Manuals
Once you generate a contingency table in the ‘ANALYSE’ – ‘Statistics’ – ‘Crosstabs’ tab, the Chi-squared value is displayed. Within the table, cells will be displayed in different colours, based on residuals.
Residuals provide an extremely simple and effective analysis of developments in the table. Unlike the Chi-square value, which gives only a general diagnosis of the correlations in the table, residuals accurately show where we can find correlations. Chi-square can prove to be statistically significant due to correlations in a single cell, but it does not tell us where it is.
A residual is a term used in connection with analysis of nominal variables. A residual is simply the difference between the actual frequency of the given cell and the theoretical frequency, as it would have been if the variables of the two-dimensional table in this cell were not related (assumption of the null hypothesis). Theoretically, the frequency is calculated very simply as the product of two margins, divided by the total size of the table.
If basic residuals – which with the standard assumption follow the Poisson distribution – are standardised (subtract the expected value and divide by the standard deviation), we get standardised residuals, which are asymptotically normally distributed. With standardised residuals we utilize the commonly used interpretation of hypothesis testing and the usual critical values, i.e. 1.65 or 1.96 at 10% or 5% risk.
Adjusted residuals additionally correct for un-equal margin dimensions. Some researchers have proven that they are more suitable than conventional standardized residuals, which is also our recommendation, and is used with analysis.
The 1KA application uses and colours the values 1.0, 2.0 in 3.0 for values of adjusted residuals, which roughly signal the strength of the correlation in a particular cell, i.e. the strength of deviation from the assumptions of the null hypothesis. The meaning of the values for standardised residuals:
- above 1.0 implies a certain increase and attention,
- above 2.0 (this is a simplification of the value 1.96) implies a statistically significant difference (sign<0.05), thus with a relatively low risk, the residuals differ from zero,
- above 3.0 constitutes a strong deviation (sign<0.01), which means that the residuals will almost certainly be different from zero, and, therefore, there is something "going on" in the cell.
Blue coloured cells indicate that the cell contains less units than expected, while red coloured cells indicate that the cell contains more units than expected.
For example, if the cell contains 30 units, and the expected value is 20, the basic residual in 10. Thus there are 10 more units in this cell than would have been expected if the variables in these two categories were not related. For example, if we are looking at gender and opinion, we could say that men are more IN FAVOUR than expected if the gender did not have an effect. If we subtract the expected value for the residual 10 and divide it by its root (root of 20 is 4.5, since the Poisson distribution has an expected value that is equal to variance), we get a standardized residual which is larger than 2, since we get (20-10) /4.5>2.0.
If we correct this on the basis of the formulas found in the annexes below, we get an adjusted residual, which has – if there are no exceptional asymmetries in the margins (YES: NO, male: female) – a rather similar value. A detailed example of calculating residuals is found here >>. In any case, we can conclude that in this cell there are statistically significant deviations, and on this basis we can form the substantive interpretation (e.g. reasons why men are more IN FAVOUR).
The colouration of 1KA is indicative, simplified, and simply functions as a screening (exploratory) analysis. In the formal interpretation of either the exact standardized or - even better - adjusted residual, we interpret it in the standard way, as indicated in the examples below.
The exact value of the residuals is obtained by selecting their calculation in the ‘Settings’ option, in one of the horizontal links above the table.
We can of course interpret the entire table and its Chi-squared value. However, residuals are more precise than the entire Chi-squared value, since they focus precisely on the individual cells where deviations occur. Further insight is obtained by analysis of the difference in shares based on the t-test.
Of course, all of this is only valid for nominal variables. In case of a ‘good’ ordinal arrangement of one of the variables - even more so in the case of unequivocal interval or ration scales – we use the T-test or variance analysis.
Some useful links:
- Example of calculating residuals
- Calculations - basic formulas >>
- Definition of residuals - Agresti (slightly different terms are used)
- Interpretation >>
Related content:
Manuals
Manuals (117)
- ZOOM
- Your first survey
- Voting
- Verification of user’s attention with the use of a “trap” question
- Using the IP address and cookies to control duplicate entries
- Use of editor when editing questions
- Usage of 'location' question type
- Usable respondents (surveys)
- Transfering values from the answer of one question into the text of another question (...
- The use of conditions
- The response rate
- The most common mistakes and recommendations in the creation of online surveys
- The double grid table
- Test entries
- Telephone survey
- Tabs in the questionnaire
- System variables in conditions
- Survey settings
- Survey duration based on date or the number of responses
- Survey data, paradata, identifiers, and system variables
- Survey archive
- Sum
- Structuring questions into blocks
- Step by step mode with table question type
- Status of units, relevance, validity and missing values
- Standard demographics
- Social networks
- Slideshow creation
- Settings for respondent access: cookies and passwords
- Settings for exporting PDF/RTF files with responses
- Setting up a static first page (introduction)
- Setting a custom URL for a survey
- Set up of drag and drop question type
- Sending emails via an arbitrary server (e.g. Gmail)
- Sending email invitations and obtaining authorization
- Residuals in tables
- Registration form
- Referrals
- Recommendations for questionnaire creation
- Recommendations for minimizing non-response
- Recommendation in case of 1KA tool upgrade
- Recoding
- Quiz
- Questionnaire Entry
- Questionnaire archives
- Public link to access data and analysis
- Principles of 1KA public library use
- Preview
- Placing answers on stripe
- Organizing surveys in folders
- Options of editing questions in the toolbar
- Option to hide radio and checkbox buttons next to categories
- Notifications
- Multitables
- Mobile survey adjustments
- Merging data
- Measurement and time limitations for responses
- Means
- Manual coding
- Loop
- Limitations of displaying answers in analyses
- Labelling a question as mandatory
- Key features that an advanced user should know
- Invitation archives
- Interruptions (BETA)
- Insight into the respondents' answers
- Inserting images into your questionnaire
- Insert numerical answers with slider
- Including a video or flash player in your survey
- Image type of question layout
- Image Hotspot question type
- Hiding answers in already active survey
- Granting access to helpdesk
- Glossary
- Frequencies
- fa
- Export to text file
- Export to SPSS
- Export to Excel
- Evaluation of websites
- Embedding the survey on a website
- Editing options in the question taskbar
- Drill-down: sequential filtering of questions
- Display restrictions for responses
- Detailed computations of questionnaire usability
- Design
- Descriptive statistics
- Default answer labels
- Data updates (file vs. database)
- Data archive
- Custom reports
- Crosstabs
- Criteria for usable respondents
- Creating sub-samples: half of the respondents gets one question, while the other half a different question...
- Creating respondent groups
- Computed values
- Computations
- Comments
- Combining lists of email invitations
- Combined table
- Classifying or ranking
- Changing the size of radio and checkbox buttons
- Can I enable respondents to change answers after completion of the survey?
- Break
- Basic data analysis
- Archives - survey changes
- Analysis archives
- Alert list
- Advanced questionnaire editing settings
- Advanced analysis options
- Advanced adding of images as an answer
- Additional settings for the introduction and conclusion
- Adding respondents when sending email invitations
- Adding data
- 1KA settings for email notifications for completed surveys and insight into the respondent's answers...
- 1KA registration and login
- 'Take a picture' question type