One-Way MANCOVA (Multivariate Analysis of Covariance)

 One-Way MANCOVA (Multivariate Analysis of Covariance)


















Purpose:

To compare the means of multiple dependent variables across multiple independent groups, while controlling for the effect of one or more covariates.


Assumptions:

 Normality of dependent variables

 Homogeneity of variances and covariances

 Linearity of relationships between dependent variables and covariates

 Independence of observations


Procedure:

1. Compute unadjusted group means: Calculate the mean values of the dependent variables for each independent group.

2. Test for homogeneity of variances and covariances: Perform a Box's M test or a Levene's test to check if the variances and covariances are equal across groups.

3. Test for linearity: Plot the residuals against the predicted values to assess whether the relationship between the dependent variables and the covariates is linear.

4. Test for independence: Check that the observations are independent and not clustered within groups.

5. Run the one-way MANCOVA: Use statistical software to perform the analysis, which involves partitioning the total variation in the dependent variables into within-group and between-group components.

6. Assess the group effects: Examine the Pillai's Trace, Wilk's Lambda, Hotelling-Lawley Trace, or Roy's Largest Root tests to determine whether there are significant differences in the multivariate means between groups.

7. Test the covariates: Use the partial eta squared or omega squared effect sizes to assess the proportion of variance in the dependent variables explained by the covariates.

8. Interpret the results: Conclude whether there are significant differences between groups in the multivariate means, taking into account the effects of the covariates.


Advantages:

 Controls for the influence of covariates on the dependent variables.

 Provides a comprehensive analysis of multiple dependent variables.


Disadvantages:

 Requires a large sample size.

 Sensitive to violations of assumptions.

 Interpretation can be complex when multiple dependent variables are involved. 


Example 1: of One-Way MANCOVA in Medicine


Objective: To investigate the effect of different treatment regimens on the cardiovascular health of patients with heart failure.


Variables:

 Independent variable: Treatment regimen (3 levels: Standard, Enhanced, Experimental)

 Dependent variables (multivariate):

     Systolic blood pressure

     Diastolic blood pressure

     Left ventricular ejection fraction

 Covariate: Age at baseline


Procedure:

1. Collect data on the cardiovascular health and age of patients with heart failure.

2. Assign patients to one of the three treatment regimens.

3. Measure the dependent variables (systolic and diastolic blood pressure, left ventricular ejection fraction) at baseline and follow-up.

4. Conduct a one-way MANCOVA with treatment regimen as the independent variable, the dependent variables as the multivariate response, and age as the covariate.


Analysis:

 Test of homogeneity of covariance matrices: Ensures that the covariate affects the dependent variables equally across treatment groups.

 Multivariate test of significance: Tests the overall effect of treatment regimen on the cardiovascular health measures, after adjusting for age.

 Univariate tests of significance: Tests the individual effects of treatment regimen on each of the dependent variables, after adjusting for age.


Interpretation:

 If the multivariate test of significance is significant, it suggests that the treatment regimen has an overall effect on the cardiovascular health measures, after controlling for age.

 The univariate tests of significance provide more specific information about which specific cardiovascular health measures are affected by treatment regimen.


Example Interpretation:

The multivariate test of significance yielded a p-value of 0.02, indicating that the treatment regimen had a significant overall effect on the cardiovascular health measures, after adjusting for age.


The univariate tests of significance showed that:

 Systolic blood pressure was significantly lower in the Enhanced and Experimental groups compared to the Standard group (p < 0.05).

 Diastolic blood pressure was not significantly different between the three treatment groups (p > 0.05).

 Left ventricular ejection fraction was significantly higher in the Experimental group compared to the Standard group (p < 0.05).


Conclusion:

The results of the one-way MANCOVA suggest that the Enhanced and Experimental treatment regimens improve cardiovascular health measures in patients with heart failure, compared to the Standard regimen. This may be due to the beneficial effects of the Enhanced and Experimental regimens on factors such as blood pressure and heart function. 


Example 2:

Objective: To investigate the effect of a new diabetes medication on glycated hemoglobin (HbA1c) levels, while controlling for the potential confounding effect of baseline HbA1c levels.


Methods:

 A randomized controlled trial is conducted with participants with type 2 diabetes.

 Participants are randomly assigned to receive either the new medication or a placebo for 12 weeks.

 HbA1c levels are measured at baseline and at the end of the study period.


Statistical Analysis:

A one-way multivariate analysis of covariance (MANCOVA) is performed with the following variables:

 Dependent variable: HbA1c level at the end of the study period

 Independent variable: Treatment group (new medication vs. placebo)

 Covariate: HbA1c level at baseline


Results:

 The MANCOVA results indicate a significant effect of treatment group on HbA1c levels at the end of the study period, even after controlling for baseline HbA1c levels.

 The new medication group has significantly lower HbA1c levels compared to the placebo group.


Conclusion:

The results of the one-way MANCOVA suggest that the new diabetes medication is effective in reducing HbA1c levels, even in individuals with high baseline HbA1c levels. 


......................................................................................................


πŸ‘‰ For the data analysis, please go to my Youtube(Ads) channel to Watch Video (Video Link) in  

      Youtube Channel (Channel Link) and Download(Ads) video.


      πŸ’— Thanks to Subscribe(channel) and Click(channel) on bell πŸ”” to get more videos!πŸ’—!!



πŸ‘‰ For Powerpoint presentation slide(Ads), please help to fill a short information, Please click here
      (Survey Link) and Download(Ads) the presentation slides from Google Drive(G_drive link)

                                 πŸ’“ Thanks for your completing the Survey πŸ’—

                                πŸ’“ Thanks for visiting and sharing my Facebook Page πŸ’—

..............................................................................................................






  1. STATA for dataset restructuring, descriptive and analytical data analysis
  2. SPSS for dataset restructuring, data entry, data check, descriptive, and analytical data analysis
  3. Epi-Info for building questionnaires, data check, data entry, descriptive, and analytical data analysis
  4. Epidata-Analysis for dataset restructuring, descriptive and analytical data analysis
  5. Epi-Collect for building questionnaires, remote data entry, mapping, and data visualization
  6. Epidata-Entry for building questionnaires, data check, data entry, and data validation

πŸ‘‰ αž…ុះឈ្មោះαž₯αž›ូαžœαž“េះαž“ឹαž„αž‘αž‘ួαž›αž”ាαž“αžαž˜្αž›ៃαž–ិសេស!🀩‼️

................................................................................................


☎️ Mobile Phone: (+855) - 96 810 0024
πŸ“³ Telegram: https://t.me/sokchea_yann
🚩 Facebook Page: Page
πŸ“Ž Please join us: Telegram Channel
🌎 Please visit the website Thesis Writing Skill: Website
πŸ‘¬ Please follow us: https://www.tiktok.com/@sokcheayann999
πŸ“© Please send an email to us: Email
🏑 Address៖ #27B, Street-271, Street-33BT, Phsar Boeng Tumpon, Sangkat Boeng Tumpon, Khan  
                      Meanchey,  Phnom Penh, Cambodia.


                                                   πŸ’– Thanks for your contribution!!! πŸ’•

ABA Account-holder name: Sokchea YAN

ABA Account number: 002 996 999

ABA QR Code:


 





or tap on link below to send payment:

https://pay.ababank.com/iT3dMbNKCJhp7Hgz6


✌ Have a nice day!!! πŸ’ž


Comments

Post a Comment

Popular posts from this blog

What is Kruskal-Wallis Test?

Image
What is Kruskal-Wallis Test? I.  Kruskal-Wallis Test The Kruskal-Wallis test is a non-parametric test used to compare the medians of two or more independent groups. It is similar to the one-way analysis of variance (ANOVA), but it does not require the assumption of normality in the data. II. Hypothesis:  Null hypothesis (H0): The medians of the samples are equal.  Alternative hypothesis (Ha): At least one median differs from the others. III. Assumptions:  The samples are independent.  The distributions of the samples are not necessarily normal.  The data must be ordinal or continuous   No outliers that could significantly affect the results IV. Procedure: 1. Calculate the ranks of all observations: Assign each observation a rank from 1 to N, where N is the total number of observations. Ties are assigned the average of the ranks they would have received if they were not tied. 2. Calculate the test statistic: The Kruskal-Wallis test statistic (H) is calc...
Read more

Kendall's Coefficient of Concordance (W)

Image
 Kendall's Coefficient of Concordance (W) is a statistical measure that assesses the level of agreement among multiple raters or judges when ranking a set of items. It's a valuable tool for understanding the consistency of opinions or evaluations across different sources. Here's a breakdown of the key aspects: 1. Purpose: • To determine the overall agreement among multiple raters when ranking items. • To measure the consistency of opinions or evaluations. • To identify if raters are generally in agreement or if there's significant disagreement. 2. Application: • Market Research: Assessing the consensus among consumers on product preferences. • Performance Evaluation: Evaluating the consistency of performance ratings by different supervisors. • Medical Diagnosis: Analyzing the agreement among doctors on patient diagnoses. • Quality Control: Evaluating the consistency of product quality assessments by different inspectors. 3. Calculation: The formula for calculating Kenda...
Read more
  For bacteriology testing aimed at identifying and conducting Antimicrobial Susceptibility Testing (AST) for GLASS (Global Antimicrobial Resistance Surveillance System) priority pathogens , various reagents and supplies are typically required. Here's a list of essential reagents for such testing: 1. Culture Media: Nutrient Agar : For general cultivation of bacteria. Blood Agar : For growing fastidious organisms and detecting hemolytic activity. MacConkey Agar : For selective isolation of Gram-negative bacteria, particularly Enterobacteriaceae. Mannitol Salt Agar : For the selective isolation of Staphylococcus aureus . Chocolate Agar : Enriched medium for fastidious organisms like Haemophilus and Neisseria species. Cetrimide Agar : For selective isolation of Pseudomonas aeruginosa . XLD Agar (Xylose Lysine Deoxycholate) : For selective isolation of Salmonella and Shigella . 2. Gram Staining Reagents: ...
Read more