Exact Type 1 Error Rates for Robustness of Student's t Test with Unequal Variances

1980 ◽  
Vol 5 (4) ◽  
pp. 337 ◽  
Author(s):  
Philip H. Ramsey
Keyword(s):  
Error Rates ◽  
T Test ◽  
Unequal Variances ◽  
Type 1 Error ◽  
Student’S T ◽  
Student’S T Test

scholarly journals Additional file to "Why Psychologists Should by Default Use Welch's t-test Instead of Student's t-test." (in press for the International Review of Social Psychology)

2017 ◽  
Author(s):  
Marie Delacre ◽  
Daniel Lakens ◽  
Christophe Leys
Keyword(s):  
Psychological Research ◽  
Error Rates ◽  
T Test ◽  
International Review ◽  
Type 1 Error ◽  
Statistical Inferences ◽  
Homogeneity Of Variance ◽  
Student’S T ◽  
Student’S T Test

When comparing two independent groups, researchers in Psychology commonly use Student’s t-test. Assumptions of normality and of homogeneity of variance underlie this test. More often than not, when these conditions are not met, Student’s t-test can be severely biased, and leads to invalid statistical inferences. Moreover, we argue that the assumption of equal variances will seldom hold in psychological research and that choosing between Student’s t-test or Welch’s t-test based on the outcomes of a test of the equality of variances often fails to provide an appropriate answer. We show that the Welch’s t-test provides a better control of Type 1 error rates when the assumption of homogeneity of variance is not met, and loses little robustness compared to Student’s t-test when the assumptions are met. We argue that Welch’s t-test should be used as a default strategy.

scholarly journals Why Psychologists Should by Default Use Welch's t-test Instead of Student's t-test (in press for the International Review of Social Psychology).

2017 ◽  
Author(s):  
Marie Delacre ◽  
Daniel Lakens ◽  
Christophe Leys
Keyword(s):  
Psychological Research ◽  
Error Rates ◽  
T Test ◽  
International Review ◽  
Type 1 Error ◽  
Statistical Inferences ◽  
Homogeneity Of Variance ◽  
Student’S T ◽  
Student’S T Test

When comparing two independent groups, researchers in Psychology commonly use Student’s t-test. Assumptions of normality and of homogeneity of variance underlie this test. More often than not, when these conditions are not met, Student’s t-test can be severely biased, and leads to invalid statistical inferences. Moreover, we argue that the assumption of equal variances will seldom hold in psychological research and that choosing between Student’s t-test or Welch’s t-test based on the outcomes of a test of the equality of variances often fails to provide an appropriate answer. We show that the Welch’s t-test provides a better control of Type 1 error rates when the assumption of homogeneity of variance is not met, and loses little robustness compared to Student’s t-test when the assumptions are met. We argue that Welch’s t-test should be used as a default strategy.

Exact Type 1 Error Rates for Robustness of Student's t Test with Unequal Variances

1980 ◽  
Vol 5 (4) ◽  
pp. 337-349 ◽  
Author(s):  
Philip H. Ramsey
Keyword(s):  
Type I Error ◽  
Error Rates ◽  
T Test ◽  
Type I ◽  
Sample Sizes ◽  
Unequal Variances ◽  
Normal Populations ◽  
Type 1 Error ◽  
Student’S T ◽  
Equal Population

It is noted that disagreements have arisen in the literature about the robustness of the t test in normal populations with unequal variances. Hsu's procedure is applied to determine exact Type I error rates for t. Employing fairly liberal but objective standards for assessing robustness, it is shown that the t test is not always robust to the assumption of equal population variances even when sample sizes are equal. Several guidelines are suggested including the point that to apply t at α = .05 without regard for unequal variances would require equal sample sizes of at least 15 by one of the standards considered. In many cases, especially those with unequal N's, an alternative such as Welch's procedure is recommended.

scholarly journals On the Statistical Testing Methods for Single Laboratory Validation of Qualitative Microbiological Assays with a Paired Design

2020 ◽  
Vol 103 (6) ◽  
pp. 1667-1679
Author(s):  
Shizhen S Wang
Keyword(s):  
Average Power ◽  
Mixed Effects ◽  
Error Rates ◽  
T Test ◽  
Type 1 Error ◽  
Minimum Detectable Difference ◽  
Microbiological Assays ◽  
Paired Design ◽  
Paired T Test

Abstract Background There are several statistical methods for detecting a difference of detection rates between alternative and reference qualitative microbiological assays in a single laboratory validation study with a paired design. Objective We compared performance of eight methods including McNemar’s test, sign test, Wilcoxon signed-rank test, paired t-test, and the regression methods based on conditional logistic (CLOGIT), mixed effects complementary log-log (MCLOGLOG), mixed effects logistic (MLOGIT) models, and a linear mixed effects model (LMM). Methods We first compared the minimum detectable difference in the proportion of detections between the alternative and reference detection methods among these statistical methods for a varied number of test portions. We then compared power and type 1 error rates of these methods using simulated data. Results The MCLOGLOG and MLOGIT models had the lowest minimum detectable difference, followed by the LMM and paired t-test. The MCLOGLOG and MLOGIT models had the highest average power but were anticonservative when correlation between the pairs of outcome values of the alternative and reference methods was high. The LMM and paired t-test had mostly the highest average power when the correlation was low and the second highest average power when the correlation was high. Type 1 error rates of these last two methods approached the nominal value of significance level when the number of test portions was moderately large (n > 20). Highlights The LMM and paired t-test are better choices than other competing methods, and we provide an example using real data.

The Power of Student's t-Test

1965 ◽  
Vol 60 (309) ◽  
pp. 320 ◽  
Author(s):  
D. B. Owen
Keyword(s):  
T Test ◽  
Student’S T ◽  
Student’S T Test

scholarly journals Nurses' leadership styles in the icu: association with personal and professional profile and workload

2009 ◽  
Vol 17 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Alexandre Pazetto Balsanelli ◽  
Isabel Cristina Kowal Olm Cunha ◽  
Iveth Yamaguchi Whitaker
Keyword(s):  
Leadership Styles ◽  
Leadership Style ◽  
T Test ◽  
Descriptive Statistics ◽  
Nursing Workload ◽  
Comparison Test ◽  
Multiple Comparison Test ◽  
Professional Profile ◽  
Student’S T ◽  
Student’S T Test

This study aims to explore the association between nurses' leadership styles and personal and professional nursing profile and workload. The sample consisted of seven nurses and seven nursing technicians who were grouped into pairs. At the end of three months, nurses were queried regarding what leadership style would be adopted when the nursing technician under their evaluation delivered care to patients admitted to the ICU. Relevant data was analyzed by applying descriptive statistics, Tukey's multiple comparison test and Student's t-test (p< 0.05). Nursing workload reached 80.1% on average. The personal and professional profile variables did not show any relation with the leadership styles chosen by nurses (p>0.05). The determine, persuade, and share leadership styles prevailed. However, whenever the nursing workload peaked, the determine and persuade styles were used (p<0.05).

scholarly journals Intravesical prostaglandin e2 effectiveness in the prevention of urinary retention after transvaginal reconstruction of the pubo-cervical fascia and short arm sling according to Lahodny: a prospective randomized clinical trial

2010 ◽  
Vol 14 (1) ◽  
pp. 15 ◽  
Author(s):  
G. QUADRI ◽  
N. NATALE ◽  
C. SPREAFICO ◽  
C. BELLONI ◽  
D. BARISANI ◽  
...  
Keyword(s):  
Prostaglandin E2 ◽  
Urinary Retention ◽  
Study Groups ◽  
T Test ◽  
Control Group ◽  
Fisher Exact Test ◽  
Test Results ◽  
Exact Test ◽  
Student’S T ◽  
Student’S T Test

Intravesical prostaglandin E2 is effective in the recovery of spontaneous voiding after transvaginal reconstruction of the pubocervical fascia and short arm sling according to Lahodny. The aim of the study was to compare the effects of intravesical prostaglandin E2 in the prevention of urinary retention after transvaginal reconstruction of the pubocervical fascia and short arm sling according to Lahodny. STUDY DESIGN: From November 1996 to June 1999 fifty women underwent the Lahodny procedure for moderate/severe cystocele and stress urinary incontinence. Women were randomly assigned to 1 of the 2 study groups: intravesical prostaglandin E2 versus controls. Data obtained were analyzed with the Student t test and the Fisher exact test. RESULTS: Two patients of the treatment group had to be excluded from the study, one because of the wrong measurement of the post-voidal residual volume and another due to a fastidious burning sensation which appeared immediately after prostaglandin instillation and required the suspension of the treatment. No other side effects such as nausea, vomiting, diarrhea or hyperthermia were observed. Patients who underwent the prostaglandin E2 treatment showed a recovery of spontaneous voiding after 7.9&plusmn;6.7 days, whereas this interval was significantly longer in the control group, being 12.9&plusmn;9.7 days (p=0.04, Two tailed Unpaired Student's T test). CONCLUSION: The effectiveness and the low associated morbidity mark the treatment with intravesical prostaglandin E2 useful in the recovery of normal voiding after transvaginal pubocervical fascia reconstruction and short arm sling with the procedure according to Lahodny.

scholarly journals Study of Relationship of Anemia among Edentulous Patients

2018 ◽  
Vol 5 (2) ◽  
pp. 105-108
Author(s):  
Lijo Isaac ◽  
A. P. Nirmal Raj ◽  
Reshma Karkera ◽  
R Naveen Reddy
Keyword(s):  
Nutritional Status ◽  
T Test ◽  
Dental Status ◽  
Adult Patients ◽  
Control Group ◽  
Age Group ◽  
Edentulous Patients ◽  
Student’S T ◽  
Relationship Of ◽  
Student’S T Test

Very little studies were done on relationship of the dental status and the nutritional status. The present study was done to study relation between edentulism and the presence of anemia. The study was included of 46 adult patients with edentulism and same numbers of patients were taken as controls. The results were tabulated and analyzed with the help of IBM SPSS statistics 20 using student’s t test. The hemoglobin levels were lower in the edentulous patients that that of the control group. The present study had shown that the nutritional status were poor resulting in anemia in case of edentulous patients as compared to control group with the same age group.  

scholarly journals The influence of proteinuria on tubular transport of Na+, K+, CL

2002 ◽  
Vol 130 (3-4) ◽  
pp. 64-67
Author(s):  
Dejan Petrovic ◽  
Radmila Obrenovic ◽  
Mileta Poskurica ◽  
Biljana Stojimirovic
Keyword(s):  
Statistical Analysis ◽  
Creatinine Clearance ◽  
Significant Influence ◽  
Fractional Excretion ◽  
T Test ◽  
The Third ◽  
Tubular Transport ◽  
Student’S T ◽  
Student’S T Test

Functional and structural damages of tubulointerstitium are caused by proteinuria. The aim of this study was to assess the influence of different proteinuria levels on Na+, K+, Cl tubular transport. We examined 50 patients (24 males, 26 females), mean age 46.50 ? 13.08 years, with mean creati-nine clearence of 87.29 ? 31.17 mL/min. They were separated in three groups depending on proteinuria value. The first group with proteinuria less than 0.3 g/24h included 19 persons (7 males, 12 females), mean age 45.12 ? 13.28 years, with mean creatinine clearance of 94.27 ? 34.70 mL/min. The second group of 18 patients (8 males, 10 females), mean age 45.39 ? 12.64 years had proteinuria of 0.3-3,0 g/24h and mean creatinine clearance of 90.07 ? 31.89 mL/min. The third group had proteinuria level higher than 3.0g/24h and mean creatinine clearance of 73.25 ? 20.44 mL/min. It included 13 patients (9 males, 4 females), mean age 50.08 ? 13.73 years. As a parameter of proteinuria influence on tubular transport of Na+, K+ and Cl-, fractional excretion of these electrolytes, was studied. Student's T test, Mann Whitney U test and c2 test were used for statistical analysis. No statistically significant influence of proteinuria was found on Na+, K+ and Cl tubular transport.

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