No, you cannot intentionally make a DNA test negative. Attempting to manipulate the results is considered fraud and is illegal. While sample contamination can lead to inaccurate results (a false positive or negative), this is not intentional manipulation of the test itself.
Understanding DNA Test Accuracy
DNA tests are highly accurate, but not foolproof. Several factors can influence the results:
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Sample Contamination: As noted in multiple sources, foreign substances like food, liquids, or even toothpaste can contaminate a sample, potentially masking the true DNA and resulting in an inaccurate result. 6 Surprising Ways Paternity Test Samples Get Contaminated This is a problem with the sample handling, not an intentional alteration of the test.
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Sample Switching: Deliberately substituting someone else's DNA for your own is the only way to get a false negative result. This is considered fraud. How to fool a DNA test - Quora
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Laboratory Errors: Although rare, errors in sample logging or laboratory processing can lead to incorrect results. My child looks exactly like her father, but the DNA test came ...
Interpreting Negative Results
A negative result on a DNA test, whether for paternity, ancestry, or genetic predisposition, should be interpreted carefully. A negative result doesn't always definitively mean the absence of a particular genetic marker or relationship; it may just indicate that the test couldn't definitively detect the presence of that marker. What do the results of genetic tests mean?: MedlinePlus Genetics Further testing or consulting a genetic counselor may be necessary. BRCA gene test for breast and ovarian cancer risk - Mayo Clinic
Conclusion
Any attempt to falsify a DNA test is unethical and illegal. While errors can occur, the integrity of the test itself cannot be intentionally compromised to produce a negative result.