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Posted 03-21-2016 11:43 AM
(9643 views)

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

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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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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.

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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

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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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