# Analysis of Variance from Summary Data

This web page performs a one-way ANOVA from summary data -- that is, from the counts, means, standard deviations (or standard errors) for each group. This can be useful if you don't have the individual numbers for the members of each group, but only the summarized data. This might happen, for example, if you're analyzing data that has been summarized in a book or published article. A one-way ANOVA can be thought of as an extension of the unpaired Student t-test to more than two groups. Or, you can think of the Student t-test as a special case of the ANOVA for only two groups (or "levels" in ANOVA terminology). A two-level ANOVA is algebraically equivalent to a t-test, and produces exactly the same p values. To use this page you must know how many observations are in each group, and you must know the average (arithmetic mean) and either the standard deviation (SD) or the standard error of the mean (SEM) for the observations in each group.

Enter your data directly, copy/paste or read from CSV file into the data area below. Use short meaningful group names into the first column. Indicate whether you've provided SD's (default) or SEM's.

The results will appear in the conventional "ANOVA Table". A p-value less than 0.05 indicates that there is a significant difference somewhere among the various groups; that is, they do not appear to have all come from the same population.
The program also performs the Tukey HSD ("Honestly Significant Difference") post-hoc test, to indicate which groups were significantly different from which others. And it provides confidence intervals around the differences between the groups.

This page extends John Pezzullo's original page to handle more than 10 groups.

DATA
• N-row × 4-column matrix
1. Group name (String) Unquoted and without blank spaces
2. Number of observations (Integer)
3. Mean (Real)
4. Variance (Real) Default SD
• Delimiter `comma` or `tab`
• Use NA for missing values

Options:
 Variance indicator Standard Deviation Standard Error of Mean Conf. level % Legend size