# Confidence Intervals

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• #48370

Robino
Member

If you know the confidence intervals of two different sets of data do not overlap, is there any statistical value-add in running the hypothesis test?

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#162819

Dillon
Participant

If the CI are close, i.e., they just barely overlap or just barely miss from overlapping, I would run a statistical analysis.  On multiple occassions I’ve seen confidence intervals that were “close” and had the hypothesis test indicate differently–the slightly overlapped but were statistically different and vice versa.  It doesn’t cost anything but a few key strokes, so it’s better to have the p-value and know for sure than to make a decision based on a graph because graphs can be misleading.

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#162835

Erik L
Participant

There’s always value in taking a Practical, Graphical, Analytical (PGA) progression to data analysis.  I would not simply make interpretations of data from two confidence intervals.  What were the sample sizes?  What were the confidence levels that generated the data?  Are there any outliers/extreme values?  Were key assumptions of the core data met in generating the intervals?
Regards,
Erik

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#162845

Robino
Member

But hypothesis testing is based on the statistics of confidence intervals and central limit theorem. So for your questions:
What were the sample sizes? This drives the confidence interval in the first place
What were the confidence levels that generated the data? Do you refer to the 95% number used to look-up the z-vale?
Are there any outliers/extreme values? If the sample size is over 30 it can be assumes normal distribution becuase of CLT
Were key assumptions of the core data met in generating the intervals? You mean random and independent?
So it looks like, unless the confidence intervals overlap or are extremely close you don’t really need to run the t-test? Of course you don’t be the farm on it!

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#162847

Dr. Scott
Participant

Robino,
Please see my comments in bold below.
But hypothesis testing is based on the statistics of confidence intervals and central limit theorem.
Not all confidence limits are base on the central limit theorem or normality, there are other distributions as well and tests for those.
So for your questions:
What were the sample sizes? This drives the confidence interval in the first place
Many things drive the confidence interval, not just sample size. Variation, distribution, mean differences, etc. also play a major role.
What were the confidence levels that generated the data? Do you refer to the 95% number used to look-up the z-vale?
I assume since you are calculating a Z value that you have EVERY SINGLE observation that could have existed. Otherwise, get off the Z and learn to use sampling statistics.
Are there any outliers/extreme values? If the sample size is over 30 it can be assumes normal distribution becuase of CLT
I don’t know what idiot told you that any sample over 30 is normally distributed, but it simply is not true. It is true that larger sample sizes can hide (reduce the effects of) outliers due to CLT and can make other types of distributions act more normal, but that does not make the sample normally distributed. Also by definition, if a sample has outliers then it cannot be normally distributed. Check stability first.
Were key assumptions of the core data met in generating the intervals? You mean random and independent?
Not enough to comment on here. I am not even sure what the question or comment pertains to.
So it looks like, unless the confidence intervals overlap or are extremely close you don’t really need to run the t-test? Of course you don’t be the farm on it!
If your distributions come from measurement processes that are the same (use MSA to determine) and they do not overlap, then you can be assured there is a difference. BUT, have you checked the measurement system (MSA) that led to both samples, have you checked stability (SPC) of both distributions, have you ran the appropriate test based on the nature of the distributions (Normal, Binomial, Poisson, etc.)?
And finally, it only takes a click or two in most analytical software programs to prove a difference after the above has been addressed. Take a stats class, 101 will answer all the questions you present above.
Dr. Scott

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