Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA
Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA
Analysis of variance (ANOVA) is a statistical procedure that compares data between two or more groups or conditions to investigate the presence of differences between those groups on some continuous dependent variable (see Exercise 18). In this exercise we will focus on the one-way ANOVA which involves testing one independent variable and one dependent variable (as opposed to other types of ANOVAs such as factorial ANOVAs that incorporate multiple independent variables).
Why ANOVA and not a t-test? Remember that a t-test is formulated to compare two sets of data or two groups at one time (see Exercise 23 for guidance on selecting appropriate statistics). Thus data generated from a clinical trial that involves four experimental groups Treatment 1 Treatment 2 Treatments 1 and 2 combined and a Control would require 6 t-tests. Consequently the chance of making a Type I error (alpha error) increases substantially (or is inflated) because so many computations are being performed. Specifically the chance of making a Type I error is the number of comparisons multiplied by the alpha level. Thus ANOVA is the recommended statistical technique for examining differences between more than two groups (Zar 2010).
ANOVA is a procedure that culminates in a statistic called the F statistic. It is this value that is compared against an F distribution (see Appendix C) in order to determine whether the groups significantly differ from one another on the dependent variable. The formulas for ANOVA actually compute two estimates of variance: One estimate represents differences between the groups/conditions and the other estimate represents differences among (within) the data.
Research Designs Appropriate for the One-Way ANOVA
Research designs that may utilize the one-way ANOVA include the randomized experimental quasi-experimental and comparative designs (Gliner Morgan & Leech 2009). The independent variable (the grouping variable for the ANOVA) may be active or attributional. An active independent variable refers to an intervention treatment or program. An attributional independent variable refers to a characteristic of the participant such as gender diagnosis or ethnicity. The ANOVA can compare two groups or more. In the case of a two-group design the researcher can either select an independent samples t-test or a one-way ANOVA to answer the research question. The results will always yield the same conclusion regardless of which test is computed; however when examining differences between more than two groups the one-way ANOVA is the preferred statistical test.
Example 1: A researcher conducts a randomized experimental study wherein she randomizes participants to receive a high-dosage weight loss pill a low-dosage weight loss pill or a placebo. She assesses the number of pounds lost from baseline to post-treatment 378for the three groups. Her research question is: Is there a difference between the three groups in weight lost? The independent variables are the treatment conditions (high-dose weight loss pill low-dose weight loss pill and placebo) and the dependent variable is number of pounds lost over the treatment span.
Null hypothesis: There is no difference in weight lost among the high-dose weight loss pill low-dose weight loss pill and placebo groups in a population of overweight adults.
Example 2: A nurse researcher working in dermatology conducts a retrospective comparative study wherein she conducts a chart review of patients and divides them into three groups: psoriasis psoriatric symptoms or control. The dependent variable is health status and the independent variable is disease group (psoriasis psoriatic symptoms and control). Her research question is: Is there a difference between the three groups in levels of health status?
Null hypothesis: There is no difference between the three groups in health status.
Statistical Formula and Assumptions
Use of the ANOVA involves the following assumptions (Zar 2010):
1. Sample means from the population are normally distributed.
2. The groups are mutually exclusive.
3. The dependent variable is measured at the interval/ratio level.
4. The groups should have equal variance termed homogeneity of variance.
5. All observations within each sample are independent.
The dependent variable in an ANOVA must be scaled as interval or ratio. If the dependent variable is measured with a Likert scale and the frequency distribution is approximately normally distributed these data are usually considered interval-level measurements and are appropriate for an ANOVA (de Winter & Dodou 2010; Rasmussen 1989).
The basic formula for the F without numerical symbols is:
F=MeanSquareBetweenGroupsMeanSquareWithinGroups
The term mean square (MS) is used interchangeably with the word variance. The formulas for ANOVA compute two estimates of variance: the between groups variance and the within groups variance. The between groups variance represents differences between the groups/conditions being compared and the within groups variance represents differences among (within) each group’s data. Therefore the formula is F = MS between/MS within.
Hand Calculations
Using an example from a study of students enrolled in an RN to BSN program a subset of graduates from the program were examined (Mancini Ashwill & Cipher 2014). The data are presented in Table 33-1. A simulated subset was selected for this example so that 379the computations would be small and manageable. In actuality studies involving one-way ANOVAs need to be adequately powered (Aberson 2010; Cohen 1988). See Exercises 24 and 25 for more information regarding statistical power.
. .
The post Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA appeared first on academicheroes.com.
Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA was first posted on October 21, 2019 at 2:11 am.
©2019 "Essay Lords | Bringing Excellence to students world wide". Use of this feed is for personal non-commercial use only. If you are not reading this article in your feed reader, then the site is guilty of copyright infringement. Please contact me at support@academicheroes.com
Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"
