Identifying problems in your data

Skewness

You can use a graph to help you examine whether your data are evenly distributed on both sides of the center or skewed in one direction. When data are skewed, which is common when the data are not normal, the mean and median have different values. If your sample is small and the data are skewed, the validity of a parametric test, such as a t-test, may be questionable. In this case, you may want to use a nonparametric test, which is not based on the normal distribution.

Right-skewed data in a histogram

The data in the histogram have most values on the left side of the graph, but a small number of values that are to the right. A tail in the direction of higher numbers indicates right-skewness.

Patterns that occur over time

If you know the order of data collection, you can use a scatterplot or time series plot of the data against time to reveal nonrandom patterns. If your data show a nonrandom pattern over time, a hypothesis test may be less appropriate than an analysis that evaluates the data in relation to time.

A plot that shows a time pattern

A strong pattern, or trend, in the data over time should usually not occur in random data that are appropriate for a hypothesis test. If you identify an increasing or decreasing trend in the data over time, investigate the data to determine the source of the trend before you collect a random sample to test.

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