Three factors make statistics hard to learn for some.
Probability vs. statistics
The whole idea of statistics is to start with a limited amount of data and make a general conclusion (stated in terms of probabilities). In other words, you use the data in your sample to make general conclusions about the population from which the data were drawn.
Probability theory goes the other way. You start with knowledge about the general situation, and then compute the probability of various outcomes. The details are messy, but the logic is pretty simple.
Statistical calculations rest on probability theory, but the logic of probability is opposite to the logic of statistics. Probability goes from general to specific, while statistics goes from specific to general. Applying the mathematics of probability to statistical analyses requires reasoning that can sometimes seem convoluted.
Statistics uses ordinary words in unusual ways
All fields have technical terms with specific meanings. In many cases, statistics uses words that you already know, but give them specific meaning. "Significance", "hypothesis", "confidence", "error", "normal" are all common words that statistics uses in very specialized ways. Until you learn the statistical meaning of these terms, you can be very confused when reading statistics books or talking to statisticians. The problem isn't that you don't understand a technical term. The problem is that you think you know what the term means, but are wrong. As you read these help screens be sure to pay attention to familiar terms that have special meanings in statistics.
When I use a word, it means just what I choose it to mean — neither more nor less.
Humpty Dumpty (amateur statistician) in Through the Looking Glass
Statistics is on the interface of math and science
Statistics is a branch of math, so to truly understand the basis of statistics you need to delve into the mathematical details. However, you don't need to know much math to use statistics effectively and to correctly interpret the results. Many statistics books tell you more about the mathematical basis of statistics than you need to know to use statistical methods effectively. The focus here is on selecting statistical methods and making sense of the results, so this presentation uses very little math. If you are a math whiz who thinks in terms of equations, you'll want to learn statistics from a mathematical book.
Parts of this page are excerpted from Chapter 2 of Motulsky, H.J. (2010). Intuitive Biostatistics, 2nd edition. Oxford University Press. ISBN=978-0-19-973006-3.
