Statistical analysis is the science of data collection and the discovery of patterns and trends. In reality it is just another way of saying “statistics”. After collecting data it is possible to analyse it:
Summarize the data. For example, make a pie chart.
Find key measurements of the position. For example, the average tells you what the average number (or “middling”) in a data set is.
Calculate the middling measurements: These tell you whether your data is tightly grouped or more widespread. The standard deviation is one of the most commonly used diffusion measurements; it tells you how widespread your data is on the average.
Make future predictions based on past behaviour. This is particularly useful in retail, manufacturing, banking, sports or any organization where knowing future trends would be an advantage.
Test the hypothesis of an experiment. Gathering data from an experiment tells a story only when you analyze the data. This part of statistical analysis is more formally called “Hypothesis Testing”, where the null hypothesis (the commonly accepted theory) is proven or disproved.
Statistical analysis and scientific method
Statistical analysis is widely used in science, from physics to social sciences. In addition to testing hypotheses, statistics can provide an approximation for an unknown that is difficult or impossible to measure. For example, the field of quantum field theory, while providing success on the theoretical side of things, has proved challenging for experimentation and empirical measurement. Some social science topics, such as the study of consciousness or choice, are virtually impossible to measure; statistical analysis can shed light on what would be the more or less likely scenario.
When statistics lie
While statistics may seem a solid basis for drawing conclusions and presenting “facts”, wary of the pitfalls of statistical analysis. They include the deliberate and accidental manipulation of results. However, sometimes statistics are simply wrong. A famous example of “simply wrong” statistics is Simpson’s Paradox, which shows us that even the best statistics can be completely useless. In a classic case of Simpson, the University of Berkeley admission averages (correctly) showed that their average admission rate was higher for women than for men, when in fact it was the opposite. For a more detailed explanation of this puzzle, see Simpson’s Paradox.