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:

BarChart

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:

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:

ANOVA_Output

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:

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

Communicate Many More Means

Business Intelligence Dashboards present frequencies, percentages and averages in one convenient location.   In this example, there are five average “Wait Time” scores compared for meaningful differences.  Each average Wait Time score represents a single week of calls to a Government Department. Total number of calls, or “n” appears in the Total Calls column.  It is important to know “n”, in this case call volumes, when interpreting averages.  Calculated Wait Time averages appear in the Average Wait Time  column (second table). There is no need to guess from the bar chart what the exact values are.

Many More Means

This example is from a Government Website (http://www.tpsgc-pwgsc.gc.ca/pension/qenrcm-hdwdtm-eng.html).  It’s a great resource with lots of interesting analytics on key performance indicators.

General Questions From an Operations Manager:

Is the Wait Time average downward trend a good thing?  Are Wait Time averages really different for each week?  Is there a significant improvement in Wait Times over the five-week period?  What does the increase in the last week suggest?  Should something be done to make improvements in our service delivery since it looks like Wait Times are going back up?  Do we hire or fire call centre staff?

Research Questions From the Analytics Manager:

Are the differences in the average Wait Times statistically meaningful?  If they are, what month(s) show the greatest improvement?  Depending on the statistical results, are the changes in average Wait Time practically meaningful?

Hypothesis From the Statistician:

Ho:  There is No statistical difference in average Wait Time for the five weeks.

Ha:  There IS a statistical difference in average Wait Time for the five weeks. 

Statistical Test:

The One-way Analysis of Variance (ANOVA) is the appropriate statistical test to use when comparing the differences between three or more averages.

Results & Interpretation:

In this example, the ANOVA will determine if the observed differences in average Wait Time is statistically different.  The chart suggests a dramatic downward trend with large differences.  The ANOVA test will help managers make a practical interpretation of the apparent trend.  For example, if the downward trend is statistically significant, managers may check customer satisfaction to confirm if a decrease in Wait Time by 41 seconds really improves service? If the trend is statistically significant, managers may also want to reward staff for their excellent performance.

More about the ANOVA test: http://www.csse.monash.edu.au/~smarkham/resources/anova.htm

ANOVA test in SPSS: https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php

Communicating t-test Results

General Question:  Your employer says, I think men take more sick days then women in this company, and we need to do something about it.  Let me know what the stats are.

Research Question:  Is there a significant difference between the average number of sick days taken by men and women in the past 12 months?

Hypotheses:  There IS NO significant difference between average number of sick days for men and women during the past 12 months (Null Hypothesis).  There IS a significant difference between average number of sick days for men and women during the past 12 months (Alternative Hypothesis).

Analysis Plan: Because the research question is about differences between two averages, Male and Female average sick days, the Independent groups t-test is the best statistic to use.

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 number of sick days for male and female employees using IBM SPSS.  Use the Independent Groups t-test to determine if the difference between the average Male and Female sick days is significant.

Compute Probability:  When the results of the t-test 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 more on the concept of the p-value please visit:

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

Communicate Results like a Statistician:

Mr. Boss, we used an Independent groups t-test to determine if there is a significant difference in the average number of sick days taken by male and female employees in the past 12 months. You will be happy to know that the results were: t=-3.7341(198), p<.01 and the results were significant.  Therefore we rejected the null hypothesis. 

Therefore there IS a significant difference between the average sick days for men (50.1) and the average sick days of women (54.99) in the past 12 months.  

Women in this company took more sick days than men in the past 12 months.

IBM SPSS Output for Independent Groups t-test:

IBM SPSS t-test Output

IBM SPSS t-test Output

To learn more about the t-test used in this article please visit:

http://www.ats.ucla.edu/stat/spss/output/Spss_ttest.htm

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 (http://stattrek.com/hypothesis-test/hypothesis-testing.aspx).

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