Timeline for How to check for normal distribution using Excel for performing a t-test?
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| Nov 21, 2018 at 14:08 | history | edited | whuber♦ | CC BY-SA 4.0 |
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Mar 16, 2017 at 12:38 | history | edited | whuber♦ | CC BY-SA 3.0 |
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| Mar 16, 2017 at 12:31 | comment | added | whuber♦ | @Glen_b Thank you for catching that. I had misquoted the formula. My source is (my own page!) at quantdec.com/envstats/notes/class_02/…, where the correct formula is given and justified: generally one uses $$\frac{r-a}{n+1-2a}$$ where $r$ is the rank (from $1$ through $n$) and $a$ typically is a number between $0$ and $1$, often $1/6$. That yields $(r-1/6)/(n+2/3)$ as the desired formula. ($a=1/3$ gives the Tukey formula you quote.) I have fixed the formula and the Excel illustration. | |
| Mar 16, 2017 at 6:19 | comment | added | Glen_b | The formula (rank + 1/6) / (n+1/3) doesn't seem to be symmetric as we might anticipate. e.g. with the middle observation of 3 the rank is 2 and this would suggest a corresponding percentile of 0.65 rather than what would seem to be natural to take for the middle observation (0.5). Did I miss something obvious? [ I've seen Tukey use a few different formulas in different places, including (i-1/3)/(n+1/3). The formula at your link fits into the common (i-a)/(n+1-2a) scheme but the formula you give in your answer doesn't] | |
| Jun 20, 2015 at 14:15 | comment | added | whuber♦ | @Michael Good questions. $1/6$ is one simple, well-known way to establish probability plotting points. I recall John Tukey recommending this in his book, EDA. The hinge rank formula is mysterious: I should have explained that I am picking two points equally far in from the ends at the $100\times 1/6$ and $100\times 5/6$ percentiles. Any multiplier substantially greater than $0$ and less than $1/2$ would work. $1/4$ is popular: it corresponds to the quartiles. So is $0.16$, corresponding to 1 SD for a Normal distribution. | |
| Jun 20, 2015 at 13:19 | comment | added | user80236 | For the formulas in Col B, would you explain the reason to add 1 and divide by 6 and 3 (“+ 1/6” and the “+ 1/3”)? Also is there a reason you chose to divide by 6 in the Hinge Rank Cell? | |
| Feb 4, 2014 at 22:23 | history | edited | whuber♦ | CC BY-SA 3.0 |
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| Oct 10, 2013 at 6:11 | history | answered | whuber♦ | CC BY-SA 3.0 |