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 |
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.
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.
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
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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