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In This Topic
Mean
Formula
The average of the observations at a given factor level.
Notation
| Term | Description |
|---|---|
| ni | number of observations at factor level i |
| yij | value of the j th observation at the i th factor level |
Standard deviation (StDev)
Notation
| Term | Description |
|---|---|
| yij | observations at the i th factor level |
 | mean of observations at the i th factor level |
| ni | number of observations at the i th factor level |
Pooled standard deviation
Formula
The common variance for all observations. The pooled variance is:
The pooled standard deviation is the square root of the above formula. An equivalent form follows:
The pooled standard deviation is equivalent to S, which is in the output and is equal to:
Notation
| Term | Description |
|---|---|
| yij | j th observation of the response for the i th factor level |
 | sample mean for factor level i |
| ni | number of observations for the ith factor level |
| nT | total number of observations |
| si 2 | variance of observations |
| r | number of levels of the factor |
| MS | Mean Square |
Individual confidence intervals
Formula
The confidence intervals are calculated for each factor level mean using the pooled standard deviation. The formula is:
Notation
| Term | Description |
|---|---|
| nT | total number of observations |
| r | number of factor levels |
| S | pooled standard deviation |
 | inverse cumulative distribution function from the t distribution at 1− α/2 with nT − r degrees of freedom |
