# Statistics For Dummies

From Statistics For Dummies by Deborah Rumsey

Statistics is about discovering mathematical relationships within collected data. To do that, you come up with a hypothesis, test that hypothesis, and find out how accurate your educated guess turned out to be. You use a variety of formulas to come up with all this statistical data.

Common Statistics and Their Formulas

Statistics is about gathering data and then analyzing it. That analysis means finding the standard statistics for that data. The most commonly used statistics are in the following list, along with their formulas and a short description of what each one measures.

Statistical Confidence Intervals

In statistics, a confidence interval is an educated guess about some characteristic of the population. A confidence interval contains an initial estimate (say, the average starting wage based on a sample of 1,000 recent graduates) plus or minus a margin of error (the amount by which you expect your results to vary, if a different sample were taken). The following table shows formulas for the most common confidence intervals:

Statistical Hypothesis Tests

In figuring statistics, you use hypothesis tests to determine whether some claim about a population is true. (For example, someone may claim that 40% of Americans own a cellphone. Is that true?) To test a statistical hypothesis, you take a sample, collect data, form a statistic, standardize it to form a test statistic (so it can be interpreted on a standard scale), and decide whether the test statistic supports the claim. The formulas in the following table are the most common hypothesis tests:

Statistical Confidence Coefficients, or Z-Values

Confidence coefficients (Z-values) are an important component of confidence intervals — the educated guess you make about a population before you collect statistical data about it. The Z-value is part of the margin of error — the amount you have to add or subtract in order to have a certain level of confidence in your results. The larger the Z-value, the more confidence you can have in your results.

The following table shows confidence levels and corresponding Z-values:

Confidence Level Z-Value Confidence Level Z-Value
80% 1.28 95% 1.96
85% 1.44 98% 2.33
90% 1.64 99% 2.58