# [ncl-talk] NCL serial correlation and student_t

Sri Nandini snandini at marum.de
Fri Jan 19 08:16:49 MST 2018

```Hello

I had an NCL 2 fold question:

1) In the NCL page https://www.ncl.ucar.edu/Document/Functions/Built-in/ttest.shtml  the ttest function uses  the Student's t-test with the 2 tailed returned probabilities.  BUT

NCL has a function called student_t which calculates the two-tailed probability of the Student-t distribution.

So which one should i take if i wish to do a ttest (2tailed) that takes the serial correlation from the data into account say between 2 temperature datasets?

With the NCL function equiv_sample_size you can get the true degrees of  freedom. You can then calculate the p-values using the function student_t ,which  allows you to prescribe the correct degrees of freedom. BUT: i already use the equiv_sample_size function to do my ttest as shown here: in example 4:https://www.ncl.ucar.edu/Document/Functions/Built-in/ttest.shtml

dimXY = dimsizes(x)
ntim  = dimXY(0)
nlat  = dimXY(1)
mlon  = dimXY(2)
(1)
xtmp = x(lat|:,lon|:,time|:)       ; reorder but do it only once [temporary]
ttmp = y(lat|:,lon|:,time|:)

(2)
xAve = dim_avg (xtmp)              ; calculate means at each grid point
yAve = dim_avg (ytmp)
xVar = dim_variance (xtmp)         ; calculate variances
yVar = dim_variance (ytmp)

Specify a critical significance level to test the lag-one auto-correlation coefficient and determine the (temporal) number of
equivalent sample sizes in each grid point using equiv_sample_size.

sigr = 0.05                        ; critical sig lvl for r
xEqv = equiv_sample_size (xtmp, sigr,0)
yEqv = equiv_sample_size (ytmp, sigr,0)
(4)
xN   = wgt_areaave (xEqv, wgty, 1., 0)    ; wgty could be gaussian weights
yN   = wgt_areaave (yEqv, wgty, 1., 0)
(5)
iflag= False                        ; population variance similar
prob = ttest(xAve,xVar,xN, yAve,yVar,yN, iflag, False)

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