Eta squared and partial eta squared as measures of effect size in educational research

Purpose of the study: The purpose of this study was to determine the differences in scientific attitudes and cognitive knowledge of students between guided inquiry and direct learning models in practical activities by controlling students' prior knowledge. Methodology: This quasi-experimental study employed a Non-Equivalent Pretest-Posttest Control Group Design. From a population of 88 students, 57 were selected using purposive sampling. Instruments included multiple-choice tests and Likert scale observation sheets. Data were analyzed using Microsoft Excel and IBM SPSS 23 with One-Way MANCOVA and Partial Eta Squared for effect size. Main Findings: The guided inquiry learning model is effective in improving students' scientific attitudes and cognitive knowledge. The average scientific attitude of students in the experimental class was 85, compared to 70 in the control class. The average post-test cognitive knowledge score was 75.17 in the experimental class and 50.93 in the control class. The One Way MANCOVA test showed significant differences between groups (p = 0.0001; partial eta squared = 0.840). Partial eta squared is a measure of effect size that indicates the proportion of variance in the dependent variables explained by the independent variable. A value of 0.840 suggests a large effect, meaning the learning model had a strong influence on students’ outcomes. Novelty/Originality of this study: This study integrates guided inquiry learning into food testing on the digestive system topic, uniquely controlling prior knowledge to examine its impact on scientific attitudes and cognitive outcomes, thus enhancing inquiry-based learning insights.

Two different approaches have been used to derive measures of effect size. One approach is based on the comparison of treatment means. The standardized mean difference is an appropriate measure of effect size when one is merely comparing two treatments, but there is no satisfactory analogue for comparing more than two treatments. The second approach is based on the proportion of variance in the dependent variable that is explained by the independent variable. Estimates have been proposed for both fixed-factor and random-factor designs, but their sampling properties are not well understood. Nevertheless, measures of effect size can allow quantitative comparisons to be made across different studies, and they can be a useful adjunct to more traditional outcome measures such as test statistics and significance levels.

BackgroundUniversal health care (UHC) may assist families whose children are most prone to early childhood caries (ECC) in accessing dental treatment and prevention. The purpose of this study was to determine the association between UHC, health expenditure and the global prevalence of ECC.MethodsHealth expenditure as percentage of gross domestic product, UHC service coverage index, and the percentage of 3–5-year-old children with ECC were compared among countries with various income levels using one-way analysis of variance (ANOVA). Three linear regression models were developed, and each was adjusted for the country income level with the prevalence of ECC in 3–5-year-old children being the dependent variable. In model 1, UHC service coverage index was the independent variable whereas in model 2, the independent variable was the health expenditure as percentage of GDP. Model 3 included both independent variables together. Regression coefficients (B), 95% confidence intervals (CIs), P values, and partial eta squared (ƞ2) as measure of effect size were calculated.ResultsLinear regression including both independent factors revealed that health expenditure as percentage of GDP (P < 0.0001) was significantly associated with the percentage of ECC in 3–5-year-old children while UHC service coverage index was not significantly associated with the prevalence of ECC (P = 0.05). Every 1% increase in GDP allocated to health expenditure was associated with a 3.7% lower percentage of children with ECC (B = − 3.71, 95% CI: − 5.51, − 1.91). UHC service coverage index was not associated with the percentage of children with ECC (B = 0.61, 95% CI: − 0.01, 1.23). The impact of health expenditure on the prevalence of ECC was stronger than that of UHC coverage on the prevalence of ECC (ƞ2 = 0.18 vs. 0.05).ConclusionsHigher expenditure on health care may be associated with lower prevalence of ECC and may be a more viable approach to reducing early childhood oral health disparities than UHC alone. The findings suggest that currently, UHC is weakly associated with lower global prevalence of ECC.

The objective of this study was to analyze the scientific literature in public oral health regarding calculation, presentation, and discussion of the effect size in observational studies. The scientific literature (2015 to 2019) was analyzed regarding: a) general information (journal and guidelines to authors, number of variables and outcomes), b) objective and consistency with sample calculation presentation; c) effect size (presentation, measure used and consistency with data discussion and conclusion). A total of 123 articles from 66 journals were analyzed. Most articles analyzed presented a single outcome (74%) and did not mention sample size calculation (69.9%). Among those who did, 70.3% showed consistency between sample calculation used and the objective. Only 3.3% of articles mentioned the term effect size and 24.4% did not consider that in the discussion of results, despite showing effect size calculation. Logistic regression was the most commonly used statistical methodology (98.4%) and Odds Ratio was the most commonly used effect size measure (94.3%), although it was not cited and discussed as an effect size measure in most studies (96.7%). It could be concluded that most researchers restrict the discussion of their results only to the statistical significance found in associations under study.

The objective of this study was to analyze the scientific literature in public oral health regarding calculation, presentation, and discussion of the effect size in observational studies. The scientific literature (2015 to 2019) was analyzed regarding: a) general information (journal and guidelines to authors, number of variables and outcomes), b) objective and consistency with sample calculation presentation; c) effect size (presentation, measure used and consistency with data discussion and conclusion). A total of 123 articles from 66 journals were analyzed. Most articles analyzed presented a single outcome (74%) and did not mention sample size calculation (69.9%). Among those who did, 70.3% showed consistency between sample calculation used and the objective. Only 3.3% of articles mentioned the term effect size and 24.4% did not consider that in the discussion of results, despite showing effect size calculation. Logistic regression was the most commonly used statistical methodology (98.4%) and Odds Ratio was the most commonly used effect size measure (94.3%), although it was not cited and discussed as an effect size measure in most studies (96.7%). It could be concluded that most researchers restrict the discussion of their results only to the statistical significance found in associations under study.

BackgroundSelecting chromosome substitution strains (CSSs, also called consomic strains/lines) used in the search for quantitative trait loci (QTLs) consistently requires the identification of the respective phenotypic trait of interest and is simply based on a significant difference between a consomic and host strain. However, statistical significance as represented by P values does not necessarily predicate practical importance. We therefore propose a method that pays attention to both the statistical significance and the actual size of the observed effect. The present paper extends on this approach and describes in more detail the use of effect size measures (Cohen’s d, partial eta squared - ηp2) together with the P value as statistical selection parameters for the chromosomal assignment of QTLs influencing anxiety-related behavior and locomotion in laboratory mice.ResultsThe effect size measures were based on integrated behavioral z-scoring and were calculated in three experiments: (A) a complete consomic male mouse panel with A/J as the donor strain and C57BL/6J as the host strain. This panel, including host and donor strains, was analyzed in the modified Hole Board (mHB). The consomic line with chromosome 19 from A/J (CSS-19A) was selected since it showed increased anxiety-related behavior, but similar locomotion compared to its host. (B) Following experiment A, female CSS-19A mice were compared with their C57BL/6J counterparts; however no significant differences and effect sizes close to zero were found. (C) A different consomic mouse strain (CSS-19PWD), with chromosome 19 from PWD/PhJ transferred on the genetic background of C57BL/6J, was compared with its host strain. Here, in contrast with CSS-19A, there was a decreased overall anxiety in CSS-19PWD compared to C57BL/6J males, but not locomotion.ConclusionsThis new method shows an improved way to identify CSSs for QTL analysis for anxiety-related behavior using a combination of statistical significance testing and effect sizes. In addition, an intercross between CSS-19A and CSS-19PWD may be of interest for future studies on the genetic background of anxiety-related behavior.Electronic supplementary materialThe online version of this article (doi:10.1186/s12863-016-0411-4) contains supplementary material, which is available to authorized users.

This chapter reviews the independent-samples t-test and the one-way analysis of variance, inferential statistics that are commonly used to test null and alternative hypotheses about mean differences among independent populations. Because both procedures assume equal population variances, Levene’s test for homogeneity of variances is discussed, as are methods for hypothesis testing when homogeneity of variances cannot be safely assumed. The chapter continues by using a measure of effect size, partial eta squared, to distinguish between statistical and clinical significance, and concludes with a discussion of post hoc multiple comparisons and contrast analysis.

The aim of this study was to examine changes in various intensities of physical activity - PA (moderate, low – walking, total, and vigorous) and their relationship with mental health parameters (anxiety, depression, and stress) among working-age adults after recovering from COVID-19; The study was conducted between February and May 2022 and included 288 participants aged 20–60 years (M = 47.06; SD = 12.41), of whom 95 were men and 193 were women. PA levels were assessed using the long form of IPAQ, while depression, anxiety, and stress levels were evaluated using the long form of DASS-42 questionnaire. Differences between the initial and final measurements were analyzed using a one-way repeated measures ANOVA, with partial eta squared (η²) reported as a measure of effect size. Statistical significance was set at p &lt; 0.05, and data were processed in SPSS (version 23.0); Total PA showed the largest increase over time (Wilks’ Λ = 0.94, F(1, 287) = 16.00, p &lt; 0.001, η² = 0.05), followed by moderate PA (Wilks’ Λ = 0.96, F(1, 287) = 10.45, p = 0.001, η² = 0.03). Low-intensity activity in the form of walking also significantly increased (Wilks’ Λ = 0.97, F(1, 287) = 7.57, p = 0.006, η² = 0.02), whereas vigorous PA did not show a significant change (Wilks’ Λ = 0.99, F(1, 287) = 0.64, p = 0.423, η² = 0.00). Re-garding mental health, anxiety significantly decreased (Wilks’ Λ = 0.98, F(1, 287) = 3.99, p = 0.047, η² = 0.01). Depression (Wilks’ Λ = 0.99, F(1, 287) = 1.24, p = 0.266, η² = 0.00) and stress (Wilks’ Λ = 0.99, F(1, 287) = 0.65, p = 0.418, η² = 0.00) demonstrated downward trends without significant differences; Increases in total and moderate PA, alongside reg-ular walking, were associated with reductions in anxiety and favorable trends in other mental health domains. Although this association between increased PA and reduced anxiety was observed, it was not directly tested statistically in the presented model. These findings underscore the importance of integrating simple and sustainable forms of PA into prevention and rehabilitation programs for working-age adults in the post-COVID period.

Problem There has been a high level of marital conflict in immigrant families from patriarchal cultures. There are negative attitudes toward women that contribute to couple conflict. Coupled with this are issues relating to immigration challenges that confront marriage stability among immigrant couples in North America. In the same vein, African American couples experience conflicts that militate against the stability of their marriages. Most of these marital upheavals stem from historical antecedents relating to this ethnic group, as well as the societal dialectics confronting them. By and large, regarding couple conflict, a better understanding of the challenges facing African immigrant couples, and the impact of the African heritage on African American couples, are germane to this study. Method This was a non-experimental comparative exploratory study of conflict in African immigrant and African American marriages in terms of their scores on the Conflict Tactics Scale (CTS2) and its subscales. This involved administering a combined questionnaire comprised of the CTS2, Attitude Toward Women Scale (AWS), and a short immigration questionnaire specific to African immigrants. The target populations for this research work fell into two groups: African immigrant and African American ethnic groups living in North America. A One-Way MANCOVA was conducted to determine the effect of ethnicity on each of the five conflict tactics (negotiation: self and partner; physical assault: self and partner; injury: self and partner; psychological aggression: self and partner; and sexual coercion: self and partner) after controlling for attitude towards women. A Pearson bivariate correlation analysis was used to test whether there was a significant bivariate relationship between attitude towards women and the total score of conflict tactics self and total partner. Analyses were carried out using the IBM Statistical Package for the Social Sciences (SPSS). Descriptive statistics were used to describe the responses of African immigrants to the Immigrant Questionnaire. Results In testing for the hypotheses, the main effect of ethnicity [Wilks’ Lambda = .868, F (5, 171) = 5.192, sig. = .000, multivariate eta squared = .132] indicated a significant effect on the combined conflict tactics. The covariate attitude towards women had a significant influence on the combined dependent variables [Wilks’ Lambda = .864, F (5, 171) = 5.368, sig. = .000, multivariate eta squared = .136, power = .99]. Univariate ANOVA results indicated that ethnicity had a significantly small effect on psychological aggression (self) [F (1,175) = 8.395, sig. = .004, partial eta squared = .046, power = .82], sexual coercion (self) [F (1,175) = 6.888, sig. = .009, partial eta squared = .038, power = .74]. The covariate attitude towards women had a significant effect on negotiation (self) [F (1,175) = 6.133, sig. = .014, partial eta squared = .034, power = .69], physical assault (self) [F (1,175) = 9.597, sig. = .002, partial eta squared = .052, power = .87], injury (self) [F (1,175) = 10.898, sig. = .001, partial eta squared = .059, power = .91], and sexual coercion (self) [F (1,175) = 11.960, sig. = .001, partial eta squared = . 064, power = .93]. Similarly, the main effect of ethnicity [Wilks’ Lambda = .895, F (5, 181) = 4.246, sig. = .001, multivariate eta squared = .105, power = .96] indicated a significant effect on the combined conflict tactics. The covariate attitude towards women had a significant influence on the combined dependent variables [Wilks’ Lambda = .916, F (5, 181) = 3.131, sig. = .007, multivariate eta squared = .084, power = .89]. Univariate ANOVA results indicated that ethnicity had a significantly small effect on psychological aggression (partner) [F (1,185) = 4.371, sig. = .038, partial eta squared = .023, power = .55], sexual coercion (partner) [F (1,185) = 4.010, sig. = .047, partial eta squared = .021, power = .52]. The covariate attitude towards women had a significant effect on physical assault (partner) [F (1,185) = 6.790, sig. = .010, partial eta squared = .035, power = .74], injury (partner) [F (1,185) = 6.499, sig. = .012, partial eta squared = .034, power = .72], and sexual coercion (partner) [F (1,185) = 9.946, sig. = .002, partial eta squared = .051, power = .88]. It is further revealed that there is no significant correlation between attitude towards women and total CT scores (self) [Pearson r = -.02, sig. = .762, N = 178], with related results showing that there was no significant correlation coefficient between attitude towards women and total CT scores (partner) [Pearson r = -.06, sig. = .417, N = 188]. The results of the immigration questionnaire showed that immigration and acculturation issues had a significant effect on the marriages of African immigrants in the US. Conclusions This study has established the reality that marital conflict is ubiquitous. The pertinent question is this: How do couples react to conflict? The reaction of couples to conflict determines the outcome to conflicts. It should be well noted that because the quality and stability of marriage and family lives are especially important in building and maintaining a healthy society, it is, therefore, to reduce conflict and violence in homes and among couples. We must work towards establishing a good community with a minimal level of violence. The task now is to underscore the point that families should be permeated by love and nurturing thoughtfulness, as opposed to the horrific psychological abuse, battering, and killing that are a tragic part of couple conflict and domestic violence. Through the cooperation of everyone; the intervention of marriage and family resource persons and counselors; and through the assistance of national governments, national organizations, and different international agencies, brilliant, practical, and meaningful approaches to bringing about the prevention and control of conflict and violence in marriage relationships can be engendered.

Crossing Traditional Boundaries: How Do Practitioners and University Faculty Describe Their Experience with Educational Research Literature?.

Consider a two-way ANOVA design. Generally, interactions are characterized by the difference between two measures of effect size. Typically the measure of effect size is based on the difference between measures of location, with the difference between means being the most common choice. This paper deals with extending extant results to two robust, heteroscedastic measures of effect size. The first is a robust, heteroscedastic analogue of Cohen's d. The second characterizes effect size in terms of the quantiles of the null distribution. Simulation results indicate that a percentile bootstrap method yields reasonably accurate confidence intervals. Data from an actual study are used to illustrate how these measures of effect size can add perspective when comparing groups.

It is shown how the difference between the success rates in two treatment groups is related to the treatment-outcome correlation and the overall success rate. A new measure of effect size is proposed, which is easily calculated and readily interpretable in terms of the ratio of success rates in the treatment groups.

Finance, incubation, managerial support initiatives, and technological innovation have all been identified as major drivers of SMEs’ business location. Despite the importance of SMEs, little attention has been paid to business research regarding the impact of government support, business style, and entrepreneurial sustainability on SME activities in rural, semi-urban, and urban areas. Identifying the necessary support for SMEs in rural, semi-urban, and urban areas is critical for the government as well as stakeholders and SME owners in assessing their survival status and other goal-setting achievements. The article’s central question is whether government support, business style, and entrepreneurship sustainability affect SME operations differently depending on location (rural, semi-urban, or urban). The MANOVA technique was used for the analysis to determine whether there is a significant difference between groups on a composite dependent variable as well as the univariate results for each dependent variable separately. Because conducting a series of studies (ANOVA) reveals the possibility of an inflated Type 1 error, MANOVA is preferred. The test re-test reliability method (trustworthiness assessment of the questionnaire) and the Cronbach Alpha test (internal consistency of instrument sections) yielded satisfactory results of 0.70 and 0.875, respectively. Government support (GS), business style (BS), and entrepreneurial sustainability were used as dependent variables (SE). The independent variable was the business location. On the combined dependent variables, there was a statistically significant difference between SME location: F (3, 902) = 20.388, p = 0.001, Wilks’ Lambda = 0.88, partial eta squared = 0.06. When the results for the dependent variables were considered separately, they all reached statistical significance, using a Bonferroni adjusted alpha level of 0.017. BS: F (1, 904) = 13.29, p ≤ 001, partial eta squared = 0.03. GS: F (1, 904) = 30.28, p ≤ 0.001, partial eta squared = 0.06. SE: F (1, 904) = 8.08, p ≤ 0.001, partial eta squared = 0.02. The findings show that locational effects on government support have a knock-on effect on the business plan and long-term entrepreneurship. As a result, the government must reconsider its rural activities to ensure that support is distributed equitably across levels of location.

Importance of Effect Sizes for the Accumulation of Knowledge

A recent trend in the psychological literature has been to include measures of effect size when reporting probability values. The several measures of effect size associated with the Student t test for two independent samples are appropriate only when the variances are homogeneous. In this paper, commonly used measures of effect size are considered and compared, using four data sets. A chance-corrected measure of effect size is provided for two or more treatment groups characterized by either homogeneous or heterogeneous variances.