Discussion

May-June 2021 • Vol. 30/No. 3218

Lynne M. Connelly, PhD, RN, is Professor, Benedictine College, Atchison, KS; and Research Editor, MEDSURG Nursing.

Introduction to Analysis of Variance (ANOVA)

Lynne M. Connelly

W hen researchers have multiple comparisons to make in a study, they can use Analysis of Variance (ANOVA). A one-way ANOVA or an

F test is a statistical procedure to determine if a differ- ence exists among three or more variables (e.g., different dosages of an intervention, different timeframes). In this column, I will discuss the meaning of this statistic and its use in data analysis.

T-Test and ANOVA A review of t-tests is a helpful starting point. A

Student’s t-test is used to compare the means of two dif- ferent groups. In other words, it can test the hypothesis that the means of two groups are different from each other greater than chance or that the difference is statis- tically significant. ANOVA extends this type of test to more than two groups. Why ANOVA and not multiple t-tests? Multiple t-tests would increase the chance of error (Type I error) and so ANOVA is recommended (Gray et al., 2017).

ANOVA determines if a statistical difference exists among groups, but it does not determine which groups are significantly different. In other words, if the test is significant, it indicates the means of at least one pair are different, but not which pair or pairs. That requires addi- tional tests. Inferences about means are made by analyz- ing variance, thus the name of the test (Mishra et al., 2019).

One-Way ANOVA In a one-way ANOVA, the independent variable is

categorical, such as before and after the implementation of different interventions, such as interventions to decrease medication errors, and a dependent variable which is continuous, such as the prevalence of medica- tion errors. ANOVA can be more complex than this with several independent factors (two-way ANOVA).

A one-way ANOVA has certain assumptions. First, it is assumed each sample has been selected independent- ly from other samples (sample independence). In other words, the samples are not related in any way, such as from the same people at different times; different tests are available for that situation. Second, the variance of the data in the different groups should be similar (vari- ance equality) on the dependent variable. The final assumption is that each sample is from a normally dis- tributed population (normality). There are tests for vari- ance equality and normality, but these results often are not reported in articles. Violations of these assumptions can invalidate results of the statistic (Larson, 2008).

The result of calculating this statistical test is called an F ratio (or just F), which is the ratio of how much variabil- ity there is between the groups compared to the variability within the groups (Polit & Beck, 2018). If the null hypoth- esis is true, there would be no difference between groups and the ratio would be close to 1. The larger the value of F, the more likely it is the difference between the groups on the independent variable is real (Mishra et al., 2019). If the p value is significant (<0.05), then it can be conclud- ed the groups’ means varied from each other by a large enough amount for that difference to be significant. In addition, the results for this test include the degrees of freedom (number of participants minus 1). This is usually written in paratheses after the F (Emerson, 2019).

To isolate which pairs of data are statistically differ- ent, researchers must conduct further post hoc tests or multiple comparison procedures (Polit & Beck, 2018). There are different tests for different situations, but the basic idea is that they statistically take into considera- tion the multiple comparison of the groups examined. Essentially, the alpha level (p-value) is reduced in pro- portion to the number of additional tests required (Gray et al., 2017) to prevent Type I errors. Commonly used tests include the Tukey HSD test, Scheff test, and Dunnett test; each is used for different circumstances (Mishra et al., 2019).

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Understanding Research

Researchers often have more than two groups they want to compare, such as different types of treatments, different age groups, or different dosages of a treatment. Analysis of variance (ANOVA) determines if a statistical difference exists among groups, but it does not determine which groups are significantly different. Analysis of variance is used frequently in nursing and medical research, and medical-surgical nurses should be familiar with this statistical procedure.

May-June 2021 • Vol. 30/No. 3158

Understanding Research continued from page 218

Because analysis of variance is used frequently in

nursing and medical research, readers should be familiar with it. Researchers often have more than two group they want to compare, such as different types of treat- ments, different age groups, or different dosages of a treatment. Readers can refer to the references for addi- tional information.

REFERENCES Emerson, R.W. (2019). Unpacking ANOVA reporting. Journal of Visual

Impairment and Blindness, 113(5), 473-474. Gray, J.R., Grove, S.K., & Sutherland, S. (2017). Burns and Grove’s the

practice of nursing research: Appraisal, synthesis, and generation of evidence (8th ed.). Elsevier.

Larson, M.G. (2008). Analysis of variance. Circulation, 117, 115-121. Mishra, P., Pandey, C.M., Mishra, P., & Pandey, G. (2019). Application of

Student’s t-test, analysis of variance, and covariance. Annals of Cardiac Anaesthesia, 22, 407-411.

Polit, D.F., & Beck, C.T. (2018). Essentials of nursing research: Appraising evidence for nursing practice (9th ed.). Wolters Kluwer.

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