# Statistical test for relationships when many samples are unknown

I'm fairly new to statistics - I'm sure this is a basic question but my google searching is failing me. Happy to just be pointed to other reading.

I have 3 datasets of varying sizes (N1 ~ 200,000, N2 ~ 80,000, N3 ~ 400). In each dataset, for each sample (row in the dataframe, I'm not even sure what the right vocabulary is here) I have 5 different data points (the columns). Each data point started life as a first name, and the thing I'm interested in is gender. I used genderize.io to test names, and they return a gender, a probability and a sample size (their dataset is based on census data, social media profiles etc).

I modified the gender variables to all be P-female (so (F, 0.95, 300) becomes (0.95, 300) and (M, 0.9, 50) becomes (0.1, 50). But the gender may also be unknown, which means there were no samples of that name in the database.

There are a couple of different tests I want to do to look for differences. The null hypothesis in all cases is that there's no difference.

I want to test:

1. whether there's a difference between columns within a single dataset (so check whether there's a difference in P-female between column 1 and column 2, or column 2 and column 3 etc within a single dataset).
2. whether there's a difference between datasets for each column (is column1 in Set1 different from column1 in Set2?).
3. If there's a difference between data sets in the difference between columns within the datasets. Eg, if the difference between column1 and column2 in Set1 is larger or smaller than the difference between column1 and column2 in Set2.

A major consideration is that the "unknown" genders are ~50% of each set of samples.

I've no idea where to start. Any help would be appreciated, and let me know if I can provide additional information.

I'm looking at authorship in scientific publications. I pulled data from Pubmed and I parsed the author lists and put them into 5 bins. First_Author, Last_Author, Second_Author, Penultimate_Author, Other_authors. My script basically fills out the positions in that order, so if there are only 3 authors, that paper gets a name in First_Author, Second_Author and Last_Author. If there are 20 authors, each of the named positions gets one name, and the Other_Authors gets an array of 16 names.
Not sure if this is relevant, but after reading some other posts here, I thought it might be important. DataSet2 should be a subset of DataSet1 and DataSet3 should be a subset of DataSet2. I say "should be" because the search terms I used should have this behavior, but I haven't actually checked. It would be possible for me to check if this information is important.
• No, each column is filled with tuples (P(f), n). The 5 columns are positions in an author list (I'm looking at scientific publications, so I have a column for first author, a column for last author etc) – kevbonham May 1 '16 at 14:43