Communicating ANOVA Results using SPSS

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


Bar Chart of Wait Time Averages

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:

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:

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:


ANOVA Output Using SPSS

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:


The Statisticians’ Way

The role of classically trained Statisticians is to answer questions with data and communicate the logic behind the results. Rarely does a statistician attempt to bridge the gap between statistical logic and practical interpretation unless there is a content expert working closely with the team.  The typical method for communicating statistical findings follows a seven step process called Hypothesis Testing.  There are many great places online to learn more about Hypothesis Testing (

Step 1 – General Question: Someone asks a question and wants an answer based on numerical evidence, and expects the closest thing to fact that is humanly possible. The questions may sound like this. Is there an HR problem in the Company? Do I need to hire new people? Why are sales higher in the Northeast? What does the public think of our new product? How can we improve our public image? None of these questions are statistically measurable until translated into research questions.

Step 2 – Research Question: This step involves translating general questions into a series smaller, measurable questions. General Question: Is there an HR problem in the Company? Research Question: How trustworthy are the employees in Company X as measured by the Employee Trustworthiness Scale? Research Question: Is trustworthiness different between genders in Company X using the same measure?

Step 3 – Hypotheses: Statisticians use data to answer questions. Since 100% certainty is not possible, statistical answers are given within a degree of measurable certainty, and written as Hypotheses. Hypotheses are “plausible” explanations among many. For example, “There is no significant difference in Trustworthiness between genders” is a plausible Hypothesis to consider. (I will write more about the mechanics of Hypothesis testing in a future article).

Step 4 – Analysis Plan: You may have many Hypotheses to test. Each Hypothesis may require a unique calculation. And, each calculation may have a unique set of assumptions to consider. A well written analysis plan is essential to understanding and communicating the statistical findings in a way that is relevant to the audience.

Step 5 – Calculate a Statistic: The Hypothesis, type of data, and sample/population size dictates the appropriate statistical test. With hundreds of test to choose from, there really is no magic for knowing what test to use. However, there are several “cheat sheets” available online (I will write more later about the mechanics of Hypothesis testing and how to use calculated statistics).

Step 6 – Compute Probability: The calculated value of a statistical test “alone” is not very informative. The Hypothesis testing process uses the calculated value to make inferences. The values are compared to computed probabilities that form the basis of the conclusion (I will write more about the mechanics of Hypothesis testing and probability in future articles).

Step 7 – Present Results: Presenting statistical results is very different from interpreting results. Presenting results follow a structure that may vary slightly depending on the statistic, but generally looks like this:

1. Chose a Test: ie: t-test
2. Calculate a Result: ie: t(df) = t-value, p = p-value
3. Significant? Yes / No
4. Null Hypothesis: Reject or Not Reject
5. Therefore: There IS or IS NOT a significant difference between two means
6. Conclusion: Make a statement that summarizes all previous steps