Chapter 1
Critical Thinking
Consider the following data derived from a 1991 record of flight arrivals. In 1987, the Department of Transportation required all US airlines to report data on whether the arrival is late or on time. For now, letâs look at the comparison between Alaska Airlines and America West.
Given this table, which airline do you think has the worse performance? Most people would conclude and say, âThe probability of Alaska Airline being late, as indicated by the percent Late column, is higher, so it has the worse performance.â Letâs see if youâre right.
Take a look at the more detailed tables below. The data is now broken down by airport.
Now what can you notice? America West has the worse performance than Alaska Airlines on every airport. Itâs the reverse of what you derived from the earlier table not broken down by airport. As you can notice, America West flies mostly out of Phoenix which has sunny days (most of the time) while Alaska Airlines flies mostly out of Seattle which experiences more rainy and cloudy days.
The above is a classic example of Simpsonâs paradox. There are many real-life examples of this occurrence whenever data are aggregated. The conclusion you might get is the reverse of what could be derived when you look at the data in more detail. Actual data in test scores, school admission rates, sports, etc., have been used as classic examples as well. Simpsonâs paradox is named after Edward Simpson who wrote about it in 1951. Although a British statistician, G. Udny Yule, first described it in early 1900s.
Making conclusionsâthe right conclusionsâis not as easy as one might think. It requires critical thinking, attention to detail, understanding of the data, and many other things.
Consider this next example.
Given that x and y are any real numbers, and y is a function of x, i.e., y = f(x). I know the function f(x) but you donât. I want you to figure it out.
The only clue I will give you is a table of sample values of x and the corresponding values of y below. Now, can you determine the function f(x)?
If you answered yes, it is f(x) = 1, you are wrong. Your hypothesis is wrong. As you can see below, the function y = sin(x) also fits the data.
The point I am making here is even if your hypothesis fits all the given data points, it doesnât mean that your hypothesis is correct. There are many other possible hypotheses that will fit the data. This is a key concept you have to understand. Evolutionists would claim that âallâ the observed data fit the predictions from the theory of evolution.
First, they provide you of the only data that fit their theory. There are many data points that do not fit their theory. I will touch on those in later parts of this book.
Second, even if the data points they provide fit their theory, it does not follow that their theory is correct.
Let me repeat one sentence in the preceding paragraph. Evolutionists would claim that âallâ the observed data fit the predictions from the theory of evolution. Now given this, they would conclude that their theory must be correct. Whatever happened to âsubstituting facts for appearances and demonstrations for impressionsâ?
Evolutionists would point to gradual changes in fossil records. They would say, âLook, this fossil of an antelope-like animal has short neck. Then we found another one. We carbon-dated it, and we detected that it lived millions of years after the first one we found, and its neck is longer.â Then they will conclude that the giraffe âevolvedâ this way.
First, evolutionists assume that the giraffesâ long necks âevolvedâ to help them feed. They call this the high-feeding hypothesis. Iâm putting quotes around âevolveâ because evolutionists are assuming that their theory is true. So whenever they write their scientific articles, they use the word âevolveâ as if it was true.
Now, theyâre finding out that the high-feeding hypothesis is weak. There are parts in Africa where giraffes really like to eat by reaching up to the top of trees. But there are also parts in Africa where even when food is scarce, the giraffes donât reach up. In the July 7, 2010, issue of Zoologger, Michael Marshall mentioned a new hypothesis. Biologists are now saying that the giraffeâs long neck is a result of sexual selection. Male giraffes fight for females using their necks, swinging it against the other male giraffes, as if in a duel. So those with long necks win. They survive. They mate and pass on that trait to their offspring.
Whoa! Wait! Stop!
Show us the proof! Donât extrapolate!
For a neck to significantly âgrow,â according to evolutionists, there has to be a series of mutations over long periods of time. I put quotes around âgrowâ because evolutionists assume the necks âgrewâ through gradual series of mutations. They say this is âprovenâ by fossil records. Whoa! Wait! Stop!
Do you even know the chance of a mutation? Most mutations are bad, like sickle cells. Instead of surviving, you die. Random mutations are rare. And even by lucky chance of a good mutation leading gradually to the desired outcome (e.g., longer neck), it could take millions and millions of lucky chances.
By all probability, it is most likely not possible due to the complexity of the DNA. Again, the giraffe thing is a data point that they claim fits their theory. But it doesnât follow that their theory is correct! We will get back to the time element and mutation rate later. It requires some basic probability theory.
Perhaps, after more data is observed in the future, they, the evolutionists, would determine that their sexual selection hypothesis is weak. They will come up with new hypotheses for sure. I got one for them. How about, well, the giraffes have long necks because that is how they were created. And all the animal fossils that the scientists have seen that have varying neck lengths? Those animals were also created that way. It just seemed to their naked eyes that there were âgradual changesâ since the necks have varying lengths. They arranged the fossils in carbon dating-produced times, and they âcorrelateâ the necksâ length pattern with the passage of time. In statistics, we know that correlation does not imply causation.
The evolutionists simply extrapolated again! But take note, the creation hypothesis also fits the data.
Now you see, as in the y = f(x) example, two possib...