In the previous article “*Communicating Many More Means”*, call wait time average is compared for five weeks. The bar chart shows the results:

However, missing is a statistical test to determine if the five-week averages are truly different.

**General Question:** A manager isn’t convinced the trend is meaningful. The department just completed Phase 1 of an organizational restructuring and modified how calls to the centre are prioritized. There is a planned Phase 2 of the project. But, before the project can begin the manager must know if the change in wait time is real effect or simply due to chance.

**Research Question:** Asking if the change in wait time is real is translated into the following research question. Is there a significant difference between the average wait time for the five-week period of data collection?

**Hypotheses:** Once the research question is agreed to, it is rewritten into a Null and Alternative Hypothesis. The Null Hypothesis for the ANOVA test is written as: there IS NO significant difference between the five group averages. The Alternative Hypothesis is written as: there IS a significant difference between the five group averages.

**Analysis Plan:** The One-Way ANOVA is the best statistic to use when testing differences between three or more group averages. In the case of wait times, there are 5 group averages, one for each week of the data collection timeframe.

For more on how to pick the best statistical test please visit:

http://www.ats.ucla.edu/stat/mult_pkg/whatstat

**Calculate Statistic:** Calculate the average Wait Time for each week using IBM SPSS Descriptive Analysis. Use the One-Way ANOVA to determine if the difference between the five group averages is significant.

**Compute Probability:** When the results of the One-Way ANOVA show that the null hypothesis has less than a 1% chance of being right, we reject it and suggest the alternative hypothesis is worth considering.

For a good discussion of p-value please visit:

http://askville.amazon.com/explain-concept-p-value-simpleEnglish/AnswerViewer.do?requestId=6438921

**Communicate Results like a Statistician:** The results of the One-Way ANOVA are: f=-53.255 (df:4), p<.01. The results are significant. Therefore the Null Hypothesis is rejected. The One-Way ANOVA test determine there IS a significant difference in the average wait times for the five weeks that were measured.

Note: For this article I generated random numbers to approximate the Call Centre Wait Times. The results of the ANOVA are pictured here:

The ANOVA test can determine if group averages are significantly different. However, the ANOVA doesn’t identify what groups, or in this example what weeks are different. For example, it is obvious that the average wait time of 121 seconds for week one is higher than the average wait time of 80 seconds for week four. But, can the same be said of weeks four and five; 80 and 85 seconds respectively? A Post Hoc test is needed to know what groups are statistically different from one another. I will discuss Post Hoc test in a future article.

To learn more about the One-Way ANOVA in SPSS please visit:

https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php