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Calculation of t-distribution, JMP 13

Eintopf

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,

Accepted answers

Mark_Bailey

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:

All comments

txnelson

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.

Eintopf

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.

Mark_Bailey

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.

Here is an example of 4 observations:

Here is the Summary Statistics report for them:

Mark_Bailey

The value used by JMP is the same as the one that you should use from the table that you cited:

(two-tails at 0.05)

Eintopf

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

Mark_Bailey

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.

Mark_Bailey

While you do not need to look up t quantiles, here is a JMP data table with the sample size N and the corresponding t quantile for a two-sided confidence interval with the given Confidence.

It might be easier to use than the table that you cited.

t Quantile Table.jmp

Eintopf

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?

Eintopf

Thanks a lot. I already looked up all values in one of germanys most recommended books for math in the field of engenieering (Papula). It should have the right values.
The whole calculation was already done with excel. I just need to double check it with the jmp software. It is recommended to use this software for boxplot at my university, but if the result is different, than my calculation, I cant use it. If both is the same, everything was done right

Eintopf

What is the exact meaning of the "upper" and "lower 95% mean"?

I attached a task and get the same value for a lower and higher 97,5% interval. It is a little bit confusing.

Or is 95% the two sided interval arround the mean? So how can I get a "upper" and "lower 90% mean", so I get the value for the lowest and highest 5%?

t6.PNG

Thank you for posting the pictures.

Your computation is for a two-sided confidence interval with 95% confidence. That is exactly what JMP is reporting in the Summary Statistics in the Distribution platform (fourth picture).

You want 95% confidence between both tails of the distribution so you center the 95% of the t distribution leaving 2.5% on either side. We still label it as Lower 95% Mean and Upper 95% Mean to indication the confidence level. It is a short label meant to convey the lower or upper bound on the location of the population mean with 95% confidence. This kind of labeling is common.

If you actually want 5% in both tails, then you want a two-sided 90% confidence interval. Click the red triangle at the top of the Distribution platform next to the name of your variable and select Confidence Interval > 0.90 and you will get the desired interval.

The numbers from your manual calculation and from JMP might not agree exactly because you are using a t quantile rounded to three decimal places and JMP is using the full precision value, but the values should be close to three or four significant digits.

Eintopf

Thanks a lot. I could find the menu and the values are woking out very good.
But one more question. Is the a possibility to set the value for the upper and lower mean to 0,90 for all "Summary Statistic" or do I have it to change for every boxplot seperately? The automatic given value is always 0,95. Even when i close and open the boxplot again.
So far I have 7 Datasheets with 4 boxplots for each.

Mark_Bailey

There are a couple of ways that might work for you.

If you use the way I showed (apply a data filter and select each group in turn), then click the red triangle next to Summary Statistics and change the confidence level at the bottom.
If you always want 90% intervals from Distribution, then change your preference: select File > Preferences > Platforms, then select Distribution in the list and you will find Confidence Interval in the second column of settings.

I hope that one of these approaches is satisfactory. The second approach might be the best because it will be a global change to JMP behavior.

Eintopf

And there is a new problem. I just tried to add some menues, some of them you can delete, but others seems like to stay there forever. See picture below.

Only way to get rid of the menu "Test Standard Deviation" was to delete the whole boxplot of "Dichte IV". Unfortunately it was part of a group with boxplots. I am missing a shortcut like "Strg"+"Z", with whom I can make changes unhappen. So now my only way is to delte everything and do it again. Any solution to avoid this?

t5.PNG