A More Powerful Post Hoc Multiple Comparison Procedure in Analysis of Variance

1998 ◽  
Vol 23 (3) ◽  
pp. 279-289 ◽  
Author(s):  
Alan J. Klockars ◽  
Gregory R. Hancock
Keyword(s):  
Analysis Of Variance ◽  
Infinite Number ◽  
Critical Values ◽  
Multiple Comparison ◽  
Treatment Groups ◽  
Small Set ◽  
F Distribution ◽  
Multiple Comparison Procedure ◽  
Post Hoc

Scheffé’s test ( Scheffé, 1953 ), which is commonly used to conduct post hoc contrasts among k group means, is unnecessarily conservative because it guards against an infinite number of potential post hoc contrasts when only a small set would ever be of interest to a researcher. This paper identifies a set of post hoc contrasts based on subsets of the treatment groups and simulates critical values from the appropriate multivariate F-distribution to be used in place of those associated with Scheffé’s test. The proposed method and its critical values provide a uniformly more powerful post hoc procedure.

Scheffé’s More Powerful F-Protected Post Hoc Procedure

2000 ◽  
Vol 25 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Alan J. Klockars ◽  
Gregory R. Hancock
Keyword(s):  
Null Hypothesis ◽  
Degrees Of Freedom ◽  
Critical Value ◽  
Current Paper ◽  
Multiple Comparison ◽  
Simple Modification ◽  
Multiple Comparison Procedure ◽  
Post Hoc ◽  
Original Derivation

<italic>In 1970 Henry Scheffé proposed a more powerful version of his well known post hoc multiple comparison procedure, only to fail to recommend it by the paper's end. The point of the current paper is to bring this simple modification to a wider audience, complete with an original derivation, in hopes that the method will be embraced by researchers despite its creator's hesitations. Specifically, whereas Scheffé's original (1953) procedure advocates testing any exploratory post hoc contrast or comparison using a critical value assuming </italic>k - <italic>1 between-group degrees of freedom, Scheffé's later modification (1970) will be demonstrated here showing that a more liberal critical value assuming </italic>k - <italic>2 between-group degrees of freedom may be used if an omnibus null hypothesis across all means has been rejected. </italic>

scholarly journals The Effects of Mouthwashes on the Color Stability of Resin-Based Restorative Materials

2020 ◽  
pp. 346-357
Author(s):  
Ayşe Tuğba Ertürk-Avunduk ◽  
Seçkin Aksu ◽  
Ebru Delikan
Keyword(s):  
Analysis Of Variance ◽  
Color Change ◽  
Resin Composite ◽  
Color Stability ◽  
Multiple Comparison ◽  
Color Measurement ◽  
Distilled Water ◽  
Significant Difference ◽  
Restorative Materials ◽  
Post Hoc

Objective: This study investigated the effects of three types of mouthwash on the color stability of three resin-based restorative materials (nanohybrid resin composite, sonic-activated bulk-fill material, and compomer). Materials and Methods: To this end, 120 cylindrical disc specimens were prepared and polished, after which they were incubated in distilled water for 24 hours for post-polymerization. The baseline color values of each specimen were measured with a spectrophotometer, then the specimens were randomly divided into four groups. Following immersion in the mouthwashes for 24 hours, the specimens were rinsed with distilled water and dried before the color measurement was repeated. The values of color change (∆E₀₀) were subsequently calculated. A two-way analysis of variance and Duncan’s post hoc multiple comparison tests were conducted to determine statistically significant differences among the restorative materials. Results: All samples showed discoloration after immersion, albeit some instances of discoloration were imperceptible. In this respect, a statistically significant difference was found among the restorative materials and mouthwashes (p<0.05). Imperceptible ∆E₀₀ values were derived on the nanohybrid resin composite and compomer, but perceptible and acceptable ∆E₀₀ values were detected on the sonic-activated bulk-fill materials (p<0.05). The clinically unacceptable discoloration was observed on the sonic-activated bulk-fill composite immersed in Listerine®. Conclusions: Clinicians should make recommendations based on the potential staining capacity of mouthwashes prescribed for daily use in restorative materials. In this way, the need for renewal of restorations due to discoloration could be avoided.

scholarly journals Analysis of Variance: The Fundamental Concepts and Application with R

2021 ◽  
Vol 09 (10) ◽  
Author(s):  
Adeniran, A. T. ◽  
Keyword(s):  
Analysis Of Variance ◽  
Statistical Significance ◽  
Data Entry ◽  
P Value ◽  
Control Groups ◽  
R Software ◽  
Treatment Groups ◽  
Anova Model ◽  
Post Hoc ◽  
Mathematical Foundations

The Analysis of Variance (ANOVA) test has long been an essential tool for researchers conducting studies on multiple experimental groups with or without one or more control groups. This article encapsulates the fundamentals of ANOVA for an intended benefit of the reader of scientific literature who does not possess expertise in statistics. The emphasis is on conceptually-based perspectives regarding the use and interpretation of ANOVA results, with minimal coverage of the mathematical foundations. Data entry, checking basic parametric assumptions of ANOVA, descriptive statistics of the data by treatment groups, fitting ANOVA model, statistical significance of the test based on p-value, and post-hoc analysis are all explored using R-software.

Influence of Light-curing Distances on Microflexural Strength of Two Resin-based Composites

2020 ◽  
Vol 45 (3) ◽  
pp. 297-305 ◽  
Author(s):  
AO Al-Zain ◽  
HY Marghalani
Keyword(s):  
Analysis Of Variance ◽  
Significant Influence ◽  
Testing Machine ◽  
Strength Test ◽  
Multiple Comparison ◽  
Specimen Surface ◽  
Crosshead Speed ◽  
Universal Testing ◽  
Light Curing ◽  
Post Hoc

SUMMARY Objective: Our objective was to investigate the influence of different curing distances on microflexural strength and the microflexural modulus of two resin-based composites. Methods: Two nanohybrid composites were used; Filtek Z250 (Z250) and Tetric EvoCeram (TEC). Rectangular specimens were prepared (2-mm wide × 1-mm deep × 6-mm long) light cured according to the manufacturer's instructions at 0-mm, 2-mm, and 8-mm distances (n=10) and were stored wet at 37°C for 24 hours. A microflexural strength test was performed using a universal testing machine at a crosshead speed of 1 mm/min. The microflexural strength and microflexural modulus data were analyzed using a two-way analysis of variance followed by a Tukey multiple comparison post hoc test (α=0.05). Results: The TEC composite had a significantly higher microflexural strength at an 8-mm distance compared with the 0-mm distance. The Z250 composite expressed significantly higher microflexural strength, at 2-mm and 8-mm compared with the 0-mm distance. TEC showed a significantly higher microflexural modulus at an 8-mm distance compared with the 0-mm and 2-mm distances. Z250 also exhibited a significantly higher microflexural modulus at the 2-mm distance, compared with the 8-mm distance. In total, Z250 presented a significantly higher microflexural strength and modulus compared with TEC. Conclusion: Curing the explored composites at 2-mm or 8-mm distances from the specimen surface did not have a significant influence on microflexural strength but did significantly affect the microflexural modulus.

scholarly journals The application of orthogonal contrasts to determine homogeneous groups

2021 ◽  
Vol 82 ◽  
pp. 31-44
Author(s):  
Zbigniew Laudański ◽  
Dariusz Mańkowski ◽  
Leszek Sieczko ◽  
Monika Janaszek-Mańkowska
Keyword(s):  
Analysis Of Variance ◽  
Multiple Comparison ◽  
Factorial Designs ◽  
Homogeneous Groups ◽  
Orthogonal Contrasts ◽  
Multiple Comparison Procedure ◽  
Effective Use

The paper presents a modified approach to analysis of data obtained from experiments carried out according to classical factorial designs. Four examples were discussed in order to present details of proposed method. Modification of the analysis of variance presented here enables more effective use of information on how studied factors affect the means of dependent variable. The specificity of this approach is based on alternative multiple comparison procedure incorporating orthogonal contrasts to determine homogeneous groups.

Study on the Interlaboratory Comparison Test of the Electronic Test Method for Raw Silk

2012 ◽  
Vol 241-244 ◽  
pp. 317-321
Author(s):  
Jian Mei Xu ◽  
Ying Zhou ◽  
Suo Zhuai Dong ◽  
Francesco Gatti ◽  
Dong Ping Wu ◽  
...  
Keyword(s):  
Analysis Of Variance ◽  
Optical Sensor ◽  
Interlaboratory Comparison ◽  
Test Method ◽  
Multiple Comparison ◽  
International Standard ◽  
Comparison Test ◽  
Testing Method ◽  
Multiple Comparison Procedure ◽  
The Difference

To establish an international standard on the electronic testing method for raw silk, the interlaboratory comparison tests of the electronic testing method for raw silk are done. Five lots of soaked silk are sampled and tested by four machines of the same type in four labs, 13 items including the defects and evenness information of each lot of silk are measured. The analysis of variance and multiple comparison procedure are used to find whether there exist significant differences among the four machines; and the result shows that there are no significant differences among the machines in testing these items except for the item of IPMe by optical sensor. The reason for the difference is analyzed, and the measure for dismissing the difference is proposed.

Psychophysically Based Physical Capability Limits For Right Angle Power Tool Operation

2020 ◽  
Vol 64 (1) ◽  
pp. 910-914
Author(s):  
Jonathan Valencia ◽  
Joel Cort
Keyword(s):  
Analysis Of Variance ◽  
The Other ◽  
Mixed Design ◽  
Joint Orientation ◽  
Physical Capability ◽  
Subject Variables ◽  
Group A ◽  
Repeated Analysis ◽  
Post Hoc

A psychophysical methodology was utilized to examine 40 non-skilled female participants performing right-angle power tool (RAPT) fastening tasks. A combination of two between subject variables were examined for a total of four between-subject groups: joint orientation (horizontal and vertical planes) and joint hardness (hard and soft joints). Participants were evenly distributed into one of four joint orientation- hardness groups. Within each group, a combination of three fastening strategies and three fastening frequencies were performed by each participant. The chosen target torque determined the physical capability limits (PCL). A mixed-design repeated analysis of variance with Tukey’ significance post hoc test were used to determine any significance with the measured variables ( p<0.05). Fastening strategy and frequency influenced the chosen torque magnitude. Participants chose significantly higher target torques with the Turbo Tight strategy in comparison to the other two strategies. Furthermore, participants chose to accept lower target torques and forces as fastening frequency increased.

scholarly journals Characteristics of anteroposterior curvatures of the spine in soccer and futsal players

2017 ◽  
Vol 18 (4) ◽  
Author(s):  
Krystyna Chromik ◽  
Anna Burdukiewicz ◽  
Jadwiga Pietraszewska ◽  
Aleksandra Stachoń ◽  
Paweł Wolański ◽  
...  
Keyword(s):  
College Students ◽  
Statistical Analysis ◽  
Injury Prevention ◽  
Analysis Of Variance ◽  
Statistical Significance ◽  
Body Posture ◽  
Soccer Players ◽  
Prevention Training ◽  
The Difference ◽  
Post Hoc

AbstractPurpose. The aim of the study was to determine differences in anteroposterior spine curvatures between futsal players, soccer players, and non-training students. The results may contribute to the development of present-day knowledge of posturometry, and its implementation in training can help reduce the risk of body posture disorders in athletes. Methods. The examined group consisted of 48 athletes and 38 non-training college students. Body posture parameters were measured with the use of Posturometr-S. The normality of distribution was checked with the Shapiro-Wilk test, and the differences between the groups were measured with ANOVA and the Bonferroni post-hoc test. The level of statistical significance was set at p < 0.05. Results. The analysis of angle values revealed the widest and most similar measurements in the group of futsal players and soccer players. The analysis of variance proved statistically significant differences between the soccer players and futsal players (p = 0.003). The difference between the soccer players and non-training students was statistically significant. The highest γ angular value was measured in non-training students, followed by futsal players and soccer players. The statistical analysis revealed significant differences between the non-training students and futsal players, as well as non-training students and soccer players (p < 0.001). Conclusions. A complex assessment of athletes’ body posture is crucial in injury prevention. Training overloads may often lead to disorders of the organ of locomotion and affect the correct body posture in athletes. This, in turn, may result in pains and injuries.

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