## GrADS Significance Scripts

**Go to:**Hovmuller and X-Y Plots

Vectors, Contours, Color Fill, Map Projections, Masks, Multiple Plots, GrADS Scripting Language

These statistical
significance scripts calculate the and shade
the grid cells that are significant at a chosen level.two-sample difference of means test There
are two different forms of the test: one in which we assume the
population variances are equal, and one in
we assume the population variances are unequal.
You can determine which form of the test to use by conducting
a F-test that compares the variances of the two samples. Step-by-step
instructions for running the scripts are listed below. In the graphic to the right (click on the map for a larger-size version), we show the results of a t-test for for DJF for FOAM GCM data, comparing model-predicted surface temperatures from 6K B.P. to current surface temperatures. The areas that are shaded gray are signficant at the 99% level. |

**Assume
Population Variances are Equal**

- Calculate your degrees
of freedom:
**df = n1 + n2 -2**, where n1 is the size of the first sample and n2 is the size of the second sample. - Decide on the significance level: .01 (99%), .05 (95%), .10 (90%)
**Example**: say we have two samples of sizes**n1=120**and**n2=120**. The

**degrees of freedom = n1+n2-2 = 120+120-2 = 238**

- Say we choose a significance
level of
**0.01**. When we enter this information in the appropriate boxes, we find that our**cutoff t**is**2.597**.

- Now, we move on to GrADS.
The script to use is ttest.equal_variances.gs.
- Put in open statements
for your data files

(e..g,**sdfopen /grove4/selin/foam_indyr/ha.F1.0k.djfi486605.TS1.nc**) - Set
**n1**and**n2**to the size of the respective samples. - In the formulas for
**x1, x2, s1,**and**s2,**you must set the time increment for*each*of the formulas according to the sample size. For example, if**n1**is**120**, then set

x1 = ave(ts1.1,t=1,t=120). - Set the contour interval
equal to the cutoff t you determined from the web page:

set clevs 2.597 - Now, run the script.
Enter GrADS, and type
**exec ttest.equal_variances.gs.**The areas that are significant will be shaded gray and the difference between the two means will be contoured.

- Put in open statements
for your data files

**Assume
Population Variances Are Unequal**

- Calculate your degrees
of freedom. In this case,
**df = min (n1-1, n2-1)**, where n1 is the size of the first sample and n2 is the size of the second sample. - Decide on the significance level: .01 (99%), .05 (95%), .10 (90%)
- This is a conservative
estimate of the degrees of freedom. Say we choose a significance
level of
**0.05***.***cutoff t**is**2.262**. - Now, we move on to GrADS.
The script to use is ttest.unequal_variances.gs.
- Put in open statements
for your data files. In this example, we used the
*xdfopen*option to open our data files because the time indices do not match. Here are the xdfopen files used in this script: xdf6kFixdjf and xdf0kdjf. - Set
**n1**and**n2**to the size of the respective samples. - In the formulas for
**x1, x2, s1,**and**s2,**you must set the time increment for*each*of the formulas according to the sample size. For example, if**n1**is**10**, then set

**x1 = ave(ts1.1,t=1,t=10).** - Set the contour interval
equal to the cutoff t you determined from the web page:

set clevs 2.262 - Now, run the script.
Enter GrADS, and type
**exec ttest.equal_variances.gs.**The areas that are significant will be shaded gray and the difference bewteen the two means will be contoured on top.

- Put in open statements
for your data files. In this example, we used the

**Example**: say we have two samples of sizes

**n1=120**and

**n2=10**.

Then

**degrees of freedom = min (n1-1, n2-1) = min (120-1, 10-1) = min(119, 9) = 9**