2 Replies Latest reply on Aug 5, 2013 12:41 PM by Scott Tennican

# Confidence Intervals using T Stat (Student's T Table)

Hi All,

I know that Tableau has Confidence Intervals that you can add as reference lines but I don't believe they use the Student's T Distribution to calculate the confidence intervals. I need to calculate Confidence Levels for Proportions.  I have also created my own Student's T Table that goes up to over 500,000 degrees of freedom and each degree of freedom has a value for either a 90%, 95%, 99% confidence level in a normalized table format. Would I would like to do is somehow use this table as a data source and blend it with another data source that has the sample size and number of observations.  So if in my data set I have a sample size column of 2000 degrees of freedom it will link to my Student's T Table and use N-1 or 1999 degrees of freedom and grab the corresponding T Stat so I can calculate the Confidence Interval depending on what confidence level (90%, 95%) I specify.

Just wondering if I can do this with Tableau?

Thanks,

Ed

• ###### 2. Re: Confidence Intervals using T Stat (Student's T Table)

Hi Ed,

The confidence band available in the reference lines is for the confidence interval for the sample mean estimating the population mean. If you add a reference line for both average and confidence band, you will notice that the confidence band centers around the mean. As for all confidence intervals, the general form of a confidence interval is (statistic) +- (critical value) * (standard error) which in this case is (sample mean) +- (tcrit(n-1)) * (s/sqrt(n)) where tcrit(n-1) is the critical value from a students-t with n-1 degrees of freedom and s/sqrt(n) is the formula for the standard error of a sample mean. Of course this is different from the standard error of a sample proportion which is what you need. Tableau uses the standard highly accurate polynomial series expansion to approximate the student's-t distribution rather than a table. But, Tableau does not provide direct access to this distribution.

Are you sure you need that much accuracy in your t-distribution. By the time you get to 2000 degrees of freedom, the normal distribution is an extremely good approximation for the students-t. I have described how to approximate the normal distribution with a Table Calc here: t-test of two independent means

You could improve on the normal approximation with an approximation for the students-t.

See my recent addition to the forum post above for the formulas.

With regard to using your table, that would probably be possible as well.

But, perhaps more complicated than necessary.

Scott