ANOVA Analysis: The Influence of Physical Activity on Stress Levels

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Table of Contents

Introduction
Research Question
Hypothesis
Variables
Sample Size
Assumptions and Limitations
Interpret Results
Conclusion
References

Introduction

Analysis of variance (ANOVA) is an inferential statistic employed in assessing if there is a marked difference between multiple means. In this scenario, one-ANOVA was applied to evaluate whether means of stress levels are different among individuals in three groups of no exercise, moderate exercise, and strenuous exercise. This type of ANOVA applies when an independent variable has more than two categories and a dependent variable exists on a continuous scale (Tanner, 2016). Physical activity has three categories showing the degree of exercise, while the level of stress has a numeric scale. A comparison of the differences in means would indicate if the degree of physical activity has a marked effect on stress levels. Therefore, the focus of this exercise is to interpret ANOVA results of the influence of physical activity on stress levels in individuals.

Research Question

The following research question was formulated based on information presented in the scenario of ANOVA analysis.

Question: Does the degree of physical activity determine the level of stress among individuals?

Hypothesis

The null hypothesis under study is that physical activity does not have a statistically significant effect on the level of stress among individuals. The alternative hypothesis is a non-directional test because the absence of means does not allow the determination of the directional effect of physical activity. While a hypothesis without direction tests whether a mean is greater than or less than a test value, a non-directional one focuses on the magnitude of differences (Tanner, 2016). The provided data lacks background information to indicate whether physical activity increases or decreases the level of stress in individuals.

Variables

The independent variable of this research is the degree of physical activity, while the independent variable is the level of stress. The study assumes that physical activity has a measurable influence on the level of stress. The type of inferential statistic employed in the analysis of data is one-way ANOVA. According to Tanner (2016), one-way ANOVA applies in the comparison of means between more than two groups. The scenario displays that the study compared three groups of individuals with varying degrees of physical activity. The study does not qualify to be a repeated-measures ANOVA because the post-test scores only were used in the analysis. In essence, the pre-test data formed the baseline scores used to control individual variations in the levels of stress at the time of measurement.

Sample Size

As indicated by the total degrees of freedom, the sample size is 30 (N-1 = 29). From the ANOVA table, the number of groups is 3 (k-1 = 2). Degrees of freedom of within-subjects (N – k) and total (N -1) indicate the sample size, while those of between subjects (k-1) show the number of treatments (Tanner, 2016). These three groups are individuals who received different interventions, namely, no exercise (control group), moderate exercise, and strenuous exercise.

Assumptions and Limitations

Data used in one-way ANOVA has to meet several assumptions to generate robust and valid findings. The independent variable should exist on a continuous scale to allow the determination of group means and variations (Blanca, Alarcón, Arnau, Bono, & Bendayan, 2017). The level of stress meets the assumption of interval scale as shown by the sum of squares (SS) and the mean sum of squares (MS). In contrast, the independent variable should be on a categorical scale with more than two independent groups (Blanca et al., 2017). The independent variable has three categorical groups, which measure the degree of physical activity into no activity, moderate activity, and strenuous activity. The participants of the study should exhibit independence of observations during the experiment (Blanca et al., 2017). In this case, the participants were in three independent groups without interacting in the course of the study. As other key assumptions, the independent variable should not have significant outliers, follow the normal distribution, and exhibit homogeneity of variance to avert skewed distributions and distorted variations.

The limitations of the analysis are lack of background information to allow interpretation of data. Descriptive statistics such as means are necessary to permit a directional test of hypothesis, and demographic information is required to extrapolate findings.

Interpret Results

Outcomes of one-way ANOVA fail to reject the null hypothesis that physical activity does not have a statistically significant effect on the level of stress among individuals, F(2, 27) = 0.766, p > 0.05. When the p-value is greater than the significance level, an inferential test fails to rejects the null hypothesis (Tanner, 2016). These outcomes suggest that individuals who performed strenuous exercise, moderate exercise, and no exercise had insignificant differences in means of the stress levels. Therefore, the examination of results answers the research question that the degree of physical activity does not determine the level of stress among individuals.

Conclusion

The level of stress among individuals depends on the influence of physical, social, and psychological factors. This scenario sought to demonstrate the effect of physical activity on stress levels among individuals. As the dependent and independent variables met the assumptions of one-way ANOVA, outcomes of analysis provided valid information. Based on p-value, results indicated that physical activity has no statistically significant influence on means of the stress levels.

References

Blanca, M. J., Alarcón, R., Arnau, J., Bono, R., & Bendayan, R. (2017). Non-normal data: Is ANOVA still a valid option?Psicothema, 29(4), 552-557. Web.

Tanner, D. (2016). Statistics for the behavioral & social sciences (2nd ed.). San Diego, CA: Bridgepoint Education

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