Hypothesis testing, type I and type II errors

Banerjee, Amitav; Chitnis, Uday B; Jadhav, Sudhir; Bhawalkar, Jitendra S; Chaudhury, Suprakash

doi:10.4103/0972-6748.62274

Cited by 266 publications

(164 citation statements)

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“…Two types errors are considered when calculating the minimum sample size. The more the sample size the less these two errors can be occurred (Banerjee et al, 2009). The first error must be considered is the first kind (the ) and by convention is set to 0.05 for 95% confidence, the second kind (the ) and the power (1 − ) which was set to 0.9 for 10% of missing association.…”

Section: Methodsmentioning

confidence: 99%

An exploratory study for investigating the critical success factors for cloud migration in the Saudi Arabian higher education context

Alharthi

Alassafi

Walters

et al. 2017

Telematics and Informatics

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Section: Methodsmentioning

confidence: 99%

An exploratory study for investigating the critical success factors for cloud migration in the Saudi Arabian higher education context

Alharthi

Alassafi

Walters

et al. 2017

Telematics and Informatics

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“…The poor performance of Student's t-test when variances are unequal becomes visible when we look at the error rates of the test and the influence of both Type 1 errors and Type 2 errors. An increase in the Type 1 error rate leads to an inflation of the number of false positives in the literature, while an increase in the Type 2 error rate leads to a loss of statistical power (Banerjee et al, 2009 s are variance estimates from each independent group, and where n 1 and n 2 are the respective sample sizes for each independent group: …”

Section: The Mathematical Differences Between Student's T-test Welchmentioning

confidence: 99%

Why Psychologists Should by Default Use Welch’s t-test Instead of Student’s t-test

Delacre¹,

Lakens²,

Leys

2017

International Review of Social Psychology

590

331

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When comparing two independent groups, psychology researchers commonly use Student's t-tests. Assumptions of normality and 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 lead to invalid statistical inferences. Moreover, we argue that the assumption of equal variances will seldom hold in psychological research, and choosing between Student's t-test and 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 it 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. Keywords:Welch's t-test; Student's t-test; homogeneity of variance; Levene's test; Homoscedasticity; statistical power; type 1 error; type 2 error Independent sample t-tests are commonly used in the psychological literature to statistically test differences between means. There are different types of t-tests, such as Student's t-test, Welch's t-test, Yuen's t-test, and a bootstrapped t-test. These variations differ in the underlying assumptions about whether data is normally distributed and whether variances in both groups are equal (see, e.g., Rasch, Kubinger, & Moder, 2011;Yuen, 1974). Student's t-test is the default method to compare two groups in psychology. The alternatives that are available are considerably less often reported. This is surprising, since Welch's t-test is often the preferred choice and is available in practically all statistical software packages.In this article, we will review the differences between Welch's t-test, Student's t-test, and Yuen's t-test, and we suggest that Welch's t-test is a better default for the social sciences than Student's and Yuen's t-tests. We do not include the bootstrapped t-test because it is known to fail in specific situations, such as when there are unequal sample sizes and standard deviations differ moderately (Hayes & Cai, 2007).When performing a t-test, several software packages (i.e., R and Minitab) present Welch's t-test by default. Users can request Student's t-test, but only after explicitly stating that the assumption of equal variances is met. Student's t-test is a parametric test, which means it relies on assumptions about the data that are analyzed. Parametric tests are believed to be more powerful than non-parametric tests (i.e., tests that do not require assumptions about the population parameters; Sheskin, 2003). However, Student's t-test is generally only more powerful when the data are normally distributed (the assumption of normality) and the variances are equal in both groups (homoscedasticity; the assumption of homogeneity of variance; Carroll & Schneider, 1985;Erceg-Hurn & Mirosevich, 2008).When sample sizes are equal between groups, Student's t-test is robust to violations of the assump...

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“…The likelihood of these errors occurring can be reduced by increasing the sample size. By convention, α is set to 0.05 for a 95% confidence and (1-β) is set to 0.9 or 10% for missing an association (Banerjee 2009)The effect size refers to the magnitude of the association between the predictor and outcome variables. Cohen (1988) defines three different effect sizes: small (d=0.2), medium (d=0.5) and large (d=0.8).…”

Section: It Questionnaire Design and Analysismentioning

confidence: 99%

A framework for critical security factors that influence the decision of cloud adoption by Saudi government agencies

Alassafi

Alharthi

Walters

et al. 2017

Telematics and Informatics

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Hypothesis testing, type I and type II errors

Cited by 266 publications

References 1 publication

An exploratory study for investigating the critical success factors for cloud migration in the Saudi Arabian higher education context

An exploratory study for investigating the critical success factors for cloud migration in the Saudi Arabian higher education context

Why Psychologists Should by Default Use Welch’s t-test Instead of Student’s t-test

A framework for critical security factors that influence the decision of cloud adoption by Saudi government agencies

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