I have a dataset with 100 paired values (pre- and post intervention X). In 20 couples 1 of the 2 values is missing. When I compare pre- to post-intervention values, those 2 couples / rows will be excluded, as I use a paired test.
But how to plot this data set?
1. Do I also need to exclude the 20 couples from the graph? That would result in a graph that perfectly fits the results of the analysis.
OR
2. Should I include those 20 couples in the graph although they are not part of the analysis, but that way the "true result" is better represented? That is what e.g. Graphpad Prism does, when I plot the data.
Very looking forward to your help!
Kind regards
Mathias
The best way to show paired data is in a 2D scatterplot. There is no way to plot singletons in this plot because there is only one dimension given.
However, it is important to show how many singletons there are and what their values are. You can do this by plotting these values above the plot and at the right side of the plot (depending on which of the two values is given).
An additional note: In your analysis, 20% of your sample is not used, and it may be relevant to check if the values are missing at random or if the missingness is associated with something related to your experiment. If the latter is the case, these missing values leave a biased sample, what might be problematic (this might be assessed with a sensitivity analysis, replacing the missing values by optimistic and by pessimistic guesses).
Thank you very much for your reply!
But I want to plot the results in box plots as in the example images attached: One is with all data (full), one only containing the data with complete couples.
The graphs differ and I am not sure which to choose.
As I said, I strongly recommend a scatterplot.
You could add these boxplots at the sides of the scatterplot, something similar to this: https://www.machinelearningplus.com/wp-content/uploads/2018/11/7_Marginal_boxplot_Matplotlib-min.png
You might check out: https://www.researchgate.net/post/What_is_the_best_graph_to_compare_mean_before_and_after_an_event
Jochen Wilhelm 's suggestion of a scatterplot wins out there too, and providing dots for the missing in margins seems a good add-on. Box plots don't show the association between the pre and the post, so are not very useful here. You could adjusted this to be within subject boxplots, like several people have done for confidence intervals (e.g., Article Graphing within-subjects confidence intervals using SPSS and S-Plus
), but it seems like scatterplots will be better in your situation.
1) As mentioned by Jochen Wilhelm , scatterplots would be a good solution.
2) As mentioned by Jochen Wilhelm , simply excluding 20% of cases may be not a great idea as this may lead to biased estimates.
3) Btw, there's an approach to show 3 variables simultaneously: value_id, pre-intervention X, and post-intervention X.
Please have a look at the "X_vs_PID" graph (LISTING 4) we introduced in this work:
Poster A Visual Framework for Longitudinal and Panel Studies (with ...
For your data you can adapt this graph using the following approach:
A. Use x-axis for value_id.
B. Plot pre-intervention X vs value_id using some specified color and mark.
C. Plot post-intervention X vs value_id using another color and mark.
Thank you everybody for the suggestions!
Regarding the remark of Andrey "Excluding 20% of cases may be not a great idea as this may lead to biased estimates.": That is correct. On the other hand, 20 % missing values in the calculation without pairing leads to a bias, too. The question is, which bias is better.... As I think, that the information the pairing gives me is more important, I finally decided to go for paring and excluded the cases.
The augmented scatter-plot idea could usefully be extended adjusting the graphical representation along each axis so that you show those values included in pairs distinguished from those not in pairs.
You can look for analysis that included both paired and unpaired values in the theory for dealing with missing values, starting perhaps with the EM algorithm for normal-distribution theory. However, you would need to be able to justify to yourself and others the extra assumptions on which that relies. In particular, assumptions about why values are missing and assumptions about the marginal distributions. An alternative approach would be a Bayesian analysis of a full model, but that would suffer from the same problems.
But including all the data in a simple analysis does not need to be "biased", although you might not be able to do it with blind usage of a statistical package. Usually the basic test statistic is an estimate the difference of two means divided by an estimate of the standard deviation of that difference. You just need to get a good estimate of the standard deviation of the difference ... one that takes account of both paired and unpaired data types.
Mathias Roth I think your decision is OK since any modelling is based on some assumptions. Here you need the missing-at-random assumption (as mentioned above in the discussion). One question a reviewer can have: is the distribution of pre-intervention X the same for 'coupled' values and 'uncoupled' values. So you can just add side-by-side boxplots to compare those.
If the boxplot shows that the distribution of pre-intervention X for 'coupled' values differs from that of 'uncoupled' values, this may indicate a potential problem making your analysis highly unreliable.
My sugestion is to add "blind" cathegory for missing values in both samples. In this way it's possible visualy (and logicaly) to identify such values.
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