Statsitics, Research Methods, SAS, R, HLM, Rasch model
This SAS code adjusts weights (e.g., sample weights) such that the sum of weights equals the sample size. Weight1 is the original weight and weight 2 is the result.
proc sql;
create table comp2 as
select *,
psweight * (count(weight1)/Sum(psweight1)) as weight2
from comp;
run;
What works Clearinghouse considers an effect size of .25 as “substantively important” and interpreted as “qualified positive” even when the effect size is not statistically significant.
See page 23.
https://ies.ed.gov/ncee/wwc/Docs/referenceresources/wwc_procedures_v3_0_standards_handbook.pdf
Mathematically, you only need the coefficient for the predictor to derive an odds ratio (you don't need the intercept value).
oddsratio=exp(coefficient_size)
When describing statistical models and results in writing, the following are tricky issues and require decisions and standardized way of description (and they must be brief, intuitive, full of meaning):
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).
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.
Simple random sampling given the population size
Confirm that regular regression analysis produces larger standard errors. Using the total sample size as a part of the modeling process, PROC SURVEYREG achieves smaller standard errors (more precise measurement).
data IceCream;
input Grade Spending Income Kids @@;
datalines;
7 7 39 2 7 7 38 1 8 12 47 1
9 10 47 4 7 1 34 4 7 10 43 2
7 3 44 4 8 20 60 3 8 19 57 4
7 2 35 2 7 2 36 1 9 15 51 1
8 16 53 1 7 6 37 4 7 6 41 2
7 6 39 2 9 15 50 4 8 17 57 3
8 14 46 2 9 8 41 2 9 8 41 1
9 7 47 3 7 3 39 3 7 12 50 2
7 4 43 4 9 14 46 3 8 18 58 4
9 9 44 3 7 2 37 1 7 1 37 2
7 4 44 2 7 11 42 2 9 8 41 2
8 10 42 2 8 13 46 1 7 2 40 3
9 6 45 1 9 11 45 4 7 2 36 1
7 9 46 1
;
run;
proc surveyreg data=IceCream total=4000;
model Spending = Income / solution;
run;
proc reg data=icecream;
model spending=income;run;
Stratified Sampling
http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_surveyreg_sect004.htm
data IceCream;
input Grade Spending Income Kids @@;
datalines;
7 7 39 2 7 7 38 1 8 12 47 1
9 10 47 4 7 1 34 4 7 10 43 2
7 3 44 4 8 20 60 3 8 19 57 4
7 2 35 2 7 2 36 1 9 15 51 1
8 16 53 1 7 6 37 4 7 6 41 2
7 6 39 2 9 15 50 4 8 17 57 3
8 14 46 2 9 8 41 2 9 8 41 1
9 7 47 3 7 3 39 3 7 12 50 2
7 4 43 4 9 14 46 3 8 18 58 4
9 9 44 3 7 2 37 1 7 1 37 2
7 4 44 2 7 11 42 2 9 8 41 2
8 10 42 2 8 13 46 1 7 2 40 3
9 6 45 1 9 11 45 4 7 2 36 1
7 9 46 1
;
run;
data StudentTotals;
input Grade _TOTAL_;
datalines;
7 1824
8 1025
9 1151
;run;
data IceCream2;
set IceCream;
if Grade=7 then Prob=20/1824;
if Grade=8 then Prob=9/1025;
if Grade=9 then Prob=11/1151;
Weight=1/Prob;
run;
proc surveyreg data=IceCream2 total=StudentTotals;
strata Grade /list;
class Kids;
model Spending = Income / solution;
weight Weight;
run;
proc reg data=icecream2;
model spending=income;
weight Weight;
run;
This is a question post.
Imagine that I have a regression model:
Y=b0+b1*black+b2*white+b3*asian+ error
where the ommited category is hispanic. Because of this omission, each of race variable coefficients corresponds to the difference between each one of the race variables and Hispanic subjects (in other words, Hispanic is being the reference group).
If I want to know if the difference between white and black is statistically significant, I could omit black and see if the coefficient for white subjects is statistically significant (or I can omit white instead). This, however, requires running of one whole separate model (though it is a mathematically equivalent model as the original model).
Another approach in SAS would be to request stat tests evaluating every possible contrast between the race groups, but this again involves an extra step.
Is there an easy to just to read information I already have from the original model and evaluate the between-group differences statistically (e.g., black vs. white, asian vs. black, white vs. black)? For example, if I have this table below (w/ hypothetical values), is it possible to know if the black vs. white difference is statistically significant? Does this table give me sufficient information to know if the white vs black difference (2.1-3) is statistically significant?
coeff. stderr. prob.
Intercept 1.2 (0.2) 0.1
black 2.1 (0.1) 0.6
white 3 (0.2) 0.05
asian 4 (0.01) 0.01
My hunch is that I can pool two standard errors (one from black and the other from black) and use it to evaluate the black and white difference (and somehow I have to figure out what DF should be). However, I don't think pooled standard errors are utilized for stats tests that are being reported already in this table (e.g., black effect is evaluated only based on its own standard error). It would strange that I had to rely on pooled standard errors.
My goal is to create an Excel sheet that does this calculation, so people can conduct the test without necessarily rerunning the models again (and they just rely on result tables).
Reference:
Example results:
www.nippondream.com/file/dummy variable interpretation of reg results.xlsx
Thank you for your input on this (please email k u e k w a @ GMAIL) or leave a comment below.