What is the Difference between Percentile and T-Score, where to use which one ?

Hi

Could someone please explain in simple words, what is the Difference between Percentile and T-Score, and how should one decide about where to use which one ? Is there some proper explanation available somewhere, which would tell about the PRACTICAL USER CASE SCENARIOS, like use T-Score in such and such situation and use Percentile Scores in such situation, and so on. Please share such links.

Please see the attached snaps for reference.
Norms-and-Units-for-Measurement.jpg
Normal-Distribution.jpg

Where can I find the exact corresponding values, so that I can do a Direct Comparison between the Percentile Values and the T Score Values ? Like, if I want to know the T Score value, which would represent the Percentile Value of 30 or 75, then how do I find that ?

I have to use them within Excel Sheet for doing some scoring, but I am getting confused regarding which particular method should I use.

Thanks
Wanu SanAsked:
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xtermieConnect With a Mentor Commented:
Differences explained here:  www.springer-ld.org/blog/mmulcahey/09/20/2013

A short brief, however follows:
A percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the 20th percentile is the value (or score) below which 20% of the observations may be found. The term percentile and the related term percentile rank are often used in the reporting of scores from norm-referenced tests.

Good article with percentile practical examples here:  https://en.wikipedia.org/wiki/Percentile

In statistics, the standard score is the signed number of standard deviations by which an observation or data is above the mean.  In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

Good article with practical examples here:  https://en.wikipedia.org/wiki/Student%27s_t-distribution
and here http://stattrek.com/probability-distributions/t-distribution.aspx (with calculator)

A calculator that converts t-scores to percentiles can be found here:
http://keisan.casio.com/exec/system/1180573204
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Austin TexasConnect With a Mentor Systems EngineerCommented:
Percentile tells you the value below which a given percentage of results in your test group are found. For example, the 50th percentile is the value below which 50% of the results were found.

T-Scores (and z-scores) tell you how your results compare to the results of other tests. To calculate a T-Score, you take your z-score and multiply by 10 and ad 50. To calculate your z-score, you take your raw score minus the mean and divide by the standard deviation. For example, T-Score = (Your raw scores - Average scores) / Standard Deviation * 10 + 50

I hope that helps!
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Wanu SanAuthor Commented:
Thank you so much Austin and xtermie. Both replies are very helpful.
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xtermieCommented:
You are welcome, glad we could help :)
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Austin TexasSystems EngineerCommented:
What xtermie said!  Hope it helped.
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