# paired t vs two sample t

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• #48421

Nwajei
Participant

Can I get a clear explanation, of what the difference between these two test are???
when is it best to use a paired t, over a two sample t test?

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#163101

Six Sigma guy
Member

Giving an example would make it clear:
1) Two Sample T-  Used to make inference about the difference between two population means based on data from two independent samples. For Example: If you want to check if the productivity of process A is significantly different from productivity of process B then you go for two sample T
2) Paired T – Used to make inference about the difference between paired observations – which means two data sets/observations are dependant or related to each other. For example – If you want to check for differences in mean productivity of a person before and after taking a training then you can go for paired – t test.
Thanks
Six Sigma guy

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#163102

Nwajei
Participant

thats what i was looking for…dependent vs idependent…that explanation really clears it up in a simplistic way…
thanks champ!

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#164075

Mikel
Member

When the data meet the paired T-test requirements, it is preferable because it has more degrees of freedom.

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#164090

Bob Rome
Participant

To be a little more specific, each data point is paired with another data point and has a dependent relationship, so you are testing that difference, not the difference between pairs.  That variation is cancelled out.  I use a trainig example to explian this using tennis shoe wear testing on boys – using 2 different rubber compounds on say 10 boys.  Some boys sit and play x-box all day and some are climbing trees right, but you’re only interested in the difference in within (rt/lt foot) wear not between (boy/boy) – that would muck up the results.  That’s what the paired t tests, but you have to pair the data like you would for corelation/regression analysis.  Hope that helps.

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#164102

Chris Seider
Participant

And do you know where that example comes from?…..
It is great example.

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#164103

Tennis shoe example
Member

Tennis shoe example: Rath & Strong, before that Oriel consulting, before that ask Linda.

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#164104

Erik L
Participant

Umm…Try, BH^2

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#164105

Chris Seider
Participant

It is always interesting to see how history is forgotten….of course, I have forgotten or not known many myself.
It would be fascinating to see how much interpollination has occurred among the old (or is it original?) sources and the how many of the various pieces of training material out there have commonality.

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#164106

Bob Rome
Participant

It’s from the help file in MiniTab.  If you have it, go to the paired t test dialog box, click help and then “example”.  There is a worksheet with the data in there too.

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#164108

Tennis shoe example
Member

This exercise would happily profit a few lawyers :-). Moral of the story: If you don’t license Minitab, don’t use the tennis shoe example. If the consultant uses the example, and you don’t have Minitab, you know the consultant may have a problem :-).

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#164110

clb1
Participant

It may be from the Minitab help file but, as Erik noted, you might want to look at Box, Hunter, Hunter Statistics For Experimenters, 1978, pp.97-102.  It wouldn’t surprise me to find out this book was the source of the Minitab example.

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#164113

Bob Rome
Participant

From time to time I do see Six Sigma training slides and examples that are near identical from different sources.  I think they float around like urban legends – it’s rampant.  MiniTab doesn’t show a source credit for the example and I doubt, as a previous poster eluded, any lawyer would take the case.  You know what they say – “Steal one thin and it’s plagerism, steal a bunch of stuff and that’s research!”

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#164114

Tennis shoe example
Member

Yep, clb1 that’s where the example comes from. But there are now ways to take the data collection plan right into the field. You’ll love the attached site: Make Six Sigma data collection real time with real life experience. Way to GO!!!
http://walkacrosstexas.tamu.edu/Data/WAT/wat.html

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#164118

BTDT
Participant

Frank:The best example make sense to everyone listening. In the old ads for washing detergent, they would show the difference between Brand X and Scudzo using a paired two sample t-test. They didn’t say so, but the logic would ‘prove’ the different between the two detergents.The idea was to have a variety of stains and fabrics and compare the performance owing to JUST the detergent.If they did not tear the dirty shirt in half and wash each half in each detergent, they would have a set of twins play soccer and wash the two uniforms in the separate detergents. The side-by-side comparison is logically valid, even if the fabric or stains differ.No-one, even the dim witted consumer typical of the ads, would not accept a comparison between socks vs. shirts, or shorts vs. socks (2 sample t-test). Everyone would accept the comparison of left sock vs. right sock or shirt vs. twins shirt.It all has to do with minimizing the variation to only one variable and holding all others constant.Cheers, Alastair

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