Paired TTest Confidence Intervals
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February 14, 2008 at 7:43 pm #49354
I have performed a paired ttest on 77 samples before and after a process step. The paired ttest result has rejected the null hypothesis (Ho was outside the 95% tconfidence interval with a pvalue of 0.001).
My question is: am I correct in being able to use the 95% tconfidence lower and upper bound values to quantitatively say how much of a difference the process may be affecting the metric?0February 14, 2008 at 8:46 pm #168618Are you sure its a paired t that you should be using?
0February 14, 2008 at 9:04 pm #168619Hi Stan – I believe so, because each part is first QC’d inprocess while it is being manufactured to meet two specifications (metrics “A” & “B”), then continues through other process steps until the part is done (i.e. the final product), then this is when the final QC is performed. Each pair of data comes from both the inprocess QC and the final QC on the same part, the only difference on the part is that the final QC is performed after the additional process steps.
0February 14, 2008 at 9:15 pm #168620What is your null hypothesis?
0February 14, 2008 at 9:25 pm #168621My null hypothesis was that the Ttest of mean difference = 0 (pulled from the Minitab session window).
0February 14, 2008 at 9:35 pm #168622In plain English, your hypothesis is the process step has no effect
on the two metrics?The answer to your original question is yes the confidence interval
predicts the amount of difference the process is making.0February 14, 2008 at 9:42 pm #168623Correct. We are investigating whether or not we can stop end inspection of the parts and just use the inprocess QC results. Knowing how much the process impacts the results will help us determine if the maximum difference is very significant.
Thanks for your help Stan!0February 14, 2008 at 9:54 pm #168625Regarding your null and alternate hypotheses, are you only looking for a difference, or are you looking for a difference in a specific direction? I would presume that you want your difference to be in a specific direction, not simply “not equal to zero.”
Therefore your null hypothesis might be “sample 1 is less than or = to sample 2.” and your alternate hypothesis would be sample 1 > sample 2 (or whatever makes sense for your process).0February 15, 2008 at 6:26 am #168629Never really understood the need for a onetail T test…Why not run the twotailed test and simply note the obvious direction of difference?
0February 15, 2008 at 1:12 pm #168634
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.If direction matters then a one sided test will test the direction and it will provide a higher level of signficance than a two tailed test. For a small sample this could easily be the difference between detecting a signficant difference and not detecting one.
Section 9.5 of An Introduction to Medical Statistics 3rd Edition – Bland has a good discussion of the issue.0February 15, 2008 at 3:47 pm #168638Thank you Mr. Butler,
My point in raising this question is that the original poster was suggesting using the results of these paired ttests in place of inspection (which I agree with the idea). My concern then is that with a 2tailed test it could be very easy for the process to show significance in the wrong direction and if the person reviewing the results wasn’t paying attention might miss that fact by only looking at the pvalue. With a one tailed test, you build in some robustness so that you only see significance in the direction you are looking for.0February 15, 2008 at 4:45 pm #168642I am confused somewhat by this. The alpha level (typically 0.05) denotes the amount of alpha risk you are willing to take. (i.e. saying something is significant, when it is not.) If you are using a 2 sided test then you split that alpha between the 2 tails so that basically each tail has 0.025 of that alpha level. This determines the critical value that on the low end () if the results are greater than this critical value then the thing you are testing is significant.
When you do a one sided test then the whole alpha risk is just on that one side, so it would seem the critical value would change. For example if you are test > (rather than ) , then does the critical value at which you deem the results significant change?
It seems that if you do a one sided test, then you would have a lower value at which to claim a difference than you would if you did a 2sided test.
Can someone explain if that is right or wrong.0February 15, 2008 at 7:21 pm #168647Thanks Robert! But “providing a higher level of significance” is confusing to me….I thought the significance level (alpha) was a fixed value chosen by the investigator for tests of significance, not determined/provided by the test. Could you briefly explain? Thank you again!
0February 15, 2008 at 7:46 pm #168650
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.T Test – anon’s earlier post summarizes the situation.
For a two sided test the critical t statistic is
t1á/2(n1) whereas for a one sided test the critical value is t1á(n1)
So for a two sided test at the 95% the critical t value in the limit is 1.96 whereas for a one sided test the critical value is 1.645 thus the value of the t statistic is smaller for the one sided than the two sided which means you wouldnt need as large a value for your one sided test statistic before you declared a significant difference.
0March 1, 2008 at 9:23 am #169152As you know one to the key characterisitics of the Paired T test is the data pairing must be consistant throughout the test, unlike any other hypothesis test. So I would check that the entered data has remained in pairs this includes the samples order too. The test is based off comparing the difference for each paired measure. So you are correcty in terms of stating the absolute difference between measured samples.
I would just check for typo’s or data entry issues if you have got an unexpected Ho.
What may be interesting and may be beyond the bounds of your question is to plot the relationships between the measured samples and see if there are one or more of the 77 samples which you struggled to get the same measure. If you can explain them being there you may want to remove them from the data set and rerun to see if Ho still stands?0 
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