Applying a T-test to Answer a Business Question

The Problem

Nonprofit X provides transportation services. One way that Nonprofit X generates revenue is by entering into incoming-generating contracts. One such contract is longstanding with the local mass transportation system, Y. Nonprofit X operates some of Y’s transportation services.

Recently, the deployment structure of Y’s transportation service has changed, causing the Nonprofit X to lose money on a historically profitable contract. Previous deployments filled the day with back-to-back trips. Now deployments have significant gaps during the day.

Primarily, Nonprofit X suspects that drivers are spending more time driving to their first pick up and returning to base from their last drop off (deadhead time). This is causing Nonprofit X to lose money because they must pay the employee drivers to wait long periods between trips. In other words, Nonprofit X believes it is paying employees for time spent not generating income, resulting in a net loss.

The question posed for this analysis project is:

Is there a difference between “deadhead times” of drivers operating under the contract with Y in Quarter 2 of 2018 and Quarter 2 of 2019?

The Data

To answer the question posed in section A, I compared shift data from a profitable quarter with an unprofitable quarter to identify any difference in deadhead time (time spent paying employees without generating income). The severity of the change and correlated loss of income was analyzed.

I collected driver shift data comparing from Q2 of 2019 (net loss contract) with Q2 of 2018 (net profit contract). The data provided a picture of how time was spent during a shift. Specifically, I collected driver shift data, including: Time Clocked In, Time Left Base, First Pick Up Time, Last Drop Off Time, Time Returned to Base, and Time Clocked Out. Time data was quantified as military time.

I created a spreadsheet of driver shift data in part by pulling a report from Nonprofit X’s operations management database. This report contained driver shift data for drivers assigned to the contract with Y, including: Time Clocked In, First Pick Up Time, Last Drop Off Time, and Time Clocked Out. The spreadsheet was completed by manually entering shift data from paper manifests (documentation of a summary of each drivers’ daily trips). Manifests contained the missing data: Time Left Base and Time Returned to Base. 

Then I reviewed the data and deleted any erroneous entries to clean it. For example, one deadhead time value was >800 hours; this is incorrect because the value was higher than the 24 hours available in a day. A coworker also reviewed the data to check for errors before I began the analysis.

Using a T-test to Analyze the Data

I leveraged inferential statistics by conducting a two-sample t-test that compared the mean deadhead times of driver shifts of Q2 of 2018 and Q2 of 2019. According to the National Institute of Standards and Technology (n.d.) two-sample t-tests can be used to determine whether or not a new process is better or worse than a current one. In this case, we are curious to see if the deadhead times are more significant in quantity in 2019 than in 2018.

In total, I collected 1,035 deadhead times for Q2 2018 and 1,870 deadhead times for Q2 2019.

I calculated deadhead times using the following formula for every shift in a Google Spreadsheet. The method finds the difference in minutes between leaving the base and the first pick, plus the difference between the last drop and returning to base.

Deadhead time = ((First Pick Time  - Time Left Base) + (Time Returned to Base - Last Drop Time)) * 24

I installed the statistical analysis add-in, “XLMiner Analysis Toolpak,” and ran a data analysis. (XLMiner is equivalent to Microsoft Excel’s “Data Analysis” add-in.) Then, I ran the “t-Test: Two Sample Assuming Unequal Variances” test, resulting in the following:

t-Test: Two-Sample Assuming Unequal Variances

Q2 2018Q2 2019
Hypothesized Mean Difference0
t Stat6.668674376
P(T<=t) one-tail1.61E-11
t Critical one-tail1.645511763
P(T<=t) two-tail3.22E-11
t Critical two-tail1.960988757

The t-test helped to determine if there was a significant difference between the means of deadhead times in each quarter (MindEdge, 2017). Using this information, we can identify whether or not the recent changes in the contract deployment structure are likely to have contributed to the measurable loss in profit. Such information might be leveraged to renegotiate the contract terms.

The Results

The absolute value of the t-stat is 6.668674376 which is greater than the t-critical two-tail value of 1.960988757. The two-tail p-value of 3.22E-11 is less than the significance level of 0.05. Both methods indicate the alternative hypothesis that there is a difference in the means. The null hypothesis is rejected.

It is important to note that the significant difference reflects higher deadhead times in Q2 2018 than in Q2 2019 – the opposite of what I expected to find. Since the deadhead times were reduced with the contract’s new deployment structure, a different factor is causing Nonprofit X to lose money with the current contract with Y.

Next Steps

The next step is to share the information with Nonprofit X’s leadership team. This is an opportunity to confirm that our expectations were not correct and discuss other ideas.

Another recommendation is to complete data analyses of other factors that changed with the contract. For example, the new agreement subjects Nonprofit X to increased penalty fees that can be compared with previous, more profitable quarters. A different factor may be causing Nonprofit X to lose money with the current contract.

Zoe’s Skills and Behaviors Demonstrated:

  • Data analysis
  • Decision making
  • Organizational development
  • Problem solving


MindEdge (2017). Data-driven decision making. Waltham, MA: MindEdge, Inc.

National Institute of Standards and Technology (n.d.). Two-Sample t-Test for Equal Means. Retrieved from

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