## CI for Transformed data Unbalanced study [General Statistics]

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» Can you help me with the formula for LSM (I wish to do a manual calculation, for verification purposes) and a brief explaination about why this method is used for unbalanced study?

The calculation is not different from a balanced study.

I’ll give you an example for the reference:

Calculate the (arithmetic) mean of log-transformed values in sequence 1 (if seq 1 = RT from

Calculate the (arithmetic) mean of log-transformed values in sequence 2 (if seq 2 = TR from

LSM for the reference is the arithmetic mean of

The difference

A better estimate of the true difference is MVUE (the Minimum Variance Unbiased Estimator), however, its calculation is a little bit tricky (involves the

For details see Chow & Liu’s book.

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*Xt*

the LSM of the test, and *Xr*

the LSM of the reference (log-scale).»

» Can you help me with the formula for LSM (I wish to do a manual calculation, for verification purposes) and a brief explaination about why this method is used for unbalanced study?

The calculation is not different from a balanced study.

I’ll give you an example for the reference:

Calculate the (arithmetic) mean of log-transformed values in sequence 1 (if seq 1 = RT from

*period 1*) as*Xr1* = sum ( *Xr1 … n1* ) / *n1*

Calculate the (arithmetic) mean of log-transformed values in sequence 2 (if seq 2 = TR from

*period 2*) as*Xr2* = sum ( *Xr1 … n2* ) / *n2*

LSM for the reference is the arithmetic mean of

*Xr1*

and *Xr2*

*Xr* = ( *Xr1* + *Xr2* ) / 2 )

The difference

*Xt* – *Xr*

is also called MLE (the Maximum Likelihood Estimator) of the true difference *Mu(t)* – *Mu(r)*

, which is slightly biased according to the degree of ‘unbalancedness’.A better estimate of the true difference is MVUE (the Minimum Variance Unbiased Estimator), however, its calculation is a little bit tricky (involves the

*Γ*-distribution).For details see Chow & Liu’s book.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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*Dif-tor heh smusma*🖖Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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### Complete thread:

- Confidence Interval for Transformed data Unbalanced study usfda_emea 2007-03-06 14:39 [General Statistics]
- CI for Transformed data Unbalanced study Helmut 2007-03-06 16:46
- CI for Transformed data Unbalanced study drshiv 2007-03-06 18:49
- CI for Transformed data Unbalanced study usfda_emea 2007-03-07 06:21
- CI for Transformed data Unbalanced studyHelmut 2007-03-07 12:04
- CI for Transformed data Unbalanced study usfda_emea 2007-03-07 12:34
- CI for Transformed data Unbalanced study Ohlbe 2014-07-30 15:04
- LSM limbo Helmut 2014-07-31 02:54
- LSM limbo Ohlbe 2014-07-31 09:47
- 90% CI limbo VStus 2017-03-01 14:07
- RSABE ⇒ ABEL Helmut 2017-03-03 13:34
- RSABE ⇒ ABEL VStus 2017-03-03 15:31
- s2wR != mse, FDA != EMA d_labes 2017-03-04 14:49
- s2wR != mse, FDA != EMA ElMaestro 2017-03-04 19:13
- s2wR from ISC in FDA approach d_labes 2017-03-05 12:18
- s2wR from ISC in FDA approach ElMaestro 2017-03-05 13:50

- s2wR from ISC in FDA approach d_labes 2017-03-05 12:18
- s2wR != mse, FDA != EMA VStus 2017-03-04 21:41
- s2wR != mse, FDA != EMA Helmut 2017-03-06 13:40

- s2wR != mse, FDA != EMA ElMaestro 2017-03-04 19:13

- s2wR != mse, FDA != EMA d_labes 2017-03-04 14:49

- RSABE ⇒ ABEL VStus 2017-03-03 15:31

- RSABE ⇒ ABEL Helmut 2017-03-03 13:34

- LSM limbo Helmut 2014-07-31 02:54

- CI for Transformed data Unbalanced studyHelmut 2007-03-07 12:04

- CI for Transformed data Unbalanced study Helmut 2007-03-06 16:46