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The phrase "a close analysis of" is correct and commonly used in written English.
It is typically used to introduce a detailed examination or investigation of a particular subject or topic. Example: A close analysis of the data reveals a strong correlation between sleep patterns and academic performance.
Exact(59)
A CLOSE analysis of Bush I may help.
Fine words, but a close analysis of the core texts shows all the old, male-blaming biases are still there.
Yet a close analysis of U.S. Census data shows that the true number is just 30percentt.
Here he uncovers sources all but unknown to non-Iranians and still has time and breath for a close analysis of the disputed presidential election last June.
He can accurately read a person with a small sniff of his nose and a close analysis of their shoes and handbag.
He is allied with the French spectralist school, which draws musical material from a close analysis of overtones and other properties of sound.
It does exactly what a work of historical scholarship should do: provide a close analysis of editorial decisions, and interpret them.
With a close analysis of data, he rebuts claims about the criminalisation of children in residential homes, and makes recommendations to ensure young people aren't be "needlessly criminalised".
His simplicity was hewn out of a close analysis of others and their place in a society riven by class interests.
A close analysis of the three break points reveals the brilliance of Federer and how he plays the big points on his terms.
Often, a close analysis of vibrational spectra of labeled molecules offers the best means for testing the soundness of the prevailing theoretical understanding of molecules.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com