Hypothesis test – advice please
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January 30, 2008 at 9:32 am #49228
I have 80 units running. They need an average of just over 1 repair per month but of course the actual number varies month to month (Std Dev = 1.3) The plan is to modify 40 of them and compare results to see if the reliability is improved. The target is to reduce the repairs by 25%. So I would expect 40 repairs per month on the control group and hopefully 30 on the modified group. But how many months data do I need to collect?
The two sample t test sounds appropriate – correct?
Using Minitabs power and sample size I am unsure what difference to input – is it the difference in the number of repairs e.g. 40 – 30 = 10 or is it the difference in the mean 1 – 0.75 = 0.25?0January 30, 2008 at 1:34 pm #167977
6Sigma Below The BeltParticipant@6SigmaBelowTheBelt Include @6SigmaBelowTheBelt in your post and this person will
be notified via email.Your 25% will represent the hypothesized p BUT you still need to determine the difference to detect. Let’s say you would like to detect difference by 10% then your alternative p (in mtb) will be 15% or 35% (any which way will do since mtb will adjust the right sample size as it approaches 0.5)
0February 1, 2008 at 12:08 pm #168070I wold say 8 months, if you want a power of 0,8.
Power and Sample Size
2Sample t Test
Testing mean 1 = mean 2 (versus >)
Calculating power for mean 1 = mean 2 + difference
Alpha = 0,05 Assumed standard deviation = 1,3
Sample Target
Difference Size Power Actual Power
0,25 336 0,8 0,801006
The sample size is for each group.
Jan0February 1, 2008 at 1:01 pm #168072Thanks Jan
For 40 machines x 8 months I have
Power and Sample Size
2Sample t Test
Testing mean 1 = mean 2 (versus <)
Calculating power for mean 1 = mean 2 + difference
Alpha = 0.05 Sigma = 1.3
Sample
Difference Size Power
0.25 320 0.7838
0.17 320 0.5030
So, quoting Minitab
The power of a test is the probability of correctly rejecting H0 when it is false. In other words, power is the likelihood that you will identify a significant difference (effect) when one exists. © All Rights Reserved. 2000 Minitab, Inc.
The null hypothesis is that there is no change.
If the modification does in fact achieve 0.25 we have 78% probability of correctly concluding this but if the result of the modification is say only 0.17 we have 50% probability of drawing correct conclusion?
0February 1, 2008 at 1:20 pm #168073Yes, if you only get 0,17 your power is reduced.
If you want a bigger power, you need more data.0February 1, 2008 at 1:32 pm #168074Jan,
Thanks again – I think I now have this clear in my head.
Glen0February 4, 2008 at 12:18 pm #168139So, while you’re waiting your 5 to 8 months (you can get reduced power of the test with a shorter time period too), make sure you are graphing the repair rates of the units. If in the first month, the 40 control units have each 1 repair and the 40 modified units have, say only 10 repairs, you’d be feeling pretty good about the modification. If in the second month, the trend is still the same, 40 vs 10, you’d be feeling even better. Suppose the third month brings 40 vs 25, you’d lose some confidence but overall, your disposition would still be sunny. Now, come the 4th month and you have 40 vs 30, you’d probably be about ready to claim the modification is a success but the upward trend might give you pause.
My point is to keep an eye on the overall output and judge it practically and graphically, as well as analytically. You might find that within a few months, you can declare victory and move onto the next battle.
Good luck!0February 4, 2008 at 1:12 pm #168141Good advice. I suspect my problem will be either to
calm down the optimists who want to declare victory after one month of 40 v 30
or
ask for patience from the doom mongers if the first month turns out 36 v 340 
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