##### One-way analysis of variance (ANOVA)

One-way analysis of variance (ANOVA)

**Order Instructions:**

Your Data Interpretation Practicum

This week, you will run either t tests or ANOVA on your chosen data. This Application requires you to engage in data interpretation and to select the appropriate analyses for your hypotheses and for the data that you have at your disposal. Toward that end, you should consider which analyses will inform the reader and allow you to pursue your questions.

Your submission to your Instructor should include your SPSS output file of your selected statistical analyses in a Word document, along with each of the following elements:

your SPSS output, including graphical representations;

your narrative interpretation; the governing assumptions of the analyses you ran; the viable and nonviable hypotheses (null and alternative); and the relevant values (such as a P value indicating statistical significance or a lack thereof).

Be sure to indicate to your Instructor why you selected the analyses that you did. In other words, why did you select t test over ANOVA or vice versa? Why one-way or two-way? How is this analysis related to the hypothesis?

I will send the data set to be use via email.

**SAMPLE ANSWER**

**One-way analysis of variance (ANOVA) **

The one-way analysis of variance (ANOVA) is a powerful data analysis tool which is used in determining if there are any significant differences between the means of two or more independent groups (even though what is often used in cases where the minimum number of groups is three, instead of two groups). For instance, in this data interpretation practicum the one-way ANOVA will used to carry out the data analysis with an aim of understanding whether injury rate differed based on the site of work, dividing workers into three independent groups (e.g., Boston, Phoenix and Seattle). In addition, it is imperative to recognize that the one-way ANOVA is an *omnibus* test statistic meaning that it cannot provide information on the specific independent groups with significant differences from each other, but only provides information on at least two significantly different groups.

The governing assumptions of the one-way ANOVA include: (1) the dependent variable measurement should be done at the ratio or interval level meaning they are continuous; (2) there should be two or more categorical independent groups of the independent variable; (3) the observations should be independent; (4) there should be no significant outliers; (5) there should be normal distribution of the dependent variable for each independent variable category; and (6) there should be homogeneity of variances. The data analysis and interpretation is guided by the proposed null and alternative hypothesis. For example, considering that that study variable in this task is the injury rates across three independent work sites (e.g., Boston, Phoenix and Seattle), then one-way ANOVA can be conducted to determine if there significant differences in injury rates across the three work sites. Thus, the null and alternative hypotheses are stated as follows:

Null hypothesis (H_{0}): mean_{boston} = mean_{phoenix} = mean_{seattle}

Alternative hypothesis (H_{A}): mean_{boston} ≠ mean_{phoenix} ≠ mean_{seattle}

**SPSS Output **

** **The null hypothesis stated as H_{0}: mean_{boston} = mean_{phoenix} = mean_{seattle}; is not rejected because the overall F statistic was not significant [*F*(2, 15) = 0.31, *p* > .05]. This indicates that the injury rate means across the three work sites are not significantly different. The reason why ANOVA was chosen over t-test is that it enables comparison of more than two means making it the appropriate choice because the dataset consisted of three independent group means (i.e. Boston, Phoenix and Seattle).

** ****References**

Bernard, H. R. (2000). *Social research methods: Qualitative and quantitative approaches.* Thousand Oaks, CA: Sage Publications.

Boslaugh, S., & Watters, P. A. (2008). *Statistics in a Nutshell – Research Design.* Sebastopol, California: O’Reilly Media, Inc. Retrieved from http://proquest.safaribooksonline.com/book/-/9781449361129 (Accessed on November 29 2015).

Campbell, D. T., & Stanley, J. (2010). *Experimental and quasi-experimental designs for research, *(Laureate Education, Inc., custom ed.)*. *Mason, OH: Cengage Learning.

Creswell, J. W. (2008). *Research design: Qualitative, quantitative, and mixed methods approaches*, (3^{rd} ed.). Thousand Oaks, CA: Sage.

Green, S. B., & Salkind, N. J. (2008). *Using SPSS for Windows and Macintosh: Analyzing and Understanding Data, *(6^{th} ed.). Upper Saddle River, NJ: Pearson Publishers.

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