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

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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