## How to derive standard deviation from standard error

Algorithm:

SD=Standard error * sqrt(N);

Reference:

http://handbook.cochrane.org/chapter_7/7_7_3_2_obtaining_standard_deviations_from_standard_errors_and.htm

QC: I checked the algorithm using SAS.  The result was consistent with the algorithm (i.e., SD=standard error*sqrt(N)).

proc means data=sashelp.class mean std stderr n;
var height;
run;

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Mean 62.3368421

SD 5.1270752

N 19
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## SAS T-test for proportions

data YesNo;
input Gender \$ NumYes Total;
Response=”Yes”; Count=NumYes; output;
Response=”No “; Count=Total-NumYes; output;
datalines;
Men 30 100
Women 45 100
;

proc print noobs;
var Gender Response Count;
run;

proc freq order=data;
weight Count;
table Gender * Response / chisq riskdiff;
exact riskdiff;
run;

## How to QC the result of random assignment

QC 1:

Check the number of cases within each group (i.e. treatment and control group).

Q2:

Check if the number of treatment school and control school is balanced within block.

## Cronbach’s alpha

The UCLA site explains Cronbach’s alpha as the average internal correlation among survey items.  It also says that it is not a measure of unidimensionality.  Rather, it is a measurement of internal consistency (though just intuitively I feel what is coherent tends to be also uni-dimensional… I think the point is that the measure is most optimal by design for the assessment of internal correlation, not dimentionality.

http://www.ats.ucla.edu/stat/spss/faq/alpha.html

Standardized versus Raw

This SAS website says one should use the standardized version of the measure (as opposed to raw).

https://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_corr_sect032.htm

It says: “Because the variances of some variables vary widely, you should use the standardized score to estimate reliability.”

A note to myself: Does this mean if I standardized all items before the analysis, I get the same value for raw and standardized?  I can experiment this.

## Excel function to replicate t-test off SAS PROCs (e.g., GLIMMIX)

Phil of SAS helped me identify this function. Thank you.

T-test conducted in PROC GLIMMIX (or most likely other regression procedures) is expressed in Excel function as:

=2*(1-T.DIST( T_VALUE , DEG_OF_FREEDOM ,TRUE))

where T_value must be an absolute value of the original t-value (e.g., if -2 then 2).

This expresses CDF (cumulative distribution function), not PDF (probability density function).  I will explicitly discuss what these are in the near future.

I wanted to know how much of statistical results (off PROC GLIMMIX in this case) comes from SAS’s internal computation (i.e., I can’t replicate results outside SAS) and how much of it can be done in Excel given what I get from SAS output.