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In this article the quote:

The result? Since border wall construction began in Tucson, Arizona, illegal crossings are down 24 percent. In San Diego, California, they’re down 27 percent. And in Yuma, Arizona, they are down over 78 percent.

I was wondering since it's illegal, how do they measure the numbers? 78% in Yuma is impressive. Is this claim supported by the real numbers or is this just an estimate or wishful thinking?

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    Given that construction has only begun it would seem odd to attribute a drop in numbers to it. In fact if the Great Wall of Trump was going to be effective you would expect numbers to increase in the short term as people made a last dash to get through. – Paul Johnson Jan 15 at 13:41
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    I've heard (though I don't have time right now to look for a source) that Trump's anti-immigrant rhetoric was deterring people from crossing the border even before the wall started to go up. Why would you want to move to a country whose leader so openly loathes you? Stories about the conditions in ICE detention centres may also have been a factor. – F1Krazy Jan 15 at 14:15
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    Correllation does not equal causation, correllation does not equal causation, correllation does not equal causation... I.e., "thanks to" is not even claimed in the quoted text. They just make it look that way. Are you asking for the correlation (which is claimed), or the causation specifically (which can't really be proven, see above comments)? – DevSolar Jan 15 at 14:26
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    Edited the title for now to match the claim in the question. – DevSolar Jan 15 at 14:29
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    My downvote is because the answer is obvious. Three miles of new wall has been constructed, but many other punitive measures have been taken to curb immigration (legal and illegal). Would any person really believe that it is the tiny amount of wall that has made the difference rather than the other measures? – DJClayworth Jan 15 at 15:14
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You know that Larry David gif when he made the "I can't make sense out of it" gesture?
This is the thing. The claim in linked article is unquoted. Yet on FoxNews you can, again without a quotation marks, read

Wolf said the wall was top of border officials’ priority list and cited stats suggesting that the wall acted as a deterrent for illegal immigration, drug smuggling and human trafficking. He said that since border wall construction began in Tucson, Arizona, illegal crossings are down 24 percent. In San Diego, crossings are down 27 percent, and in Yuma crossings are down by over 78 percent.

Both bolding by me. So we have a statement that it was Chad Wolf who said those number backed up with stats. So there should be some data to look at and conclude those numbers

And there are - U.S. Border Patrol Southwest Border Apprehensions by Sector Fiscal Year 2020. There the apprehensions that are noted. With divide by age and family status. Now for Yuma we see that Alien Children (0-17 yr old) Apprehensions dropped by 79%. Family units by 88% and single adults by 50% . (To compare, in Del Rio it was up 50% children and families. And in Tucson up by 120% for families). Those are all "compared to previous year"

So it's not the immigration that is down. It's the amount of people who are caught that is down.
Second thing is that, as you can see, there is no "78%". With such exact numbers it would be easy to calculate overall apprehensions OR rounded up for better impact "almost 80%".

So from where the 78% comes from? We know that the quote state since border wall construction began. In Yuma there as already a vehicle barriers, and on October 10 2019 the work started to replace it with 30-foot bollards. We need to assume that this is what means "wall construction".
Based on method of comparision we would need to measure the apprehensions from 10.10.2019 till 01.14.2020 with similar date of october 2018 to January 2019 (to December as January data for 2020 is not yet avaiable).

And the data show that the apprehensions were down by around 30%. So 78%. Where it is? It's in the article by AzCentral.com

More than three quarters of the apprehensions (78 percent) this year are unaccompanied minors and family units, the term the Border Patrol uses to refer to adults traveling with one or more family members.

The only problem is that the article if from May 2018.

So, NO illegal immigration is not down. It's the apprehention rate that is down. And only compared to previous year. For example for December 2017 and 2019 the rate was almost the same, 40 thousand.

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    Just a quick point, its impossible to know how many illegal immigrants aren't apprehended. The best we're going to get is apprehensions. – Ryan_L Jan 16 at 0:15

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