# Is it ever okay to ignore a low Cramer's V value?

I conducted a survey on college students to assess what demographic variables affected their views of and knowledge towards climate change. There are 11 variables total:

• Gender
• Religion
• Political affiliation
• Hometown size (rural or urban)
• Hometown region
• Did they have a childhood pet (yes/no)
• Degree of discussion of climate change in high school
• Type of high school
• High school's graduating class size
• University region
• University major

I ran a Chi-squared test of independence (X2) between each variable pairing to determine which showed a significant (P ≤ 0.05) association, then calculated Cramer's V (V) for each significant pairing. Interpretations of effect size were made according to Cohen 1988 (synopsis borrowed from the R Handbook):

r=2: Small = 0.10-0.30, Medium = 0.30-0.50, Large ≥ 0.50
r=3: Small = 0.07-0.20, Medium = 0.20-0.35, Large ≥ 0.35
r=4: Small = 0.06-0.17, Medium = 0.17-0.29, Large ≥ 0.29
r=smallest number of rows or columns in the contingency table for each pairing

I have 35 pairings with significant chi-squared values, but most of these have small effect sizes. For example, the pairing Gender and Religion have a significant association (X2=7.5, P=0.02), but a small effect size (V=0.06, r=2). Now I'm trying to build my models with uncorrelated variables, but this will be difficult given the number of significant pairings.

My question is this: is there a basis for ignoring significant correlations that have small effects? Again using the example with Gender and Religion, can I include these variables in the same model since the Cramer's V value is so small? Being able to do this would make model building much easier, but I haven't found any basis for it and don't want this to bite me down the road. Any thoughts or suggestions would be appreciated.