Multiple Comparison Procedures Research Articles

U.S. Regional Scorecard: Comparing U.S. Regions for Selected Economic Variables

In this paper, the patterns of differences of some key economic variables among the four major U.S. regions are investigated. These four regions include: Northeast, Midwest, South and West. The grouping of individual U.S. states into these four regions is in accordance with the U.S. Census Bureau and the U.S. Department of Commerce classification. Two main points are explored in this study. The first one examined and summarized the descriptive statistics of the variables for states in these four regions. These variables and data were culled from the databases of U.S. Census Bureau, the Bureau of Economic Analysis (BEA), the U.S. Department of Commerce, the Bureau of Labor Statistics, World Population Review and the U.S Department of Agriculture. The second one covered the identification of the four regions’ similarities and dissimilarities for the identified variables. One-way analysis of variance (ANOVA) is the statistical tool for the testing hypothesis of four regions’ means equality. To ascertain whether the regions that ranked the highest actually differ from another and from the remaining regions, the researcher made use of multiple comparison procedures, specifically the Scheffe test.

Multiple Comparisons for Exponential Median Lifetimes with the Control Based on Doubly Censored Samples

Under doubly censoring, the one-stage multiple comparison procedures with the control in terms of exponential median lifetimes are presented. The uniformly minimum variance unbiased estimator for median lifetime is found. The upper bounds, lower bounds and two-sided confidence intervals for the difference between each median lifetimes and the median lifetime of the control population are developed. Statistical tables of critical values are constructed for the practical use of our proposed procedures. Users can use these simultaneous confidence intervals to determine whether the performance of treatment populations is better than or worse than the control population in agriculture and pharmaceutical industries. At last, one practical example is provided to illustrate the proposed procedures.

Multiple positron emission tomography tracers for use in the classification of gliomas according to the 2016 World Health Organization criteria.

BackgroundThe molecular diagnosis of gliomas such as isocitrate dehydrogenase (IDH) status (wild-type [wt] or mutation [mut]) is especially important in the 2016 World Health Organization (WHO) classification. Positron emission tomography (PET) has afforded molecular and metabolic diagnostic imaging. The present study aimed to define the interrelationship between the 2016 WHO classification of gliomas and the integrated data from PET images using multiple tracers, including 18F-fluorodeoxyglucose (18F-FDG), 11C-methionine (11C-MET), 18F-fluorothymidine (18F-FLT), and 18F-fluoromisonidazole (18F-FMISO).MethodsThis retrospective, single-center study comprised 113 patients with newly diagnosed glioma based on the 2016 WHO criteria. Patients were divided into 4 glioma subtypes (Mut, Codel, Wt, and glioblastoma multiforme [GBM]). Tumor standardized uptake value (SUV) divided by mean normal cortical SUV (tumor–normal tissue ratio [TNR]) was calculated for 18F-FDG, 11C-MET, and 18F-FLT. Tumor–blood SUV ratio (TBR) was calculated for 18F-FMISO. To assess the diagnostic accuracy of PET tracers in distinguishing glioma subtypes, a comparative analysis of TNRs and TBR as well as the metabolic tumor volume (MTV) were calculated by Scheffe's multiple comparison procedure for each PET tracer following the Kruskal–Wallis test.ResultsThe differences in mean 18F-FLT TNR and 18F-FMISO TBR were significant between GBM and other glioma subtypes (P < .001). Regarding the comparison between Gd-T1WI volumes and 18F-FLT MTVs or 18F-FMISO MTVs, we identified significant differences between Wt and Mut or Codel (P < .01).ConclusionCombined administration of 4 PET tracers might aid in the preoperative differential diagnosis of gliomas according to the 2016 WHO criteria.

Analysis goals, error-cost sensitivity, and analysis hacking: Essential considerations in hypothesis testing and multiple comparisons.

The "replication crisis" has been attributed to perverse incentives that lead to selective reporting and misinterpretations of P-values and confidence intervals. A crude fix offered for this problem is to lower testing cut-offs (α levels), either directly or in the form of null-biased multiple comparisons procedures such as naïve Bonferroni adjustments. Methodologists and statisticians have expressed positions that range from condemning all such procedures to demanding their application in almost all analyses. Navigating between these unjustifiable extremes requires defining analysis goals precisely enough to separate inappropriate from appropriate adjustments. To meet this need, I here review issues arising in single-parameter inference (such as error costs and loss functions) that are often skipped in basic statistics, yet are crucial to understanding controversies in testing and multiple comparisons. I also review considerations that should be made when examining arguments for and against modifications of decision cut-offs and adjustments for multiple comparisons. The goal is to provide researchers a better understanding of what is assumed by each side and to enable recognition of hidden assumptions. Basic issues of goal specification and error costs are illustrated with simple fixed cut-off hypothesis testing scenarios. These illustrations show how adjustment choices are extremely sensitive to implicit decision costs, making it inevitable that different stakeholders will vehemently disagree about what is necessary or appropriate. Because decisions cannot be justified without explicit costs, resolution of inference controversies is impossible without recognising this sensitivity. Pre-analysis statements of funding, scientific goals, and analysis plans can help counter demands for inappropriate adjustments, and can provide guidance as to what adjustments are advisable. Hierarchical (multilevel) regression methods (including Bayesian, semi-Bayes, and empirical-Bayes methods) provide preferable alternatives to conventional adjustments, insofar as they facilitate use of background information in the analysis model, and thus can provide better-informed estimates on which to base inferences and decisions.

Electrical characteristics of deep septal vs. left bundle branch (area) pacing

Abstract Background/Introduction Recent studies have described transvenous left bundle branch (LBB) pacing as a new conduction system pacing strategy. However, information on effect of pacing depth within the septum and the additional effect of LBB capture is unknown. Purpose To investigate the relation of electrocardographic characteristics with transseptal LV lead implantation depth and LBB capture. Methods 20 consecutive patients referred for pacemaker implantation were enrolled. The right atrial (RA) lead was positioned according to routine practice. The LV septal pacing lead (Medtronic 3830) was transvenously positioned against the right side of the interventricular septum and advanced in small steps of 1–2mm towards the left side of the septum. At each depth in the septum 12-lead ECG's were recorded during pacing, from which vectorcardiograms (VCG) were calculated. QRS duration and QRS area were measured, the latter being the integral of the QRSarea in X, Y and Z directions. Successful LBB capture was defined as paced right bundle branch block (RBBB) morphology, stable and short stimulus to LV activation time (LVAT; R in V5) and recorded LBB potential. Differences were compared among pacing conditions using repeated measures ANOVA with Bonferroni multiple comparisons procedure applied to pairwise comparisons. Statistical significance was assumed at p&amp;lt;0.05. Results LV septal lead implantation was successful in all patients. Left bundle branch capture was achieved in 10/20 patients (50%). Post-procedural LV pacing threshold, impedance and sensing was 0.7±0.1 V at 0.5 ms pulse width, 658±5 Ω and 13±10 mV, respectively. Compared to intrinsic rhythm, QRS duration was significantly increased by both RV septum (RVS; 124±5 vs. 161±3 ms) and LV septum pacing (LVS; 142±3 ms). QRS area increased significantly during RVS pacing as compared to intrinsic rhythm but decreased when moving from RVS to LVS to values close to intrinsic rhythm (panel A &amp; B). LVS-pacing derived QRS area was significantly lower in patients with LBB capture (36±6 mV*ms) compared to patients without LBB capture (deep septal pacing; 46±12 mV*ms). The reduction in QRS area between RVS and LVS pacing coincided with normalization of the QRS vector in the transverse plane (panel C), which is characterized electrocardiographically by predominantly negative-to-positive inversion of the QRS complex in the precordial leads (V1-V3). Conclusions Compared to RV septal pacing, LV septal pacing restores ventricular electrical synchrony, as determined by QRS area, and normalizes the activation vector in the transverse plane to a level comparable to intrinsic rhythm. Differences in resynchronization between left bundle branch pacing and deep septal pacing are small. LBBAP restores ventricular synchrony Funding Acknowledgement Type of funding source: None

Influence of clinical and therapeutic indicators on the severity of neurocognitive deficits in patients with schizophrenia

Aim. To assess the association of clinical and therapeutic parameters with the severity of the neurocognitive deficits in patients with schizophrenia. Materials and methods. We examined 118 patients with schizophrenia, aged 34 [29; 41] years, and with a disease duration of 10 [4; 16] years. 33 patients (28%) received conventional antipsychotic drugs (CAD), and 85 (72%) patients received atypical antipsychotic drugs (AAD). As concomitant therapy, 58 people (49.1%) took trihexyphenidyl, 60 people did not take it (50.9%). Assessment of cognitive functions was carried out for all patients using the Brief Assessment of Cognition in Schizophrenia (BACS), and clinical psychopathological symptomatology was evaluated using the Positive and Negative Syndrome Scale (PANSS). Statistical analysis of the data was performed using the Kruskal-Wallis test ANOVA with the multiple comparison procedure, the Pearson’s chi-squared test, and K-means cluster analysis. Results. Neurocognitive deficits formed three clusters of disturbances that differ in clinical severity: 1) mild, 2) moderate, 3) severe. According to the subscale of positive PANSS symptoms, patients with mild neurocognitive deficits had a lower average total score compared to patients with severe neurocognitive deficits ( p = 0.011), who, in turn, received significantly longer antipsychotic therapy compared with patients with moderate ( p = 0.014) and mild ( p = 0.01) neurocognitive deficits. Herewith, the duration of CAD treatment did not differ between clusters; consequently, the obtained results on antipsychotics as a whole were obtained due to AAD ( p = 0.005 and p = 0.001, respectively). Trihexyphenidyl did not affect the severity of neurocognitive deficits. Conclusion. The severity of positive symptoms of schizophrenia was lower in patients with mild neurocognitive deficits. The most pronounced neurocognitive deficits are observed in patients receiving AAD.

Statistical considerations on implementing the MCP-Mod method for binary endpoints in clinical trials

The Multiple Comparison Procedure – Modelling (MCP-Mod) method was qaulified by regulatory agencies (e.g., EMA in 2014 and FDA in 2016) as an efficient statistical method for Phase 2 dose-finding studies when there is uncertainty about dose-response relationship. As this is a relatively new approach, there is limited literature providing practical guidance on its application. In this paper, we evaluated the performance of the MCP-Mod method for clinical trials with a binary primary endpoint, focusing on (1) the impact of sample size, data variability and treatment effect size on the performance of the MCP-Mod, (2) the impact of candidate model mis-specification, and (3) optimal sample allocation under a fixed sample size. The evaluation was performed via simulations under different scenarios.

Regression: Determining Which of p Independent Variables Has the Largest or Smallest Correlation with the Dependent Variable, Plus Results on Ordering the Correlations Winsorized

In a regression context, consider p independent variables and a single dependent variable. The paper addresses two goals. The first is to determine the extent it is reasonable to make a decision about whether the largest estimate of the Winsorized correlations corresponds to the independent variable that has the largest population Winsorized correlation. The second is to determine the extent it is reasonable to decide that the order of the estimates of the Winsorized correlations correctly reflects the true ordering. Both goals are addressed by testing relevant hypotheses. Results in Wilcox (in press) suggest using a multiple comparisons procedure designed specifically for the situations just described, but execution time can be quite high. A modified method for dealing with this issue is proposed.

In vivo and in vitro radiotherapy increased dentin enzymatic activity

ObjectivesThe present study investigated the effects of in vitro and in-vivo radiotherapy on endogenous enzymatic activity in dentin using gelatin zymography and in-situ zymography. MethodsGelatin zymographic assays were performed on protein extracts obtained from dentin powder of sound non-irradiated (NRT), in vitro irradiated (VTRT) and in vivo irradiated (VIRT) human teeth. Their proteolytic activities were quantified using band densitometric evaluation. For in-situ zymography, dentin specimens from NRT, VIRT and VTRT were covered with fluorescein-conjugated gelatin and examined with confocal laser-scanning microscopy. Fluorescence intensity emitted by the hydrolyzed fluorescein-conjugated gelatin was quantified and statistically analyzed. In-situ zymography data were statistically analyzed using Kruskal-Wallis ANOVA and Dunn’s multiple comparison procedures (α = 0.05). ResultsNo difference between in vitro and in vivo radiotherapy treatment was found. Both VTRT and VIRT groups showed increase in MMP-9 expression when compared to NRT group. Significant increases (p < 0.05) in gelatinolytic activity (26 % for VTRT; 55 % for VIRT) were observed when compared to the NRT group. ConclusionRadiotherapy increase endogenous enzymatic activity in non-restored dentin.

Comparing adaptive interventions under a general sequential multiple assignment randomized trial design via multiple comparisons with the best

This paper considers screening of adaptive interventions or adaptive treatment strategies embedded in a sequential multiple assignment randomized trial (SMART). As a SMART typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in efficiency after accounting for multiplicity. We propose simultaneous confidence intervals that compare the values of interventions of interest to that of the unknown best intervention by generalizing the method in Edwards and Hsu (1983). The multiple comparison with the best (MCB) intervals are applied as screening tool: an intervention with MCB interval excluding zero will be declared as inferior to the true best at a pre-specified confidence level, and hence excluded from further exploration. Simulation studies show that the proposed method outperforms the multiple comparison procedures based on Bonferroni’s correction in terms of width of confidence intervals for estimation. The method is applied to analyze data from the CODIACS trial in patients with depression.

The effect of two composite placement techniques on fracture resistance of MOD restorations with various resin composites

ObjectiveThe aim of this in vitro study was to compare the effect of two restorative placement techniques, centripetal incremental technique (CIT) and bulk-fill technique (BT) on the fracture resistance of Class II MOD restorations with various resin composites in molar teeth. Materials and methodsFifty-six extracted, caries free third molars were prepared with MOD preparations and restored with resin composites. The specimens were divided into two groups by placement technique, centripetal incremental technique (CIT) and bulk-fill technique (BT). Each group was subdivided into four groups according to resin composite: hybrid (Aelite LS), nano-hybrid (Virtuoso Universal), bulk fill (Filtek One Bulk Fill) and the micro-hybrid (Herculite XRV) as the control. ResultsTwo-way analysis of variance test (ANOVA) followed by the multiple comparison procedure, Student-Newman-Keuls Method showed no a statistically significant difference between placement techniques and fracture resistance of Class II resin composite restorations (P > 0.05). Herculite XRV resisted a significantly higher load before fracture than the other three materials at a 0.05 level of significance, while Virtuoso Universal scored the lowest load. ConclusionsThere was no significant effect of the two placement techniques on the fracture resistance of Class II resin composite restorations Clinical significanceResin composite restorations in Class II MODs using a simplified bulk fill placement technique showed no significant difference in fracture resistance with the centripetal technique in molar teeth.

Inferences about which of J dependent groups has the largest robust measure of location.

Recently, a multiple comparisons procedure was derived with the goal of determining whether it is reasonable to make a decision about which of J independent groups has the largest robust measure of location. This was done by testing hypotheses aimed at comparing the group with the largest estimate to the remaining J-1 groups. It was demonstrated that for the goal of controlling the familywise error rate, meaning the probability of one or more Type I errors, well-known improvements on the Bonferroni method can perform poorly. A technique for dealing with this issue was suggested and found to perform well in simulations. However, when dealing with dependent groups, the method is unsatisfactory. This note suggests an alternative method that is designed for dependent groups.

Daridorexant, a new dual orexin receptor antagonist, in elderly subjects with insomnia disorder.

To assess the dose-response of daridorexant, a new dual orexin receptor antagonist, on wake after sleep onset (WASO). Elderly (≥65 years) participants (n = 58) with insomnia were randomly allocated (Latin square design) to receive 5 treatments (5, 10, 25, and 50 mg daridorexant and placebo) during 5 treatment periods, each consisting of 2 treatment nights followed by a 5- to 12-day washout period. Main efficacy endpoints were the absolute change from baseline in WASO (primary) and latency to persistent sleep (LPS; secondary) to days 1 and 2 (mean of 2 treatment nights assessed by polysomnography) in each period. Safety and tolerability were also assessed. Of 58 participants included, 67% were female, and the median age was 69 years (range 65-85 years). WASO and LPS were dose-dependently reduced from baseline to days 1 and 2 after daridorexant administration (multiple comparison procedure modeling, p < 0.0001 and p = 0.004, respectively); reductions were statistically significant for doses ≥10 mg compared with placebo (WASO: -32.0, -45.1, -61.4 minutes; LPS: -44.9, -43.8, -45.4 minutes for 10, 25, and 50 mg, respectively, p ≤ 0.025). Treatment-emergent adverse events were similar for daridorexant and placebo; the most frequent were fatigue, nasopharyngitis, gait disturbance, and headache (≤7% in any group). Daridorexant was well tolerated. Dose-dependent improvements in WASO and LPS were statistically significant (dose range 10-50 mg) in elderly people with insomnia disorder. NCT02841709. This study provides Class I evidence that, for elderly people with insomnia, daridorexant reduced WASO.

Testing for independence of high-dimensional variables: [formula omitted]-coefficient based approach

We treat the problem of testing mutual independence of k high-dimensional random vectors when the data are multivariate normal and k≥2 is a fixed integer. For this purpose, we focus on the vector correlation coefficient, ρV and propose an extension of its classical estimator which is constructed to correct potential sources of inconsistency related to the high dimensionality. Building on the proposed estimator of ρV, we derive the new test statistic and study its limiting behavior in a general high-dimensional asymptotic framework which allows the vector’s dimensionality arbitrarily exceed the sample size. Specifically, we show that the asymptotic distribution of the test statistic under the main hypothesis of independence is standard normal and that the proposed test is size and power consistent. Using our statistics, we further construct the step-down multiple comparison procedure based on the closed testing strategy for the simultaneous test for independence. Accuracy of the proposed tests in finite samples is shown through simulations for a variety of high-dimensional scenarios in combination with a number of alternative dependence structures. Real data analysis is performed to illustrate the utility of the test procedures.

Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data

In sequential tests, typically a (pairwise) multiple comparison procedure (MCP) is performed after an omnibus test (an overall equality test). In general, when an omnibus test (e.g., overall equality of multiple proportions test) is rejected, then we further conduct a (pairwise) multiple comparisons or MCPs to determine which (e.g., proportions) pairs the significant differences came from. In this article, via likelihood-based approaches, we acquire three confidence intervals (CIs) for comparing each pairwise proportion difference in the presence of over-reported binomial data. Our closed-form algorithm is easy to implement. As a result, for multiple-sample proportions differences, we can easily apply MCP adjustment methods (e.g., Bonferroni, Šidák, and Dunn) to address the multiplicity issue, unlike previous literatures. We illustrate our procedures to a real data example.

Serological evidence of enzootic bovine leukosis in the periurban dairy cattle production system of Al Ain, United Arab Emirates.

The serostatus of enzootic bovine leukosis (EBL) was determined at three dairy farms and the Al Ain Livestock Market (AALM), within the Al Ain region of Abu Dhabi, UAE. Of the 957 bovine sera tested by ELISA, 657 were from Holstein-Friesians from three dairy farms, and 300 from Bos indicus cattle at AALM. The chi-square homogeneity test (CSHT) and the Marascuilo multiple comparison procedure (MMCP) assessed the level of significance between the proportions of EBL-seropositive cattle (ESPC) across the study farms and AALM, and between the age groups at farms 1 and 3. Overall, the proportion of ESPC was 25.7% at dairy farms and AALM, 37.0% for farms and 1.0% for AALM. Furthermore, the proportions of ESPC at farms 1, 2 and 3 were 54.7%, 0.0% and 26.3% respectively, and statistically significant differences were seen across the farm/farm and farm/AALM comparisons, and between two age groups at farms 1 and 3. The 37-72-month-old age group showed the highest proportion of ESPC. This is the first serological evidence of EBL in the UAE. As previously reported, the ESPC are comparatively higher in dairy than Bos indicus cattle. Molecular and more extensive serological studies are needed to further corroborate the present data. Meanwhile, the UAE veterinary authorities will need to formulate national EBL control policies.

Efficacy and Safety of Upadacitinib in a Randomized Trial of Patients With Crohn’s Disease

We evaluated the efficacy and safety of upadacitinib, an oral selective Janus kinase 1 inhibitor, in a randomized trial of patients with Crohn's disease (CD). We performed a double-blind, phase 2 trial in adults with moderate to severe CD and inadequate response or intolerance to immunosuppressants or tumor necrosis factor antagonists. Patients were randomly assigned (1:1:1:1:1:1) to groups given placebo; or 3 mg, 6 mg, 12 mg, or 24 mg upadacitinib twice daily; or 24 mg upadacitinib once daily and were evaluated by ileocolonoscopy at weeks 12 or 16 of the induction period. Patients who completed week 16 were re-randomized to a 36-week period of maintenance therapy with upadacitinib. The primary endpoints were clinical remission at week 16 and endoscopic remission at week 12 or 16 using the multiple comparison procedure and modeling and the Cochran-Mantel-Haenszel test, with a 2-sided level of 10%. Among the 220 patients in the study, clinical remission was achieved by 13% of patients receiving 3 mg upadacitinib, 27% of patients receiving 6 mg upadacitinib (P < .1 vs placebo), 11% of patients receiving 12 mg upadacitinib, and 22% of patients receiving 24 mg upadacitinib twice daily, and by 14% of patients receiving 24 mg upadacitinib once daily, vs 11% of patients receiving placebo. Endoscopic remission was achieved by 10% (P < .1 vs placebo), 8%, 8% (P<.1 vs placebo), 22% (P < .01 vs placebo), and 14% (P < .05 vs placebo) of patients receiving upadacitinib, respectively, vs none of the patients receiving placebo. Endoscopic but not clinical remission increased with dose during the induction period. Efficacy was maintained for most endpoints through week 52. During the induction period, patients in the upadacitinib groups had higher incidences of infections and serious infections vs placebo. Patients in the twice-daily 12 mg and 24 mg upadacitinib groups had significant increases in total, high-density lipoprotein, and low-density lipoprotein cholesterol levels compared with patients in the placebo group. In a phase 2 trial of patients with CD, upadacitinib induced endoscopic remission in a significant proportion of patients compared with placebo. Upadacitinib's benefit/risk profile supports further development for treatment of CD. (Clinicaltrials.gov, Number: NCT02365649).

Strategies in adjusting for multiple comparisons: A primer for pediatric surgeons

Background/PurposeIn pediatric surgery research, the issue of multiple comparisons commonly arises when there are multiple patient or experimental groups being compared two at a time on an outcome of interest. Performing multiple statistical comparisons increases the likelihood of finding a false positive result when there truly are no statistically significant group differences (falsely rejecting the null hypothesis when it is true). In order to control for the risk of false positive results, there are several statistical approaches that surgeons should consider in collaboration with a biostatistician when performing a study that is prone to the issue of false discovery related to multiple comparisons. It is becoming increasingly more common for high impact journals to require authors to carefully consider multiplicity in their studies. Therefore, the objective of this primer is to provide surgeons with a useful guide and recommendations on how to go about taking multiple comparisons into account to keep false positive results at an acceptable level. MethodsWe provide background on the issue of multiple comparisons and risk of type I error and guidance on statistical approaches (i.e. multiple comparisons procedures) that can be implemented to control the type I false positive error rate based on the statistical analysis plan. These include, but are not limited to, the Bonferroni correction, the False Discovery Rate (FDR) approach, Tukey's procedure, Scheffé's procedure, Holm's procedure, and Dunnett's procedure. ResultsWe present the results of the various approaches following one-way analysis of the variance (ANOVA) using a hypothetical surgical research example of the comparison between three experimental groups of rats on skin defect coverage for experimental spina bifida: the TRASCET group, sham control, and saline control. The ultimate decision in accounting for multiple comparisons is situation-dependent and surgeons should work with their statistical colleagues to ensure the best approach for controlling the type I error rate and interpreting the evidence when making multiple inferences and comparisons. ConclusionsThe risk of rejecting the null hypothesis increases when multiple hypotheses are tested using the same data. Surgeons should be aware of the available approaches and considerations to take into account multiplicity in the statistical plan or protocol of their clinical and basic science research studies. This strategy will improve their study design and ensure the most appropriate analysis of their data. Not adjusting for multiple comparisons can lead to misleading presentation of evidence to the surgical research community because of exaggerating treatment differences or effects. Type of studyReview article. Level of evidenceN/A

Effect of phoneme variations on blind reverberation time estimation

This study focuses on an unexplored aspect of the performance of algorithms for blind reverberation time (T) estimation – on the effect that speech signal’s phonetic content has on the value of the estimate ofTthat is obtained from the reverberant version of that signal. To this end, the performance of three algorithms is assessed on a set of logatome recordings artificially reverberated with room impulse responses from four rooms, with theirT20value in the [0.18, 0.55] s interval. Analyses of variance showed that the null hypotheses of equal means of estimation errors can be rejected at the significance level of 0.05 for the interaction terms between the factors “vowel”, “consonant”, and “room”, while the results of Tukey’s multiple comparison procedure revealed that there are both some similarities in the behaviour of the algorithms and some differences, where the latter are stemming from the differences in the details of algorithms’ implementation such as the number of frequency bands and whetherTis estimated continuously or only on the selected, the so-called speech decay, segments of the signal.

Alternative to Tukey test

ABSTRACT In order to search for an ideal test for multiple comparison procedures, this study aimed to develop two tests, similar to the Tukey and SNK tests, based on the distribution of the externally studentized amplitude. The test names are Tukey Midrange (TM) and SNK Midrange (SNKM). The tests were evaluated based on the experimentwise error rate and power, using Monte Carlo simulation. The results showed that the TM test could be an alternative to the Tukey test, since it presented superior performances in some simulated scenarios. On the other hand, the SNKM test performed less than the SNK test.