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- Calculation of t-distribution, JMP 13

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Feb 23, 2017 10:39 AM
(3838 views)

Hello,

I would like to knwo, how the t-distribution is calculated in the programm. The results I got from the programs are different with the results I calculated by myself, with the help of methods, mentioned in various books and scientific researches.

In addition I would like to know, how it is possible to set up an own quantil in the t-distribution. When I make a box plot, I just can change it in the standard normal distribution.

My calculation way is

n = 4

calculate mean and variance

calculate c = value from table http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf for a 95% each side

df = n-1

(c*root(variance))/(root(n))=k

mean+-k = result

Thanks for you ideas,

Solved! Go to Solution.

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Mar 8, 2017 7:16 AM
(5973 views)

You are calculating a two-sided confidence interval for the mean using the quantile from the *t* distribution for (1-alpha)% confidence and (n-1) degrees of freedom. The function for this in JMP is **t Quantile( probability, df )**. Here is the quantile for a two-sided 95% confidence interval for the mean:

I used the script editor and an embedded log but you could also enter it into a column as a formula. This quantile is correct.

If you enter your 4 observations into a column, then select **Analyze** > **Distribution**, select the data column and click **Y, Columns**, then click **OK**. You will find the 95% CI in the **Summary Statistics** report.

Here is an example of 4 observations:

Here is the Summary Statistics report for them:

Learn it once, use it forever!

26 REPLIES

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Feb 23, 2017 1:11 PM
(3830 views)

I suspect that you are having a mismatch of t-tests, in that you may be comparing a t-test for unequal variances, with a t-test for equal variance. You can get the details of what JMP is doing from it's documentation

Help==>Books==>Basic Analysis==>The t-test Report

Here is a cut and paste from that document

**The t-test Report**

Note: This option is applicable only for the Means/Anova/Pooled t option.

There are two types of t-Tests:

• Equal variances. If you select the Means/Anova/Pooled t option, a t-Test report appears.

This t-Test assumes equal variances.

• Unequal variances. If you select the t-Test option from the red triangle menu, a t-Test

report appears. This t-Test assumes unequal variances.

The t-test report contains the following columns:**t Test plot** Shows the sampling distribution of the difference in the means, assuming the null

hypothesis is true. The vertical red line is the actual difference in the means. The shaded

areas correspond to the p-values.**Difference** Shows the estimated difference between the two X levels. In the plots, the

Difference value appears as a red line that compares the two levels.**Std Err Dif** Shows the standard error of the difference.**Upper CL Dif** Shows the upper confidence limit for the difference.**Lower CL Dif** Shows the lower confidence limit for the difference.**Confidence** Shows the level of confidence (1-alpha). To change the level of confidence, select

a new alpha level from the Set Level command from the platform red triangle menu.**t Ratio** Value of the t-statistic.**DF** The degrees of freedom used in the t-test.**Prob > |t|** The p-value associated with a two-tailed test.**Prob > t** The p-value associated with a lower-tailed test.**Prob < t** The p-value associated with an upper-tailed test.

Jim

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Mar 8, 2017 5:27 AM
(3753 views)

Thanks for the information

Apparently, there is no formular given. I found in a math book different ways to handle the t-test. I need the results to be the same.

Is it possible to draw boxplots with my calculated data in JMP? Otherwise I need to look for a new programm.

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Mar 8, 2017 7:16 AM
(5974 views)

You are calculating a two-sided confidence interval for the mean using the quantile from the *t* distribution for (1-alpha)% confidence and (n-1) degrees of freedom. The function for this in JMP is **t Quantile( probability, df )**. Here is the quantile for a two-sided 95% confidence interval for the mean:

I used the script editor and an embedded log but you could also enter it into a column as a formula. This quantile is correct.

If you enter your 4 observations into a column, then select **Analyze** > **Distribution**, select the data column and click **Y, Columns**, then click **OK**. You will find the 95% CI in the **Summary Statistics** report.

Here is an example of 4 observations:

Here is the Summary Statistics report for them:

Learn it once, use it forever!

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Mar 8, 2017 8:53 AM
(3739 views)

Do i have to write the script new for every number of N ? Cause I made several experiments, and N is changing many times.

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Mar 8, 2017 9:25 AM
(3733 views)

No, of course not.

You enter your data into a JMP data table and then use one of the platforms in the Analyze menu. The confidence intervals for the mean in Distribution, the slope in Bivariate (Fit Y by X), tests in Oneway (Fit Y by X), and all the platforms through the platforms launched by Fit Model will calculate the confidence limits automatically. (It sounds like each of your 'experiments' is a sample drawn for a different population and you want a new confidence interval for the mean, so Distribution will do it for you.)

There is no need for you to look up the t quantile or calculate the intervals by hand.

Learn it once, use it forever!

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Mar 8, 2017 9:45 AM
(3727 views)

I was doing some experiments but many samples got damaged, thats why the number varies.

I have done the boxplots but the only data I can get out of it is like shown in the picture

But I need the Minimum, 5%, mean, 95%, Maximum, variance, standard deviation

Leftclick on the chart let me "format column", but after click "ok" nothing changes.

How can I change that?

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Mar 8, 2017 10:00 AM
(3722 views)

The quantiles in the report that you show are fixed. You could enter the same data in the Distribution platform and put the factor column in the By role. This launch will give the the quanitile and mean information for each level separately.

Learn it once, use it forever!

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Mar 8, 2017 10:19 AM
(3719 views)

How can I make an empty cell, wish is not calculated for the quantiles? So far I get wrong values. E.g. for the last column the mean is about 18 but all results are higer, so there must be a mistake.

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Mar 8, 2017 10:21 AM
(3715 views)