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Obsidian | Level 7

## How to interpret SE for lsmeans

Hi All,

I am working on studying the variability of a new medical device. We took repeated measurements (12 on each of 30 subjects) on the device. Now I want to see the varaibility of measurements in gender groups, bmi groups etc. I ran a mixed model in sas with repeated measurements and got lsmeans for men, women, bmi groups and so on and their Standard errors. I am not sure how do I interpret the SE from LSMEANS in this case to PI? or do I get the Standard Deviation from SE's (SE*SQRT(N)), but my total sample size is 30 and here DF for gender is 350, so what is N in my case?

``````proc mixed data=icc; ;
class  pt bmi gender  bf skinfold;
model vp_dl=gender  bmi  bf  gender*bf gender*bmi ;
repeated pt/ type=cs;
lsmeans gender bf bmi;
run;``````

Any help is greatly appreciated.

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
gender 1 350 144.60 <.0001
BMI 2 350 32.57 <.0001
BF 2 350 75.36 <.0001
gender*BF 2 350 5.38 0.0050
BMI*gender 2 350 18.10 <.0001

Least Squares Means
Effect BMI gender BF Estimate Standard Error DF t Value Pr > |t|
gender   0   477.45 1.9367 350 246.53 <.0001
gender   1   438.69 2.5761 350 170.30 <.0001
BF     1 484.45 2.4906 350 194.51 <.0001
BF     2 468.57 2.8455 350 164.67 <.0001
BF     3 421.19 4.2231 350 99.74 <.0001
BMI 1     447.18 3.8360 350 116.57 <.0001
BMI 2     444.38 2.8957 350 153.46 <.0001
BMI 3     482.65 2.7025 350 178.60 <.0001
1 ACCEPTED SOLUTION

Accepted Solutions
SAS Super FREQ

## Re: How to interpret SE for lsmeans

Tell the PI that standard deviations are for data. It is associated to the mean in the sense that a standard deviation provides a measure of how close some random future observation will be to the mean estimate.

In a similar way, you can think of a standard error as a way to think about how widely the parameter estimates will be expected to vary if you collect new data. A SE gives you a sense for how accurate your parameter estimate is.

If that is too abstract, you can also use the more familiar notion of a confidence interval. A confidence interval says that, given the data, the true parameter is probably within a certain interval (with some confidence).  Standard errors are often used to construct confidence intervals. A big standard error leads to a wide CI; a small SE leads to a small CI.

3 REPLIES 3
SAS Employee

## Re: How to interpret SE for lsmeans

The approximate standard errors for the LS-mean is computed as the square root of L*(X'*(V_hat)^-1*X)^-1*L'. The standard error is appropriate statistic for the LSMEANS not standard deviation. The standard deviation is a characteristic of the data itself, not of estimates such as the LS-means. If you want a standard deviation of a group of data, use the PROC MEANS.

The default is the denominator degrees of freedom taken from the "Type III Tests of Fixed Effects" table corresponding to the LS-means effect, 350 is the denominator degrees of freedom for the tests of fixed effects resulting from the MODEL. The documentation points out -

"The DDFM=BETWITHIN option is the default for REPEATED statement specifications (with no RANDOM statements). It is computed by dividing the residual degrees of freedom into between-subject and within-subject portions. PROC MIXED then checks whether a fixed effect changes within any subject. If so, it assigns within-subject degrees of freedom to the effect; otherwise, it assigns the between-subject degrees of freedom to the effect (see Schluchter and Elashoff 1990). "  Check the documentation of DDFM = option on the MODEL statement in PROC MIXED procedure.

Obsidian | Level 7

## Re: How to interpret SE for lsmeans

Ok, but I am not still not sure how do one explain SE from LSMEANS to a PI. They want to have an explanation about SE , because they understand std as how far a person is from the mean of the group.  They try to understand SE in the same way.

Thanks

SAS Super FREQ

## Re: How to interpret SE for lsmeans

Tell the PI that standard deviations are for data. It is associated to the mean in the sense that a standard deviation provides a measure of how close some random future observation will be to the mean estimate.

In a similar way, you can think of a standard error as a way to think about how widely the parameter estimates will be expected to vary if you collect new data. A SE gives you a sense for how accurate your parameter estimate is.

If that is too abstract, you can also use the more familiar notion of a confidence interval. A confidence interval says that, given the data, the true parameter is probably within a certain interval (with some confidence).  Standard errors are often used to construct confidence intervals. A big standard error leads to a wide CI; a small SE leads to a small CI.

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