Standardized Residuals

Standardized residuals are a powerful tool for brand profiling. This analysis highlights brands' typical and atypical attributes and provides insight into a brand's image within a competitive landscape.  

Unlike absolute brand image analysis, standardized residuals provide a relative view by accounting for the "effect of large brands". Larger brands often receive more associations simply due to their high market presence. This method corrects for such biases, revealing a more accurate picture of brand positioning.

Methodology

The analysis is based on a Grid Report table where:

• Rows represent brand attributes;

• Columns represent brands;

• Cells contain the number of respondents who associate a particular brand with a given attribute.

A residual is the difference between the observed value (Y) and the expected value (X):

• Observed value (Y): data collected from the study

• Expected value (X): theoretical frequency assuming no association between brand and attribute, calculated as:

• R = Row total (sum of all responses for an attribute);

• C = Column total (sum of all responses for a brand);

• N = Total number of responses in the table.

Standardizing residuals

To account for variations in brand size, residuals are adjusted by standard deviation:

where

• Prow = Row total proportion

  

• Pcol = Column total proportion 

  

It is with this adjustment that the dominance of well-known brands due to higher recognition is avoided.

To apply residuals in DVI

Use the ‘SGN’ button above the table and select ‘Residuals’ in the comparison pop-up window.

To apply residuals in charts and on dashboards

Toggle the ‘Comparison’ in the left menu pane, select ‘Residuals’, and adjust the thresholds.

Interpreting the results

Standardized residuals typically range from -3 to +3, with thresholds for statistical significance:

• ±1.645 for 90% confidence

• ±1.960 for 95% confidence

• ±2.576 for 99% confidence

If the residual's absolute value exceeds the threshold, it indicates a significant association:

• A positive residual shows a strong brand-attribute link.

• A negative residual suggests the brand is associated with an opposing characteristic.

Residuals within the threshold indicate weak or insignificant associations.