David Unger

In statistics, a confidence interval gives a range of plausible values for some unknown population characteristic. It contains an initial estimate plus or minus a margin of error (the amount by which you expect your results to vary if other samples were taken). The following table shows formulas for the components of the most common confidence intervals and keys for when to use them.

After data has been collected, the first step in analyzing it is to crunch some descriptive statistics to get an initial feeling for the data. For example: Where is the center of the data located? How spread out are the data? How correlated are the data from two variables? The most common descriptive statistics are in the following table, along with their formulas and a short description of what each one measures.

Formulas — you just can’t get away from them when you’re studying statistics. Here are ten statistical formulas you’ll use frequently and the steps for calculating them. Proportion Some variables are categorical and identify which category or group an individual belongs to. For example, “relationship status” is a categorical variable, and an individual could be single, dating, married, divorced, and so on.

You use hypothesis tests to challenge whether some claim about a population is true (for example, a claim that 90 percent of Americans own a cellphone). To test a statistical hypothesis, you take a sample, collect data, form a statistic, standardize it to form a test statistic, and decide whether the test statistic refutes the claim.

Critical values (z*-values) are an important component of confidence intervals (the statistical technique for estimating population parameters). The z*-value, which appears in the margin of error formula, measures the number of standard errors to be added and subtracted in order to achieve your desired confidence level (the percentage confidence you want).

In a nutshell, the Central Limit Theorem says you can use the normal distribution to describe the behavior of a sample mean even if the individual values that make up the sample mean are not normal themselves. But this is only possible if the sample size is “large enough.” Many statistics textbooks would tell you that n would have to be at least 30.

When you make a decision in a hypothesis test, there’s never a 100 percent guarantee you’re right. You must be cautious of Type I errors (rejecting a true claim) and Type II errors (failing to reject a false claim). Instead, you hope that your procedures and data are good enough to properly reject a false claim.

The mean and median are the two most reliable and commonly reported measures of the center, and they are used in a wide variety of situations. However, if you’re seriously studying statistics, you should be familiar with two other measures of central tendency. Mode The mode is another measure of center that calculates which value (or range of values) occurs most frequently.

Simple random samples are the best way to get an unbiased, representative selection of individuals to be a part of a study. However, the process for generating a simple random sample is akin to having everyone’s name in a hat and then pulling out slips of paper until you fill your sample. How often do you really have access to the names of everyone in a population?