## 11.2 Mean Composites vs. Factor Scores

The loadings of the items onto the principal components can be used to calculate component/factor scores.

```
<- irisNout$scores[,"RC1"]
facScore1 <- irisNout$scores[,"RC2"]
facScore2 length(facScore1)
## [1] 150
mean(facScore1)
## [1] -1.816826e-16
sd(facScore1)
## [1] 1
```

facScore1 consists of n = 150 values with a mean of 0 and a standard deviation of 1. Taking the mean of standardized raw scores works well when the input variables all had similar loadings in the principal component analysis. However, if the loadings are different (e.g., the loadings for Sepal.Length, Petal.Length, and Petal.Width were 0.95, 0.65, and 0.35), the mean composite will not be a good representation of the component/factor score.

```
cor(facScore1,flowerSize)
## [1] 0.9840672
cor(facScore2,flowerSize)
## [1] -0.1776343
```

The correlation between facScore1, the component scores for the first principal component, and flowerSize, our mean composite, is r = 0.98, indicating that two strategies are generating identical results. The correlation between facScore2 and flowerSize is low because only Sepal.Width loaded on the second component. If we were going to use a combination of Sepal.Length, Petal.Length, and Petal.Width in a future study, then the mean composite would serve us well. If we simply wanted a combination of Sepal.Length, Petal.Length, and Petal.Width for one-time use, then facScore1 would do fine.