What is the importance of statistics to science?

Answer 1

This question strikes at the heart of what Science is and what it does, and the answer is not exactly the same for all fields of science. As you may know, science, in very very colloquial terms (and I will limit the rest of the language for this answer in the same way), is the search for the truth. This leads to the natural question, how do you know what is really true versus just conceptions of our imagination? In order to assure that our description of an object's properties or its behaviour is true, we simply test our notions, that is, we experiment. For example, in a very simple sense, imagine that I think that heavier objects fall faster than lighters ones to the ground. In order to make sure that my claim is correct, I can take objects of different weights and drop them to see if the heavier ones actually hit the ground first. On many occasions we end up finding that not only was our intuition incorrect but that there might be many other variables and behaviors that we didn't even foresee, but that is besides the point.

However, these is a great limitation we humans have (at least for right now) when it comes to checking the validity of our models: we can't collect exact data, and in some instances some key data may not even be available. Take your average ruler as an example. Let's say you are asked to draw 5 lines measuring exactly 3 inches each with that ruler. You face 2 problems when trying to make those 5 exact lines: 1) your ruler has an inherent error with every measurement due to the way it was manufactured. The line that reads "3 in" on your ruler is not exactly 3 inches away from zero. It may be 2.95 in or 3.01 in but it is not exact (You may be wondering why they would build it that way but having exact measurements is actually really expensive!). 2) The second error comes from the fact that when you trace the line, you are not exactly starting at 0 in your ruler and you are not exactly stopping at 3 in either either because of the limitations by your eyesight, pencil lead width etc. Anyways, you can't get exact readings from measurement devices and this is where statistics comes in.

Let's say you were asked by a group of leading scientists to prove that objects of different weights (all spherical) fall to the ground at the same time and you were provided with a set of balls of different weights and a digital stopwatch. When you do the experiment, you drop one ball at a time and stop the stopwatch when you see the ball hit the ground. You drop them all at different heights to collect meaningful data. You realize that after the ball hits the ground it takes you a little bit to stop the timer, but you collect all your data. You have two errors: 1) the human one you provide by not hitting the stopwatch exactly when the balls hit the ground and the 2) the digital watch doesn't have infinitesimally small increments (it probably increments every 0.01 seconds). You input all your data for the times it took the different balls, to hit the ground at different heights and you realize that the values are not exactly the same for balls drop from the same height. You wonder if your high school physics professor lied to you or if the whole of physics is wrong. However, you do know that you added some errors to the experiment. The question then becomes: what is the likelihood that the differences in time at the same heights were caused by errors in measurements rather than by a completely different set of laws of physics? And to answer this question, you need statistics. You contact the scientists and you tell them: "hey, all the values I got were within 2% of what theory should have predicted," and they will probably reply to you "As long as they are within 4% of each other, we consider it to be true." If this strikes you as incredibly subjective, it's because it certainly is.

There is a concept called the significance level that researchers use as a threshold for rejecting/accepting a hypothesis. This threshold represents the likelihood of observing a pattern of data if a (null) hypothesis is true (I understand this requires more explanation but bear with me). As I mentioned, the threshold is somewhat subjective, but usually things that are the most unlikely (like proving that we can communicate telepathically or that the laws of physics are wrong) require tighter tolerances to prove.

What I mentioned before is more or less thinking of the physical sciences. In the Social Sciences statistics is used more heavily to prove or disprove hypothesis. We wont test on humans because it is unethical and this puts a very big constraint on social scientists when it comes to testing hypothesis. How do they get around that? They collect large amount of data sets from a lot of individuals and use statistical tools such as regression analysis to find relationships between variables and ensure that they are not caused by chance or errors. There are many statistical methods involved in this and even what data to collect and determining the validity of the data can be a statistics problem all in itself! As you can see, statistics is used in many fields of science and it helps us gather information and find relationships even when we can't do it directly.