EXERCISE 36 ANALYSIS OF VARIANCE (ANOVA) I
STATISTICAL TECHNIQUE IN REVIEW
An analysis of variance (ANOVA)statistical technique is conducted to examine differences between two or moregroups. There are different types of ANOVA, with the most basic being the one-wayANOVA, which is used to analyze data in studies with one independent andone dependent variable. More details on the types of ANOVA can be found in yourresearch textbook and statistical texts (Burns & Grove, 2005; Munro, 2001).The outcome of ANOVA is a numerical value for the F statistic. Thecalculated F-ratio from ANOVA indicates the extent to which group meansdiffer, taking into account the variability within the groups. Assuming thenull hypothesis of no difference among groups is true; the probability ofobtaining an F-ratio as large or larger than that obtained in the givensample is indicated by the calculated p value. For example, if p= 0.0002, this indicates that the probability of obtaining a result like thisin future studies is rare, and one may conclude that group differences existand the null hypothesis is rejected. However, there is always a possibilitythat this decision is in error, and the probability of committing this Type Ierror is determined by the alpha (a) set for the study, which is usually 0.05that is smaller in health care studies and occasionally 0.01.
ANOVA is similar to the t-testsince the null hypothesis (no differences between groups) is rejected when theanalysis yields a smaller p value, such as p = 0.05, than thealpha set for the study. Assumptions for the ANOVA statistical techniqueinclude:
1.normaldistribution of the populations from which the samples were drawn or randomsamples;
2.groupsshould be mutually exclusive;
3.groupsshould have equal variance or homogeneity of variance;
4.independenceof observations;
5.dependentvariable is measured at least at the interval level (Burns & Grove, 2005;Munro, 2001).
Researchers who perform ANOVA ontheir data record their results in an ANOVA summary table or in the text of aresearch article. An example of how an ANOVA result is commonly expressed is:
F(1,343) = 15.46,p
Where:
F is the statistic
1 is the group degrees of freedom (df)calculated by K 1, where K = number of groups in the study. Inthis example, K 1 = 2 1 = 1.
343 is the error degrees of freedom (df)that is calculated based upon the number of participants or N K.In this example, 345 subjects 2 groups = 343 error df.
15.46 is the F ratio or value
p indicates the significance of the F ratio in thisstudy or p
There are different types of ANOVA,but the focus of these analysis techniques is on examining differences betweentwo or more groups. The simplest is the one-way ANOVA, but many of the studiesin the literature include more complex ANOVA techniques. A commonly used ANOVAtechnique is the repeated-measures analysis of variance, which is usedto analyze data from studies where the same variable(s) is (are) repeatedlymeasured over time on a group or groups of subjects. The intent is to determinethe change that occurs over time in the dependent variable(s) with exposure tothe independent treatment variable(s).
RESEARCH ARTICLE
Source: Baird, C. L., & Sands, L. (2004). A pilot study ofthe effectiveness of guided imagery with progressive muscle relaxation toreduce chronic pain and mobility difficulties of osteoarthritis. PainManagement Nursing, 5 (3), 97104.