Concept Summary

Measures of central tendency provide a single value representation for the middle of a group of data.
The arithmetic mean or average is a measure of central tendency that equally weighs all values; it is most affected by outliers.
The median is the value that lies in the middle of the data set. Fifty percent of data points are above and below the median.
The mode is the data point that appears most often; there may be multiple (or zero) modes in a data set.

Distributions have characteristic features that are exemplified by their shape. Distributions can be classified by measures of central tendency and measures of distribution.
The normal distribution is symmetrical. The mean, median, and mode are all the same in the normal distribution.
- The standard distribution is a normal distribution with a mean of zero and a standard deviation of one; it is used for most calculations.
- 68% of data points occur within one standard deviation of the mean, 95% within two, and 99% within three.
Skewed distributions have differences in their mean, median, and mode; the skew direction is the direction of the tail of the distribution.
Bimodal distributions have multiple peaks, although not necessarily multiple modes, strictly speaking. It may be useful to perform data analysis on the two groups separately.

Range is the difference between the largest and smallest values in a data set.
Interquartile range is the difference between the value of the third quartile and first quartile; interquartile range can be used to determine outliers.
Standard deviation is a measurement of variability about the mean; standard deviation can also be used to determine outliers.
Outliers may be a result of true population variability, measurement error, or a non normal distribution.
Procedures for handling outliers should be formulated before the beginning of a study.

The probability of independent events does not change based on the outcomes of other events.
The probability of a dependent event changes depending on the outcomes of other events.
Mutually exclusive outcomes cannot occur simultaneously.
When a set of outcomes is exhaustive, there are no other possible outcomes.

Hypothesis tests use a known distribution to determine whether a hypothesis of no difference (the null hypothesis) can be rejected.
Whether or not a finding is statistically significant is determined by the comparison of a p-value to the selected significance level (α). A significance level of 0.05 is commonly used.
Confidence intervals are a range of values about a sample mean that are used to estimate the population mean. A wider interval is associated with a higher confidence level (95% is common).

Pie charts (circle charts) and bar charts are both used to compare categorical data.
Histograms and box plots (box-and-whisker plots) are both used to compare numerical data.
Maps are used to compare up to two demographic indicators.
Linear, semilog, and log–log plots can be distinguished by their axes.
Slope can be calculated most easily from linear plots.
Tables may contain related or unrelated categorical data.

Correlation and causation are separate concepts that are linked by Hill’s criteria.
Data must be interpreted in the context of the current hypothesis and existing scientific knowledge.
Statistical and practical significance are distinct.