One-way Repeated Measures MANOVA with SPSS
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This presentation discusses the procedure involved in one-way repeated measures MANOVA. The procedure has been discussed by using the SPSS software.
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One-way Repeated Measures MANOVA with SPSS
- 1. Presented by Dr.J.P.Verma MSc (Statistics), PhD, MA(Psychology), Masters(Computer Application) Professor(Statistics) Lakshmibai National Institute of Physical Education, Gwalior, India (Deemed University) Email: vermajprakash@gmail.com
- 2. Also known as repeated MANOVA or rMANOVA Also known as To investigate the effect of an independent factor (having different levels) on a group of dependent variables Why to Use
- 3. Same subjects are tested under each level of the independent variable. Independent variable can either be different treatment conditions or different time points. Features DVs : Number of correct recalling of name, colour and shape of objects IV : Four and Six seconds visual time Example Which visual time is more effective for memory retention of the object’s characteristics?
- 4. When individuals vary widely on the experimental variable. When several dependent variables (DVs) measure different aspects of some cohesive theme. Where improvement trend needs to be investigated. Example of DVs personality (Extraversion, Psychoticism, Neuroticism) health(blood pressure, heart rate, vital capacity) product features(economy, comfort, attractiveness) fitness(cardio respiratory endurance, flexibility, strength) nature(extrovert, optimism, creativity) academic achievement(English, Maths, Commerce) Example: To study the change in physiological status((heart rate, blood pressure and vital capacity) of subjects while undergoing an exercise programme over a period of time.
- 5. 5 This Presentation is based on Chapter 7 of the book Repeated Measures Design for Empirical Researchers Published by Wiley, USA Complete Presentation can be accessed on Companion Website of the Book
- 6. Choose DVs carefully in the study DVs should be moderately correlation (.3 to .7)among themselves Highly correlated DVs Weaken the power of the analysis Uncorrelated DVs MANOVA has nothing to offer Word of Caution Thumb Rule Even if dependent variables are moderately Don’t be tempted to use RM MANOVA If combining DVs can not be justified Consider using series of univariate ANOVAs
- 7. 1. Due to demand of research question being investigated. 2. Variables explaining latent variable are often correlated hence separate rANOVA's will be redundant and difficult to integrate. 3. None of the individual ANOVAs may produce a significant effect on the DV, but if combined they might. 4. By using MANOVA, family wise error rate(α) can be controlled. 5. The sphericity assumption in rANOVA is often violated whereas RM MANOVA does not require this assumption.
- 8. To investigate as to how the personality(Extraversion, Psychoticism and Neuroticism) transformation takes place during one year of training in communication skill. To investigate as to which naturopathy intervention (pranayama, meditation and relaxation exercise) is more effective in improving mood state(confusion, depression and fatigue) An educational consultant may wish to investigate performance(numerical aptitude, reasoning and English comprehension) trend of subjects during a training programme for a competitive examination.
- 9. Data type : There should be two or more continuous DVs and one categorical IV. Sample Size Number of observations must be higher than the number of DVs. Recommended sample size of at least 20. Independence of Measurement Missing Data This design requires complete data for all the subjects. Outliers No outlier should exist in any group Linearity All DVs are linearly related among themselves in each group of the independent variable. Normality There should be multivariate normality. Multicollinearity There should be no multicollinearity among the DVs. SphericityThere should be no sphericity in data.
- 10. Case I: Levels of the within-subjects variable are different treatment conditions Example: To investigate the effect of naturopathy intervention in improving mood state of six subjects When to use One-way rMANOVA Each subject is tested on multiple dependent variables in each treatment condition Issues in the Design Carryover effect – Controlled by having sufficient gap between any two treatments Order effect – Controlled by counterbalancing IV : Naturopathy intervention (pranayama, meditation and relaxation exercise) DVs : Mood state parameters(confusion, depression and fatigue)
- 11. S2 S5 S1 S6 S3 S4 Relaxation Exercise First phase testing S2 S5 S1 S6 S3 S4 S2 S5 S1 S6 S3 S4 Second phase testing Third phase testing Testing protocol Treatment: Naturopathy intervention Confusion Depression Fatigue S1 S6 S3 S4 S2 S5 S1 S6 S3 S4 S2 S5 S1 S6 S3 S4 S2 S5 Confusion Depression Fatigue S3 S4 S2 S5 S1 S6 S3 S4 S2 S5 S1 S6 S3 S4 S2 S5 S1 S6 Confusion Depression Fatigue MeditationPranayama Figure 7.1 Layout design 1. Divide sample into groups 2. Randomized treatments on these groups and take measurements on all dependent variables Designing procedure
- 12. S1 S2 S3 S4 S5 S6 4 week Testing protocol Treatment: Time Numerical Reasoning English Aptitude Compre 2 weekZero week Numerical Reasoning English Aptitude Compre Numerical Reasoning English Aptitude Compre S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 S1 S2 S3 S4 S5 S6 Case II: levels of the within-subjects variable are different time periods When to use One-way rMANOVA Example: To investigate the performance trend of subjects during a training programme for a competitive examination. DVs : Performance parameters (numerical aptitude, reasoning and English comprehension) IV : Time(zero week, 2 week, 4 week) Figure 7.2 Layout design
- 13. Steps in One-way rMANOVA Test assumptions of design Describe layout design Write research questions to be investigated Write hypotheses to be tested Specify familywise error rates (α) Use SPSS to generate outputs Descriptive statistics MANOVA table containing Wilk’s Lambda Continue …
- 14. IsWilk’s Lambda Significant Terminate further analysis N Y Apply rANOVA for each dependent variable Use SPSS to generate following outputs Mauchly's test of sphericity F table in rANOVA for each dependent variable Pair-wise comparisons of means for each dependent variable. Means plot for each dependent variable Steps in One-way rMANOVA
- 15. Test Sphericity assumption in each rANOVA Is p<α/k Test F ratio by assuming sphericity N Y Check <.75 Test F by using Huynh-Feldt correction NTest F by using Greenhouse- Geisser correction Y If F is significant use Bonferroni correction for comparison of means Report findings k: number of DVs
- 16. Table 7.1 Marks obtained by the students in different subjects tested at different times of the day _____________________________________________________________________________________ Time of the day Morning(7 AM) Afternoon(1 PM) Evening(7 PM) _____________________________________________________________________________________ Maths English Reasoning Maths English Reasoning Maths English Reasoning 12 12 15 15 15 11 17 14 12 13 14 16 17 13 12 16 12 10 14 10 17 18 14 14 15 15 15 13 9 15 15 14 13 16 16 12 14 8 17 14 13 11 14 13 14 15 11 15 18 12 10 16 15 15 13 10 14 17 15 9 15 13 10 12 13 15 15 12 8 13 12 13 13 12 13 16 15 11 15 16 12 15 11 14 18 16 12 16 15 13 _____________________________________________________________________________________ Objective : To see the effect of time of the day on the student’s performance in different subjects. - An Illustration with SPSS
- 17. S1 S3 S2 S4 S5 S6 Evening First phase testing S1 S3 S2 S4 S5 S6 S1 S3 S2 S4 S5 S6 Second phase testing Third phase testing Testing protocol Treatment: Time of the day Maths English Reasoning S2 S4 S5 S6 S1 S3 S2 S4 S5 S6 S1 S3 S2 S4 S5 S6 S1 S3 S5 S6 S1 S3 S2 S4 S5 S6 S1 S3 S2 S4 S5 S6 S1 S3 S2 S4 AfternoonMorning Maths English Reasoning Maths English Reasoning All subjects are tested on all the three DVs but not in a particular sequence. S1 and S3 are tested on all DVs in the morning, S2 and S4 in the afternoon and S5 and S6 in the evening. Similarly treatments(time) are randomized in other phases. Procedure Figure 7.3 Layout of the one-way rMANOVA design in the illustration
- 18. Whether time of testing affects student’s academic performance together in all the three subjects?” Whether time of testing affects student’s performance in each of the subject; Maths, English and Reasoning? Which time of the day improves performance of the students in each subject?
- 19. 19 To buy the book Repeated Measures Design for Empirical Researchers and all associated presentations Click Here Complete presentation is available on companion website of the book