stat question--comparing slopes?

Factual Questions
1

Here is my data:

  1. about 50 locations
  2. use of job tool per month
  3. completed products per month
  4. 33 months

If it helps, we can start with describing how to look at the question in one month, and then move on to the time series issues.

Here are my questions:

  1. Does using the job tool increase the number of completions?
    I do know that as completions go up, tool usage goes up, but does that mean that locations who complete more products use the tool at the same rate as those completing fewer products (so if it is used once every five products, a slow location will use it twice for 10 products in a day, and a fast location will use it 3 times for 15 products in a day). What I want to know is if the faster locations use the tool significantly more often than the slow locations, e.g., they use it for every 4.5 products, say, whereas the slower stations use it every 5 products.)

The best way I can think of this is to test that the slope of the regression line predicting completions based on tool usages is sig. greater than 1.

–Am I formulating this correctly?
–Is there such a stat?

  1. Based on 1, does the relationship change over time? What stat would I use for this—time series on slopes? Is there such a thing?

Thanks! I’m trying to keep people here at work from claiming that the tool increases production, just because quicker sites use it more often. (Of course, it could increase production even if the slopes are equal, but it has done it equally at slow and fast sites.)

Just that fact that everyone uses it pretty frequently is good news in and of itself, I just don’t want to extend the claim beyond where we can support it.

Thanks for any help!

2

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3

This isn’t an easy question.

I dont’ think the problem is set up to properly answer your question. To really design the experiment from the ground up, you’d have to randomly assign each shop to a specific tool usage. You’d have to design it to account for a “time effect”.

If you had 50 shops, and you were sure they were independant of each other, and the distribution of the usage of tools and completion of jobs saitisifed certain requirements, you could do a regression for a single month, and then test whether the regression line was significantly different than 0 (not 1). That might tell you something, but I wouldn’t want to say too much about it.

Your second question, “does the relationship change over time?” is more heavy duty. I’m not sure how to handle it. Even some statistics students don’t start seeing Time Series Analysis until graduate school. Some electrical engineering students might do more with it in undergrad years.

I don’t think you want to draw any firm conclusions with what you have.