s test of sphericity provides statistical significance that the correlation matrix
o H0: all possible correlations between variables = 0
o Significant? p <0.05
- Kaiser-meyer-Olkin (KMO measure of sample adequacy (MSA)
degree of inter-correlations among variables
o MSA must exceed .50
, 2
Correlation matrix: is FA appropriate?
- KMO MSA = >.50
- Barlett’s: p < .05
How many factors?
Eigenvalue > 1 = amount of variance explained by factor
- Sum eigen values = amount of variables.
How many factors? “Elbow” rule:
▪ Look for the “elbow” (break, sudden flattening in
eigenvalues) (e.g., k)
▪ Take the number of factors before the elbow (k-1)
Communalities extracted
All communalities are very high, so no variable should be eliminated.
, 3
Communalities extracted
- How much of the variance of each variables is captured by the extracted factors.
- Of communality is very low (say <.30), the item is “quite unique” since it correlates weakly with other
variables. Such variable should be removed, as it is definitely measuring “something else”.\
Interpretation of the rotated solution
Naming the factors
- Factor 1 (planning
- Factor 2 (participation with staff)
- Factor 3 (handling stress/ efficiency)
Calculate Cronbach’s for each factor.
After a factor analysis, select high loading variables on each factor and conduct reliability analysis.
- Recode items with negative factor loading
- Calculate resulting Cronbach’s
- To increase reliability, look at item-total correlations and
Cronbach’s if item is deleted.
Create summated scales or factor scores for further
analysis
- Next, we can compute summated scales or factor scores
for subsequent analysis
- Three factor solution suggests three summated scales
(or three factor scores) should be constructed.
- These three new variables (replacing the original set of
variables) are used for further analysis.
Summated scales: compute mean scores on
dimensions
→ compute mean of the high loading variables in each
dimension.
Factor scores
Score of the individual respondent on the factor
(incorporate all variables)
Conclusion
- The 11 managerial skills can be grouped into 3 super-
variables (dimensions): Planning, participation with staff, handling stress/ efficiency.
- The scale is reliable: Cronbach’s for each dimension >.70.
- We can use the resulting 3 summated scales for subsequent analyses.
o On average, how does the company X do on employee’s managerial skills?
o How do employee’s managerial skills at company X and company Y compare?
o To reduce high correlation among predictors in a regression. E.g., how do managerial skills predict
organizational performance?
Lecture 4: Creating perceptual maps: using factor analysis
Perceptual map: representation of how the market sees a set of products or competing products in some
memory-like or cognitive sense. Percpeiton of them
