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R: t Distribution

I. Calculating P(t < x)
If X~t(df), where df is the degrees of freedom, use the pt(x, df) function to calculate P(X < x).

Example 1:
If X~t(4), use the following R code to calculate P(X < 1.2).
> pt(1.2, 4)
 0.8518243

II. Calculating P(X > x)

If X~t(df), where df is the degrees of freedom, use the pt(x, v, lower.tail=FALSE) function to calculate P(X > x). A second method would be to subtract pt(x, df) from 1.

Example 1:

If X~t(4), use the following R code to calculate P(X > 1.2).
# Method 1 - Use "lower.tail = FALSE"
> pt(1.2, 4, lower.tail = FALSE)
 0.1481757

# Method 2 - Subtract pt(x, v) from 1
> 1 - pt(1.2, 4)
 0.1481757

III. Given percentile, find corresponding t-value
If X~t(df), use the qt(percentile, df) function to find the x-value that corresponds with a given percentile.

Example:
IX~t(12), what x-value corresponds with the 75th percentile?
> qt(0.90, 12)
 1.356217

IV. Determing t*
For confidence interval calculations, under certain conditions, one may need to find t*. To calculate t* using R, use the following table on the bottom right.

Example:
Find t* for a 95% confidence interval with 8 degrees of freedom.

> qt(0.975, 8)
 2.306004

 Confidence Level R Code 99.9% qt(0.9995, df) 99.8% qt(0.999, df) 99.5% qt(0.9975, df) 99% qt(0.995, df) 98% qt(0.99, df) 96% qt(0.98, df) 95% qt(0.975, df) 90% qt(0.95, df) 80% qt(0.90, df) 70% qt(0.85, df) 60% qt(0.80, df) 50% qt(0.75, df)