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I am working with a dataset that includes demographic variables (age and sex) and purchase details for services related to body ornamentation (tattoo location, piercing location, tattoo type, etc.) over a ten year period. My aim is to see if the frequencies are different within years and between years.

For example, for the below output, I would like to investigate if there is a significant difference between female and male location choice for each category within 2007 and then to be able to compare that to other years (ex. 2015).

To be more specific, for the location "arm": females had that location tattooed 18 times in 2007 and 27 times in 2015, while males had that location tattooed 44 and 60 times, respectively. I would like to test if there is a significant difference between 18 (F) and 44 (M) in 2007, 27 (F) and 60 (M) in 2015, 18 (F) and 27 (F) between 2007 and 2015, and ultimately, if 18 (F) is significantly different from any of the other locations (foot, hand, etc.) females got tattooed in 2007.

#data output for 2007 subset    
location    female  male
arm         18      44
foot        14      2
genital     0       0
hand        5       1
head        0       1
leg         6       2
lip         4       1
neck        6       5
torso       35      22

#data output for 2015 subset    
location    female  male
arm         27      60
foot        10      1
genital     1       1
hand        14      8
head        0       2
leg         6       3
lip         0       3
neck        4       4
torso       13      16

I've been directed to the Handbook of Biological Statistics which has helped me understand that repeated goodness of fit tests (G-tests) would allow me to compare the observed frequencies with the expected (50:50).

That is, I could compare within 2007 for single locations (i.e. 18 (F) to 44 (M)) or across locations within sex (i.e. 18 arm tattoos (F) to 14 foot (F) to 5 hand (F), etc.), but I don't know how it will allow me to compare across years.

Is this approach appropriate? Is there anything else I should be considering (such as p-value problems that arise when running repeated tests)?

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It looks like you want some sort of count regression model (e.g. Poisson or negative binomial regression) with the count of tattoos as the dependent variable and independent variables including year, sex, body part and the two way interactions of those variables. You can then use various contrasts to test individual hypotheses.

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