Learning Activity 12:
Quantitative Data Analysis
Multivariant Analysis, Parametric Statistics
Method: Analysis of Variance (ANOVA)
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“The phenomena nursing researchers wish to understand are complex
and multivariate in nature. This means that the analytical techniques
we use must allow us to take into account many variables simultaneously.
Although bivariate (two variable) analyses have their place, nurse
researchers ultimately need to use basic multivariate techniques if they
are to tackle the complexity inherent in their subject matter. The selection
of the appropriate technique should be guided by a consideration of
the level of measurement attained in measuring the variables and
what the analysis is attempting to reveal.”
Gillis, A. & Jackson, W. (2002).
Research for Nurses (p. 560).
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Overview
Multivariate statistics are often used when three or more variables are being considered. One example is Multiple Regression, a correlation statistic which predicts variations in a dependent variable from two or more independent variables. "Multivariate statistics are generally used in an attempt to achieve one or more of the following goals: (1) describe and summarize the data collected during research, (2) establish the nature and degree of the relationships between different variables, and (3) determine a possible causal or predictive relationship between variables. To achieve this, it is necessary to distinguish between the cases and the variables in a data set. The cases are the individual stimuli that provide the data. These stimuli may be individual subjects, observations, items, events, or other discrete objects. Variables are those measurable characteristics that identify each case or distinguish one case from another; they may represent a condition, feature, attribute, or behaviour that can be observed or controlled," (Talbot, 1995, p. 374).
There is a close link between multiple regression and another common multivariate test, called the ANOVA. (Polit, 1996). The statistical Analysis of Variance or ANOVA is a sophisticated test to determine if there is a significant difference between several means simultaneously. The resultant differences are reported as an F ratio. ANOVA serves the same purpose as the t-test, giving the ability to process several arithmetic means at once, which significantly reduces the possibility of Type I and II errors. It compares the amount of variation between the samples with the amount of variation within each sample - hence the name, "analysis of variance." Researchers can examine several means by working with the variance, which is the square of the standard deviation (Argyrous, 2000).
A Simple or One Way ANOVA is done when there is one factor or one treatment variable and there are more than two groups within this factor. ANOVA deals with one continuous dependent variable and more than one independent variable. A more complex type of ANOVA is called a Factorial Design where there is more than one treatment factor involved. Factorial analysis determines the underlying structure of a set of variables , how they cluster together to form a unidimensional construct by analyzing all of the intercorrelations among them. Variables are sorted into categories according to how closely related they are to other variables (Gillis & Jackson, 2002).
The Analysis of Covariance or ANCOVA test is used when a confounding variable is in operation, usually due to a data group that is not truly randomly assigned. "The central question for ANCOVA is the same as for ANOVA: Are mean differences between groups "real," or are observed mean differences in a sample likely to have occurred by chance?" (Polit, 1996, p. 305). There is also a nonparametric version of ANOVA called the Friedman Two-Way Analysis of Variance by Ranks.
Another complex version of this test called Multiple Analysis of Variance or MANOVA is used when more than one dependent variable is being examined. MANOVA determines the effects of independent variables on dependent variables. The MANOVA F test provides the measure of significance between groups or a test of the group differences across the dependent variables for a given probability of significance. It is designed to test differences between two or more groups on two or more dependent variables simultaneously. "Typically, MANOVA is used in the context of experimental designs in which the investigator has randomly assigned subjects to different treatment groups," (Polit, 1996, p. 318). The MANOVA is less powerful than the ANOVA, since it requires more subjects to reject the null hypothesis, given the same effect size, significance criterion, and desired power. It also involves more assumptions and may lead to more ambiguities in the data. Another version, the Multiple Analysis of Covariance or MANCOVA is essentially the same as the MANOVA, except that it accommodates metric covariates. It involves adjustments to the composite dependent variable prior to the assessment of the effects of the independent variable. The MANCOVA adds more power, making it less likely that a Type II error will occur in the analysis. "The power increases as the correlation between the covariates and the dependent variables increase," (p. 323).
Ends In View
This learning activity is intended to provide learners with the opportunity to:
1. Explore the nature of multivariant relationships and analysis.
2. Understand the rationale for the various modes of analysis of variance.
3. Explore the process of reporting analysis of variance inferences.
4. Practice analysis of variance using a computer software program.
5. Critique the inferential data analysis process described in a select research study.
In Preparation
1.VIEW: the Powerpoint Study Presentation: Broussard, G., Graham, J., Reichig, D. & Ryan, M. (2001). Visual Noise: The Role of Site Clutter in Advertising Branding Effectiveness.
2. READ: Plonsky, M. (2001). One Way Analysis of Variance Psychology Statistics. University of Wisconsin.
3. READ: Plonsky, M. (2001). Two Way Analysis of Variance. Psychology Statistics. University of Wisconsin.
Assignment 2: Complete the assigned Worksheet 5: Analysis of Variance (will be given out in class, or can be downloaded from the Kwantlen protected site on the campus Online Courses site). Save your work and submit with the other four worksheets given out in the other four quantitative learning activities. NOTE This is NOT the worksheet in your course materials - that one is for practice.
In Practice
1.Participate in class discussion related to the process of analysis of variance.
2.In pairs, complete Worksheet No. 11 noticing the various aspects of using multivariant techniques, especially analysis of variance statistics.
3.Explore the use of display in the process of inferential data analysis with analysis of variance statistics.
4.With the class, critique the analysis of variance process used in the assigned study by Broussard, Graham, Reichig & Ryan.
In Lab - Introduction to Vassar Analysis of Variance Software Program
1. 1.Attend lab to familiarize yourself with the software and analysis of variance statistics.
2. Begin to work with quantitative data by performing Analysis of Variance statistics using the Vassar software as directed during lab session.
In Reflection
1. Reflect on your comfort level with using the software for analysis of variance.
2. How do multivariant statistics add depth and understanding to nursing research and evidenced based practice?
References
Argyrous, G. (2000). Statistics for social and health research: With a guide to SPSS. Thousand Oaks: Sage.
Dempsey, P. & Dempsey, A. (2000). Using nursing research: Process, critical evaluation, and utilization. Philadelphia: Lippincott.
Gillis, A. & Jackson, W. (2002). Research for nurses: Methods and interpretation.
Philadelphia: F. A. Davis.
Plonsky, M. (2001). One Way Analysis of Variance. Psychology Statistics. University of Wisconsin.
Plonsky, M. (2001). Two Way Analysis of Variance. Psychology Statistics. University of Wisconsin.
Polit, D. (1996). Data analysis and statistics for nursing research. Stamford, CT: Appleton & Lange.
Polit, D.,Tatano, C.& Hungler, B. (2001). Essentials of nursing research: Methods, appraisal, and utilization. (5th ed.) Philadelphia: Lippincott.
Talbot, L. (1995). Principles and practices of nursing research. Toronto: Mosby.
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