In April, not-yet-a-candidate Donald Trump tweeted enthusiastically about a new poll released by Monmouth University. "Wow," he said, "the respected Monmouth University poll has me ahead of most Republican candidates nationwide, and most people don't think I'm running!"

Over the weekend, Monmouth released another poll, this time showing Trump in second in Iowa.

"The thing with these polls," Trump said on "Morning Joe" on Tuesday, "they're all so different. One guy is up here, somebody else is up there, you see swings of 10 and 12 points and, immediately, even the same day. So right now it's not very scientific."

The polls, of course, are just as scientific now as they were in April. It's Trump's attitude toward them that has changed, as a result of the results of the polling moving in a direction he doesn't like.

Each time there's a new, unpleasant poll out, Trump retweets people who agree with him that the polls are goofy. Given that such occurrences are increasingly regular, we figured we'd debunk some of the most common arguments Trump and his fans have deployed in their own defense.

The sample sizes are too small

Example:

This person appears to be referring to a Quinnipiac poll in Iowa showing Trump down eight points. The sample size of the poll was 574, yielding a margin-of-error of plus or minus 4.1 percent.

Sample size is an admittedly tricky concept to get. How can 574 people give an accurate sense of a population of 3.1 million? But it's easy to come up with an example that's illustrative. When you go to the doctor for blood work, she does not remove all of your blood to check it. She takes only a small amount, an amount large enough to be able to conduct the necessary tests. A small sample of your blood is representative.

Well, then, surely a larger sample gives us more certainty, right? Yes, it does -- but often not much more certainty.

The graph below shows the margins of error around a 50 percent result with various sample sizes. A sample size of 100 yields a big margin of error: 9.8 percent. A sample size of 600, a smaller one, of 4 percent. But increase that sample size to 1,000, and it only drops to 3 percent. The more you increase it, the smaller the change.

Since pollsters need to balance accuracy with the expense of interviewing hundreds of people, it makes more sense to ask 600 people than 2,000, given the subtle difference in margins of error.

You're looking at the wrong polls

Example:

The beauty of the number of polls that we've seen so far in this cycle is that we have a huge amount of information to work with. The problem, though, is that it lets people cherry-pick polls, highlighting the ones they like and dismissing the ones they don't.

National polls from Morning Consult are conducted online. We talked a bit about this earlier this month, noting that online polls can't be extrapolated to the general population using traditional statistical methods.

We also noted that Trump does much better in online polls than in phone surveys.

If we compare Morning Consult polls to the Real Clear Politics polling average -- a running average of live-dial polls -- you can see much more variability in the Consult results, and, recently, much better margins for Trump.

It's easy to see why Trump fans highlight these polls versus the national average, just as it's easy to see why, in a period that four out of five polls in Iowa showed Trump trailing Ben Carson, Trump highlighted Poll No. 5.

The Iowa polls were conducted by Trump haters and are therefore biased

Example:

The tweet above is a very specific complaint that emerged shortly after the new polls showed Trump behind in the state. It appears to be conflating a private poll from the conservative group that was conducted earlier in October with Trump's recent downturn.

Most people in the media would largely ignore an in-house poll conducted for a PAC with a dog in the fight. But Trump's decline in Iowa was seen in polls from Quinnipiac University, the Des Moines Register, Loras College and Monmouth University -- none of which were paid for by Club For Growth.

It's very much worth noting that, for most of these pollsters, this is all they do. Their reputations -- and businesses -- are predicated on being as accurate as possible. Club For Growth has a motivation to have a particular result. Pollsters only want a result that they can brag about for its predictive power.