I am interested in comparing mean protein levels (dependent variable) across four groups (independent variable), while controlling for covariates/ confounders. I will perform this (essentially ANCOVA) analysis for several proteins, however the unit of measurement is arbitrary. It cannot be used to compare the levels of different proteins. Thus, I will z-score transform each protein separately and perform the ANCOVA to compare group differences for that specific protein.
In the end, I will plot the results on a single graph. Can z-scores be used for comparing mean differences? Does it also make sense to plot the mean z score for each group, or differences in z-score means?
Thank you in advance
No - you should not standardize the DV. The mean of any distribution of z scores is 0 (by definition). In other words, every group mean will simply be equal to 0.
If these different proteins cannot be meaningfully measured on the same scale, they should be assessed in separate analyses.
Hello Marc,
If the key comparison is whether the mean levels differ by group (IV), it won't matter whether you standardize the scores for a given DV (for the entire batch of data) or not. Converting to z-scores is simply a linear transformation, and linear transformations will not change: (a) shapes of distributions; (b) relative differences between groups; or (c) correlations among any pair of scores.
If doing this (z-score transform) makes it easier to display the results of multiple DVs on the same graph, go for it. However, if your audience would find it easier to digest the results if given in the original metric(s), then be sure to include a summary table with that information.
Good luck with your work.
I think the reasons David Morse and Blaine Tomkins reach different answers is Blaine is discussing standardizing within groups. While there might be some interesting things you could look at depending on how you use your covariates, as he says, the means would be equal. As David says, the usual standardizing, (x_i - mean)/sd, of the whole sample won't affect the substantive conclusions among groups. The mean and sd could be for you sample or some population values or those for a control group or whatever. I assume you mean some linear transform by z transform (not something like normalizing, which is generally not linear).
My only suggestion is this would be easier if you got of the ANOVA paradigm Take a look at the attached description of a much better way to think about this. Best wishes David Booth PS the book is available from the z-library
Thank you very much for all of your answers. Blaine Tomkins I am interested in standardizing within a single protein, while all of the groups are included, rather than standardizing within one group at a time for a given protein. The means of the groups for a given protein would no longer be 0. David Morse Your second point is my goal, to plot a single graph with all of the proteins standardized, since the original unit of measurement is arbitrary and cannot be used to compare levels across different proteins. I also noticed that indeed, David Morse Daniel Wright , standardizing the dependent variable for the whole sample (for a protein) and performing the analysis on the raw data yields the same results. This transformation would only be for graphical purposes.
My final question is whether it would make more sense to plot the beta from the multiple regression (which would be the difference in mean z-scores?). Or simply plotting the mean z score for each group? However, I am not sure if each group's mean is technically still a z-score? I don't think so
Thank you @David Eugene Booth, I will take a look.
You can certainly pool all the raw scores across protein types and convert them to standardized scores. However, the transformed means will be in standard deviation units - losing their original meaning. The mean only makes sense in the context of the original measurement scale. Once you standardize the raw scores, the relative order across the protein types will remain unchanged (largest to smallest), but the absolute differences and ratios will change.
I quickly created two bar graphs in Excel, one displaying the means in raw units and one displaying means of the z-transformed scores of the same data. Notice they look nothing alike, and one level even has a negative average now. As David mentioned, the result will be the same, but the interpretation will change.
Just my preference, but I generally avoid transforming the DV if the units are inherently meaningful (e.g., dollars, pounds, etc.,). Level of protein expression sounds like an inherently meaningful metric - but then I don't study proteins and I'm not sure if you're only interested in making relative or absolute comparisons?
- Badges
- Science topic