i made PCA graph for plant parameters (stam height, number of branches, dry plant weight etc) and different treatment (T1-T12). but I,m not getting how to discuss this graph in theory...
It depends on what kind of graph and the nature of your original variables. For example let's say that from Scores you can interpret agrupations so you are able separate your data for agrupations. Besides you can detect outliers and if you display Hotelling's Ellipse you can find out if all they belongs to the same process. From Loadings you can extract the variables that describes the most of information on the components. If you display Hotelling's Ellipse which the inner part represents 50% of variance and the outer 100%. Variables in between both are impotant for components. Besides you can know if variables are correlated among them. From Influence Plot you can figure out if you have points with more influence in your calibration phase. Even you can detect dangerous outliers.
Some days ago, I suggested these tips about PCA that I think can be useful for you:
- Scores: describe the properties of the samples and are usually shown as a map of one PC plotted against another.
Samples with close scores along the same PC are similar (they have close values for the corresponding variables). Conversely, samples for which the scores differ greatly are quite different from each other with respect to those variables.
The relative importance of each principal component is expressed in terms of how much variance of the original data it describes.
- Loadings: describe the relationships between variables and may be plotted as a line (commonly used in spectral data interpretation) or a map (commonly used in process or sensory data analysis).
For each PC, look for variables with high loadings (i.e. close to +1 or –1); this indicates that the loading is interpretable.
To study variable correlations, one studies the relative location of variables in the loadings space. Variables that lie close together are highly correlated. For instance, if two variables have high loadings along the same PC, it means that their angle is small, which in turn means that the two variables are highly correlated. If both loadings have the same sign, the correlation is positive (when one variable increases, so does the other). If the loadings have opposite signs, the correlation is negative (when one variable increases, the other decreases).
But remember: Loadings cannot be interpreted without Scores, and vice versa.
For that reason the BI-PLOT is the best plot for analyzing PCA. In the BI-PLOT, you plot Scores and Loadings in the same plot and it will help to explore their representative relationship easily. Such relationship can be found in the same way I have explained above.
The significance of each score and loadings depends of the software that you have used for processing your data. In the result, you should be able to find the P values of each score and/or loadings,