# T tests - To test for central measure (means) - Steel supplier

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#### DJN

The company wishes to use a new steel supplier and have asked the quality department to carry out an assessment. They need to know if the new steel gives better results than the old steel on certain operations. I have assumed that a t test is to be used. I say assumed, because I have been thrown in at the deep end on this one and am struggling a bit. Now, I have the results of the t test done in Excel, but, I have no idea what the figures really point to. I would be grateful if some kind soul could explain the results to me. And, is the t test the appropriate test to use?

David

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#### Dave Strouse

Devil in the detail

DJN -

I bet many of the kind souls here would be glad to help (and even some of the crusty old grumps like me!).

What is it that you are measureing? Is it attribute or variable? How many samples ? How was it collected? What do you consider better?

Dave

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#### DJN

Hi Dave. Thank you for taking the time for replying. What I am measuring is the width of a part. The data is collected using a calibrated micrometer and the dimension is a variable. The sample size is 10 parts from each batch run. There were no changes made during each run, so there were no other influences introduced. What do I consider better? Well, that is a good question. I have to say that what would be considered better is less variation from one set of parts to the other.

Many thanks

David

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#### Darius

DJN, you said:
Now, I have the results of the t test done in Excel....

and

I have to say that what would be considered better is less variation from one set of parts to the other.

t-test is just to test for central measure (means), if you are using f-test is ok for variation. I used many times to check for a change on a process "F" test for variances and afterwards "t" (because "t test"depends on the equality of the variances), to see if the mean changed.

Another way to do it (but you need a sample bigger) and is not a test on it self, is using capability/performance index (if you have specs limits), but keep on mind the limits of the the capability index, don't just calculate the index, calculate the minimum and maximum of the index because the dependence of the sample size of such indicator.

I tink the "F" and "t" test could be it.

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#### DJN

Thanks Darius. I think I will use the f test as suggested, as the sample size I have is small.

David

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#### Dave Strouse

Be aware

that estimating variances using an F-test (BTW should always be capital F, after Ronald Fisher, one of your countrymen) is a ratio test of two variances and is not very discriminating for small sample sizes.

By that I mean that you will have to see something on the order of a 40% reduction in the standard deviation of the new versus old or it will not be significant. The critical value at the commonly accepted significance of 0.95 and samples of nine degrees of freedom in both is 3.

So to claim statistical significance, you will need variances in the ratio of 3:1 and that implies standard deviations in ratio 1:0.57.

Solution: more samples or less certainty in the decision.

Nine samples is adequate to give could estimate on difference in means by t-test but is a bit light for variances.

Of course if you really have improved the variance that much with the mnaterial change it will be picked up, but a 300% improvement in variance does seem like a whole lot.

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#### Richard-jxb

Hypothesis Test Flowchart

I should like add that: (to my thinking)
1.first of all, you should do normality test,
2.F-test is necessary before t/Z-test;
3.you can set confidence level at 99.0%

sorry! I tried to attach the Flowchart but failed.

#### foxwilds

##### Starting to get Involved
I need help also.
We have a Micro-Vu vision CMM to measure plastic closures-Caps. We just added a touch probe option to the machine. I've set-up the measurement program to measure the cap with vision then by the touch probe. I' looking for input on what kind of statistical tests I should be using to compare the results. T test, Bland Altman, Coorelation Coeefficient. I'm not a real stat guy..I just play one on TV.

Thanks,

Perry