Dear sirs/madams,
Hi.
I have a question the answer to which I couldn't find. I was wondering if you could help me.
I used random matching (matched paires) based on one variable to assign 132 participants into two groups i.e. 66 participants each. However, after deleting outliers and checking the assumptions, imbalanced groups resulted in a way that one group has 58 participants and the other has 53.
Running an independent sample t-test showed no significant difference between the means of the two groups, yet i was doubtful about the numbers of the participants in each group. Should the numbers be exactly the same by deleting the counterparts of the participants that were deleted?
For an independent sample t-test, I would not delete any of the data. However, I assume that the participants were paired for a reason more than as a method for randomly assigning people to one of two groups. So I measure a variable on each participant and I match pairs that are closer together. One person of eac pair goes into each group. The goal is to make the two groups as homogeneous as possible. Now some people leave the study and the pairs are no longer matched. The groups could now be quite different if one of the unmatched pairs was unusual in some way.
I would try reanalyzing the data and delete the bad pairs and see what happens.
You will likely get a similar answer both ways.
There are lots of matching procedures, including those where one person in the control group is matched to just one experimental group, one is matched to many, and many are matched to one. See Rosenbaum's books on matching/observational studies, and google these phrases.
I find the construct of the groups and test run are little confusing here.
If you have paired data, then why run 2 independent sample t test than paired sample t test? Note, Paired t test is most suitable for before and after data and conceptually or mathematically, a paired t test with unequal sample sizes doesn't make sense.
If you have 2 groups of independent samples and you want to find if there is any significant difference between the 2 groups, you may run 2 independent sample t test, where group size of 53 and 58 wont matter much.
Thank you so much. I have two groups, and two IVs: one interval and the other nominal. I intend to run a multiple regression, but before that, I attempted to minimize the effect of the interval IV by using a matched pair design.
After discarding the outliers, the group numbers became imbalanced. I doubted if the number of participants should be exactly the same.
Now i see that the unequal numbers wont be a problem.
Thank you madam🍀☘⚘
In terms of matching as pre-processing before regression you may like to know about
Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference
https://gking.harvard.edu/files/matchp.pdf
and this software considers balance as a trade-off
" MatchingFrontier is an easy-to-use R Package for making optimal causal inferences from observational data. Despite their popularity, existing matching approaches leave researchers with two fundamental tensions. First, they are designed to maximize one metric (such as propensity score or Mahalanobis distance) but are judged against another for which they were not designed (such as L1 or differences in means). Second, they lack a principled solution to revealing the implicit bias-variance trade off: matching methods need to optimize with respect to both imbalance (between the treated and control groups) and the number of observations pruned, but existing approaches optimize with respect to only one; users then either ignore the other, or tweak it, usually suboptimally, by hand."
https://gking.harvard.edu/publications/matchingfrontier-r-package-calculating-balance-sample-size-frontier
Matched pair indicates case wise matching.one to one matching between groups.you should have same number in both groups
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