Split-half when intermediate values are equal I am trying to perform a split-half for strategy use, however, as you can see the middle most users have the same score. What is the best approach to perform a split-half in this situation? Do you have any references (ideally peer-reviewed) that covers this topic? Any help will be greatly appreciated. 

 A: I cannot find a published reference for you, but to the extent of my knowledge, there is no best way. No one really agrees what to do with them. For instance, SPSS puts values at the median in group 2 rather than group This answer using R puts the values at the median in group 1 rather than group 2. You can put them all in group 1, put them all in group 2, delete those cases (this is what was told to me all the time when I was a research assistant many years ago), or randomly assign them to one group or the other.
The reason there is no consensus is because you are arbitrarily categorizing your data. If your categories are arbitrary to begin with, then what you do with the values at the median is arbitrary. Median does not have a magical property of determining what is low and what is high. I can do a median split on income for a study of investment bankers and call people who make \$250,000 per year "low income" if greater than 50% of my respondents make \$300,000 per year. People use the median because it is defensible (somewhat). The median + 1 is just as defensible, really, which would put all the 80s into group 1. The median - 1 is also just as defensible, which would put all the 80s into group 2. Ideally you have a justification for why you are dichotomizing your data. So come up with a justification for what you do with the values at the median. You could also do a mean-split, or pick some other arbitrary cutoff point that has meaning in your field. For instance, high vs. low blood pressure is well defined (120/60 or something like that). Medical research may dichotomize their data into elevated vs. not elevated blood pressure based on whether or not someone is above (or equal to) or below that level. Does your field have cutoff points for what you are studying? If not, come up with a good justification.
However, my real suggestion is to not categorize your data at all. What you will find plenty of peer-reviewed publications for is that arbitrarily dichotomizing your data is generally a terrible idea.
DeCostner et al. (2011) Best Practices for Using Median Splits, Artificial Categorization, and their Continuous Alternatives. Journal of Experimental Psychopathology
Irwin, J.R., & McClelland, G.H. (2003). Negative consequences of dichotomizing continuous predictor variables. Journal of Market Research, 40, 366-371.
MacCallum, R.C., Zhang, S., Preacher, K.J., & Rucker, D.D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19-40.
DeCoster, J., Iselin, A. M. R., & Gallucci, M. (2009). A conceptual and empirical examination of justifications for dichotomization. Psychological methods, 14(4), 349.
I could literally post hundreds of these articles. Keep your data continuous. Analyze using regression or simple correlation for bivariate data.
