Marketing Research Methods
Week 1 - M8: until p. 273 / M19 / M9: pp. 300-306
Chapter 8
Measurement means assigning numbers or other symbols to characteristics of objects
according to certain prespecified rules. Note that what we measure is not the object, but some
characteristic of it. Thus, we do not measure consumers—only their perceptions, attitudes,
preferences, or other relevant characteristics
The level of measurement denotes what properties of an object the scale is measuring or not
measuring.
All the scales that we use in marketing research can be described in terms of four basic
characteristics: description, order, distance and origin.
- Description: the unique label or descriptor that are used to designate each value of
the scale; all scales possess description
- Order: the relative sizes or positions of the descriptor on a scale: order is denoted by
descriptors such as greater than, less than, or equal to.
- Distance: characteristics of scales indicating that absolute differences between the
scale descriptors are known and may be expressed in units. Distance has also order.
Distance implies order, but the reverse may not be true.
- Origin: characteristic of scales indicating that the scale has a unique or fixed
beginning or true zero point.
Description is the most basic characteristic that is present in all scales. If a scale has order, it
also has description. If a scale has distance, it also has order and description. A scale that has
origin also has distance, order, and description.
Primary scales of measurement
Nominal scale: A scale whose numbers serve only as labels or tags for identifying and
classifying objects with a strict one-to-one correspondence between the numbers and objects.
The only characteristic possessed by these scales is description.
Ordinal scale: a ranking scale in which numbers are assigned to objects to indicate the
relative extent to which some characteristic is possessed. Thus, it is possible to determine
whether an object has more or less of a characteristic than some other object. The ordinal
scales posses description and order characteristics but do not possess distance or origin.
Interval scale: a scale in which the numbers are used to rate objects such that numerically
equal distances on the scale represent equal distance in the characteristics being measured.
An interval scale contains all the info of an ordinal scale, but it also allows you to compare
the differences between objects. In an interval scale, the location of the zero point is not
fixed: that is; these scales do not possess the origin characteristic.
Ratio scale: the highest-level scale. It allows the researcher to identify or
classify objects, rank-order the objects, and compare intervals or differences. It
is also meaningful to compute ratios of scales. Thus, ratio scales possess the
characteristics of origin, distance, order, and description.
1
,2
,H19
Factor Analysis
- Many items into fewer dimensions
- To check a certain assumed dimensionality
- To find out which underlying dimension exist
- Always lose some info, but not too much.
Purpose: reduction of a large quantity of data by finding common variance to:
- Retrieve underlying dimensions in your dataset
- Test if the hypothesis dimensions also exist in your dataset
Two central questions:
1. How to reduce a larger set of variables into a smaller set of uncorrelated factors?
2. How to interpret these factors (underlying dimensions), and scores on these factors?
Factor analysis: what is it about?
- Ultimate goal: use dimensions in further analysis
- Data: a number of interval- or ratio scaled variables (metric), metrical data on n items,
summarize the items into m (<n) ‘factors’.(often ordinal, but assumed interval –
Likert)
- Note: no distinction is made between dependent (Y) and independent (X) variables.
FA is usually applied to your independent (X) variables. No causal relation between
variables.
Data reduction
Strong correlations between two or more items, same underlying phenomenon. So combine,
to get:
- Parsimony
- Less multicollinearity in subsequent analysis. If variables are highly correlated, it is
hard to distinguish their effects in regression.
Factor analysis: a class of procedures primarily used for data reduction and summarization.
Factors: an underlying dimension that explains the correlation among a set of variables.
Factor analysis is used in the following circumstances:
1. To identify underlying dimensions, or factors, that explain the correlation among a set
of variables
2. To identify a new, smaller set of uncorrelated variables to replace the original set of
correlated variables in subsequent multivariate analysis.
3. To identify a smaller set of salient variables from a lager set for use in subsequent
multivariate analysis.
Each variable is expressed as a linear combination of underlying factor. The amount of
variance a variable share with all other variables included in the analysis is referred to as
communality.
3
, Statistics associated with factor analysis are as follows:
Bartlett’s test of sphericity: Bartlett’s test of sphericity is a test statistic used to examine the
hypothesis that the variables are uncorrelated in the population. In other words, the
population correlation matrix is an identity matrix; each variable correlates perfectly with
itself but has no correlation with the other variables .
Correlation Matrix: A correlation matrix is a lower triangle matrix showing the simple
correlations, r, between all possible pairs of variables included in the analysis. The diagonal
elements, which are all 1, are usually omitted
Communality: Communality is the amount of variance a variable shares with all the other
variables being considered. This is also the proportion of variance explained by the common
factors.
Eigenvalue: the eigenvalue represents the total variance explained by each factor
Factor loadings: factor loadings are simple correlations between the variables and the factors
Factor loading plot: a factor loading plot is a plot of the original variables using the factor
loadings as coordinates
Factor matrix: contains the factor loadings of all the variables on all the factors extracted.
Factor scores: are composite scores estimated for each respondent on the derived factors
Factor scores coefficient matrix: This matrix contains the weights, or factor score
coefficients, used to combine the standardized variables to obtain factor scores.
Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy. The Kaiser-Meyer-Olkin
(KMO) measure of sampling adequacy is an index used to examine the appropriateness of
factor analysis. High values (between 0.5 and 1.0) indicate factor analysis is appropriate.
Values below 0.5 imply that factor analysis may not be appropriate
Percentage of variance. This is the percentage of the total variance attributed to each factor.
Residuals. Residuals are the differences between the observed correlations, as given in the
input correlation matrix, and the reproduced correlations, as estimated from the factor matrix
Scree plot. A scree plot is a plot of the eigenvalues against the number of factors in order of
extraction.
4
Week 1 - M8: until p. 273 / M19 / M9: pp. 300-306
Chapter 8
Measurement means assigning numbers or other symbols to characteristics of objects
according to certain prespecified rules. Note that what we measure is not the object, but some
characteristic of it. Thus, we do not measure consumers—only their perceptions, attitudes,
preferences, or other relevant characteristics
The level of measurement denotes what properties of an object the scale is measuring or not
measuring.
All the scales that we use in marketing research can be described in terms of four basic
characteristics: description, order, distance and origin.
- Description: the unique label or descriptor that are used to designate each value of
the scale; all scales possess description
- Order: the relative sizes or positions of the descriptor on a scale: order is denoted by
descriptors such as greater than, less than, or equal to.
- Distance: characteristics of scales indicating that absolute differences between the
scale descriptors are known and may be expressed in units. Distance has also order.
Distance implies order, but the reverse may not be true.
- Origin: characteristic of scales indicating that the scale has a unique or fixed
beginning or true zero point.
Description is the most basic characteristic that is present in all scales. If a scale has order, it
also has description. If a scale has distance, it also has order and description. A scale that has
origin also has distance, order, and description.
Primary scales of measurement
Nominal scale: A scale whose numbers serve only as labels or tags for identifying and
classifying objects with a strict one-to-one correspondence between the numbers and objects.
The only characteristic possessed by these scales is description.
Ordinal scale: a ranking scale in which numbers are assigned to objects to indicate the
relative extent to which some characteristic is possessed. Thus, it is possible to determine
whether an object has more or less of a characteristic than some other object. The ordinal
scales posses description and order characteristics but do not possess distance or origin.
Interval scale: a scale in which the numbers are used to rate objects such that numerically
equal distances on the scale represent equal distance in the characteristics being measured.
An interval scale contains all the info of an ordinal scale, but it also allows you to compare
the differences between objects. In an interval scale, the location of the zero point is not
fixed: that is; these scales do not possess the origin characteristic.
Ratio scale: the highest-level scale. It allows the researcher to identify or
classify objects, rank-order the objects, and compare intervals or differences. It
is also meaningful to compute ratios of scales. Thus, ratio scales possess the
characteristics of origin, distance, order, and description.
1
,2
,H19
Factor Analysis
- Many items into fewer dimensions
- To check a certain assumed dimensionality
- To find out which underlying dimension exist
- Always lose some info, but not too much.
Purpose: reduction of a large quantity of data by finding common variance to:
- Retrieve underlying dimensions in your dataset
- Test if the hypothesis dimensions also exist in your dataset
Two central questions:
1. How to reduce a larger set of variables into a smaller set of uncorrelated factors?
2. How to interpret these factors (underlying dimensions), and scores on these factors?
Factor analysis: what is it about?
- Ultimate goal: use dimensions in further analysis
- Data: a number of interval- or ratio scaled variables (metric), metrical data on n items,
summarize the items into m (<n) ‘factors’.(often ordinal, but assumed interval –
Likert)
- Note: no distinction is made between dependent (Y) and independent (X) variables.
FA is usually applied to your independent (X) variables. No causal relation between
variables.
Data reduction
Strong correlations between two or more items, same underlying phenomenon. So combine,
to get:
- Parsimony
- Less multicollinearity in subsequent analysis. If variables are highly correlated, it is
hard to distinguish their effects in regression.
Factor analysis: a class of procedures primarily used for data reduction and summarization.
Factors: an underlying dimension that explains the correlation among a set of variables.
Factor analysis is used in the following circumstances:
1. To identify underlying dimensions, or factors, that explain the correlation among a set
of variables
2. To identify a new, smaller set of uncorrelated variables to replace the original set of
correlated variables in subsequent multivariate analysis.
3. To identify a smaller set of salient variables from a lager set for use in subsequent
multivariate analysis.
Each variable is expressed as a linear combination of underlying factor. The amount of
variance a variable share with all other variables included in the analysis is referred to as
communality.
3
, Statistics associated with factor analysis are as follows:
Bartlett’s test of sphericity: Bartlett’s test of sphericity is a test statistic used to examine the
hypothesis that the variables are uncorrelated in the population. In other words, the
population correlation matrix is an identity matrix; each variable correlates perfectly with
itself but has no correlation with the other variables .
Correlation Matrix: A correlation matrix is a lower triangle matrix showing the simple
correlations, r, between all possible pairs of variables included in the analysis. The diagonal
elements, which are all 1, are usually omitted
Communality: Communality is the amount of variance a variable shares with all the other
variables being considered. This is also the proportion of variance explained by the common
factors.
Eigenvalue: the eigenvalue represents the total variance explained by each factor
Factor loadings: factor loadings are simple correlations between the variables and the factors
Factor loading plot: a factor loading plot is a plot of the original variables using the factor
loadings as coordinates
Factor matrix: contains the factor loadings of all the variables on all the factors extracted.
Factor scores: are composite scores estimated for each respondent on the derived factors
Factor scores coefficient matrix: This matrix contains the weights, or factor score
coefficients, used to combine the standardized variables to obtain factor scores.
Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy. The Kaiser-Meyer-Olkin
(KMO) measure of sampling adequacy is an index used to examine the appropriateness of
factor analysis. High values (between 0.5 and 1.0) indicate factor analysis is appropriate.
Values below 0.5 imply that factor analysis may not be appropriate
Percentage of variance. This is the percentage of the total variance attributed to each factor.
Residuals. Residuals are the differences between the observed correlations, as given in the
input correlation matrix, and the reproduced correlations, as estimated from the factor matrix
Scree plot. A scree plot is a plot of the eigenvalues against the number of factors in order of
extraction.
4
