Ordinal Analysis - Concatenated Orderings

Generic Question: Is there a meaningful difference between dependent observations on a set of orderings (variables)?

Data Type: Two or more quantitative orderings (variables) with identical scaling. Repeated measures / within-subjects / dependent observations

Hypotheses: The ordinal pattern in a given set of orderings (e.g., A < B;  A < B < C; [A = B] > C)

Traditional analogs: Dependent samples t-test, repeated measures ANOVA, sign test, and Wilcoxon signed-rank test

Summary: This analysis can be used when you wish to analyze observations made over time on the same persons or entities (e.g., analyze changes in attitude over time), or when you wish to analyze multiple observations made on persons or entities on one occasion (e.g., analyze ordinal patterns of personality traits). The observations for this analysis are assumed to be quantitative in nature. For instance, successive foraging times (measured in minutes) for honeybees over the course of a day might be recorded and analyzed for increasing or decreasing times, or the relative personality trait scores (all assessed with the same possible range of values) of individuals can be examined for ordinal patterns. This analysis can therefore be used instead of a dependent samples t-test or a repeated-measures ANOVA. With regard to classic non-parametric statistical tests, this analysis is most similar to the sign test or to the Wilcoxon signed-rank test for dependent samples.

Software Access: The Ordinal Analysis -- Concatenated Orderings procedure can be found by selecting "Analyses --> Ordinal Analysis --> Concatenated Orderings" from the Main Menu. The procedure window appears as:

Videos and Files: The following videos and files describe the procedure and its various options. Be sure to set the video quality to High Definition (1080p) if the browser does not automatically do so. If you wish to follow along with the analyses on your own computer, download and open the data set(s) linked at the bottom of this page. 

• Definitions (a list of definitions commonly used in the OOM software and in observation oriented modeling):
  • Definitions in a pdf file
• Introduction (a brief introduction to the procedure that describes how the analysis is conducted):
  • Ordinal Analysis -- Concatenated Orderings Introduction (two orderings, like a dependent samples t-test)
  • Ordinal Analysis -- Concatenated Orderings : II   Introduction (three orderings, like a repeated measures ANOVA)
• Specific Options (the Analyze, Missing Values, Randomization Test, etc. options in the analysis and options window above are explained and demonstrated):
  • Classification Imprecision
  • Missing Values: Omit or Include
  • Ordinal Classifications
  • Analyze: Numbers or Deep Structures
  • Randomize (with four sub-options):
    • Randomize: within Cases
    • Randomize: within Orderings / All Observations
    • Randomize: Deep Structures
    • Choosing a randomization procedure (a Powerpoint hand-out explaining what to consider when choosing between the two sub-options)
  • Pairwise Results (see the Concatenated Orderings : II video linked under Introduction above)
  • Individual Results (Append and Save)
  • Save Difference Scores
  • Separate by Ordering feature
• Creating a Profile Plot
  • Creating Profile Plot
  • Editing an OOM graph in Powerpoint (this example shows a multigram, but the steps can be followed for a saved profile plot as well).
• Comparing Two PCCs (a demonstration of how a chance-value can be determined for the difference between two PCCs):
  • Chance-value for difference between two PCCs
• Post Hoc Pattern (shows how to run the analysis in the event a predicted ordinal pattern is not available):
  • Post hoc analysis
• Planning Sample Size (based on the chance-value)
  • Description of steps in the procedure to determine sample size (review the steps on this handout before watching the videos linked below)
  • Creating a Data Set
  • Running the Analysis and Examining Randomization Results Distribution
  • Comparison of planned sample size and actual sample size for the Affective Realism study (handout)

Reporting Results

• Example APA write-ups for the Ordinal Analysis -- Concatenated Orderings procedure.
• See our Persons as Effect Sizes paper. The first study reported in this paper used the Ordinal Analysis - Concatenated Orderings procedure, sans the randomization test. The data were taken from Seigel et al.'s published study.

Data

• Data Sets (used in videos above)
  • Affective Realism Study #1, n = 45