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 more

groups. 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 and

one dependent variable. More details on the types of ANOVA can be found in your

research textbook and statistical texts (Burns & Grove, 2005; Munro, 2001).

The outcome of ANOVA is a numerical value for the

*F*statistic. The

calculated

*F*-ratio from ANOVA indicates the extent to which group means

differ, taking into account the variability within the groups. Assuming the

null hypothesis of no difference among groups is true; the probability of

obtaining an

*F*-ratio as large or larger than that obtained in the given

sample is indicated by the calculated

*p*value. For example, if

*p*

= 0.0002, this indicates that the probability of obtaining a result like this

in future studies is rare, and one may conclude that group differences exist

and the null hypothesis is rejected. However, there is always a possibility

that this decision is in error, and the probability of committing this Type I

error is determined by the alpha (a) set for the study, which is usually 0.05

that is smaller in health care studies and occasionally 0.01.

ANOVA is similar to the *t*-test

since the null hypothesis (no differences between groups) is rejected when the

analysis yields a smaller *p* value, such as *p* = 0.05, than the

alpha set for the study. Assumptions for the ANOVA statistical technique

include:

1.normal

distribution of the populations from which the samples were drawn or random

samples;

2.groups

should be mutually exclusive;

3.groups

should have equal variance or homogeneity of variance;

4.independence

of observations;

5.dependent

variable is measured at least at the interval level (Burns & Grove, 2005;

Munro, 2001).

Researchers who perform ANOVA on

their data record their results in an ANOVA summary table or in the text of a

research 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 between

two or more groups. The simplest is the one-way ANOVA, but many of the studies

in the literature include more complex ANOVA techniques. A commonly used ANOVA

technique is the **repeated-measures analysis of variance**, which is used

to analyze data from studies where the same variable(s) is (are) repeatedly

measured over time on a group or groups of subjects. The intent is to determine

the change that occurs over time in the dependent variable(s) with exposure to

the independent treatment variable(s).

RESEARCH ARTICLE

**Source:** Baird, C. L., & Sands, L. (2004). A pilot study of

the effectiveness of guided imagery with progressive muscle relaxation to

reduce chronic pain and mobility difficulties of osteoarthritis. *PainManagement Nursing, 5* (3), 97–104.