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I'm trying to calculate the number of "participant*hours" for participation in a program.

I have the following variables/data: 1) Total # of sessions given throughout the program. 2) Average duration (in hours) of each session. 3) Average # of participants in each session.

So, for example, if 84 sessions were given with a duration of 0.75 hours per session, and about 25 participants per session, what would be the proper way of calculating a figure with the units "participant*hours"?

By simple multiplication and unit cancelation, it seems the calculation should be:

Total hours = (84 sessions)*(0.75 hours / session) = 63 hours

Total # of participants = (84 sessions)*(25 participants / session) = 2,100 participants

(2,100 participants)(63 hours) = 132,300 participanthours

Is this the proper way of obtaining "participant*hours"? I ask because the figure seems very high.

Thank you in advance.

Lucas
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  • This depends on whether the 25 participants per session are the same across all sessions or different. If 25 people each participated in the same 84 sessions (which lasted a total of 63 hours), then the number of participant hours should be $25\text{ participants} \cdot 63\text{ hours}=1575 \text{ participant hours}$. If the 25 participants were different for all 84 sessions, your computation is correct. If some people did multiple sessions but not all sessions, you need more information. – kccu Dec 05 '15 at 20:31
  • Thank you for your input @kccu. That is the issue I am struggling with. I know for certain that some participants participated in multiple sessions but I don't know which ones or how many. I think I could footnote my assumption, and treat all participants across multiple sessions as unique. – Lucas Dec 05 '15 at 21:37

2 Answers2

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Your calculation of participant hours is reasonable. You don't need to worry about whether the participants in each session are the same or different. If one person comes to five sessions of 0.75 hours each, that is still $5 \cdot 0.75=3.75$ participant hours. Whether that is more or less valuable than five different people coming for $0.75$ hours each is not addressed by this statistic. As long as there were $84$ sessions, all the sessions were $0.75$ hours and the mean number of participants in each session is $25$ you are set. In this case you only have one number that varies-the number of participants. If the sessions vary enough that you care, even though the length averages $0.75$ hours, you could worry that the short sessions were more heavily attended than the long ones. If you have a correlation between length and attendance, you can't multiply the two averages. For a four session example, you might have three sessions of $0.25$ hours each and one of $2.25$ hours. The average is $0.75$ hours. Then you have only four people at the long one and $32$ at each short one. The average attendance is $25$. The number of participant hours is not 4 sessions times 0.75 hours times 25 participants, which would be 75. Instead it is $2.25\cdot 4+0.25\cdot 32=17$ This is extreme, but it shows the problem.

Ross Millikan
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  • Hi, thank you for your confirmation and further exploration of the nuances in the potential calculations. I understand your explanation on how one would go about calculating the participant hours if the number of participants and session durations varied. The data we collected / requested from the programs did not get that much specificity so I would not be able to determine if there is a correlation between # of participants and session length. If I did have such specificity in the data, your suggested approach makes sense. – Lucas Dec 06 '15 at 04:42
  • If you don't have the data, your approach makes good sense. You will be vulnerable to accusations that this correlation is present and your numbers are wrong. For example, suppose this is a continuing education requirement in some profession. The practitioners might know which courses ran short and preferentially sign up for those. You would be claiming more training goes on than is the fact. You are assuming the number of participants is independent of the actual duration. That may well be reasonable, but without the data it could also be wrong. – Ross Millikan Dec 06 '15 at 05:03
  • I agree. In phase two of the program, we plan on capturing different metrics, so this particular consideration should not be an issue in the future. – Lucas Dec 06 '15 at 05:31
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After digesting the feedback received and other resources, I believe the calculation that yields the correct units (i.e., "participation*hours") and makes conceptual sense is:

$$[(# participants × # hours) ∕ session]×(total # of sessions)$$

Lucas
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