How do I do ANOVA on this calculator?

Choose Groups in rows and put each independent group on its own line, such as A: 5 6 7, B: 8 9 10 and C: 11 12 13 on three lines. Or choose Groups in columns and paste a spreadsheet table. The results update as you edit. Read F, df and p above the inputs; the full table shows the calculation components. No installation is needed for this browser calculator.

How is the one-way ANOVA table calculated?

The grand mean uses all observations. Between-group SS sums each group's size times the squared difference between its mean and the grand mean. Within-group SS sums squared differences from each group's mean. For 5, 6, 7; 8, 9, 10; and 11, 12, 13, the group means are 6, 9 and 12 and the grand mean is 9. Between-group SS is 54, within-group SS is 6 and total SS is 60. Their degrees of freedom are 2, 6 and 8. The mean squares are 27.0 and 1.0, giving F 27.00 and p = 0.001000.

Where are F, degrees of freedom and mean squares?

F and both degrees of freedom appear in the readout and table. For k groups and N observations, between-group df is k minus 1, within-group df is N minus k and total df is N minus 1. Each mean square is its sum of squares divided by its df. F is the between-group mean square divided by the within-group mean square. Within-group mean square is also called MSE.

What does the p-value mean?

Under the classical model with equal population means, p is the probability of an F ratio at least as large as the observed ratio. The model assumes independent observations, normally distributed errors and equal variances. This page reports the number without a decision about your study.

Can I use only two groups?

Yes. Groups 1, 2, 3 and 4, 5, 6 give between-group SS 13.5, within-group SS 4, F 13.50 and p = 0.021312. For two groups, F equals the square of the pooled two-sample t statistic and gives the same two-sided p-value. This page displays F rather than a signed t statistic.

Does it calculate effect size or eta squared?

Yes. Eta squared appears in the notes and copied results. It is between-group SS divided by total SS. For the three default groups, it is 54 divided by 60, or 0.9. It describes the share of variation between these sample groups; it is not a population estimate. When total SS is zero, that ratio is undefined and no eta squared is reported.

Can groups have unequal sizes?

Yes. For groups 2, 4 and 3, 5, 7, the grand mean is 4.2, between-group SS is 4.8, within-group SS is 10, F is 1.44 and p = 0.316262. Rows may have different lengths. In columns, blank cells are gaps rather than zeros.

The within-group mean square is zero, so F would divide by zero. Groups 0.1, 0.1, 0.1 and 0.7, 0.7, 0.7 give between-group SS 0.54 and within-group SS 0. The table still shows these sums but reports no F or p-value.

Which group differs, and can I use repeated measurements?

The page runs no post-hoc test and names no pair of groups. It computes classical independent one-way ANOVA only. It does not compute two-factor, repeated-measures, mixed, Welch or rank-based ANOVA. Repeated observations of the same participants need a different model.

Can I enter means and standard deviations instead of observations?

No. Paste the raw observations for each group. There are no mean, standard-deviation and sample-size input fields, and the tool cannot fill gaps in a partially completed ANOVA table.

How much data can I paste and copy?

Up to 10,000 values across at most 100 groups, within a 200,000-character paste. Individual values support at most 20 decimal places and magnitude up to 1e15. The stage previews the first ten values per group; Copy includes every value, the full table and assumptions. Nothing you paste leaves the browser. Copy creates text, not a spreadsheet download.

How do I paste a spreadsheet or a number with thousands separators?

Choose Groups in columns and paste cells separated by tabs, commas or spaces. A first row of text can supply group names. Omit thousands separators: for a value of 11,880, enter 11880. A comma can separate observations, so the tool refuses ambiguous grouped numbers rather than guessing.

Why can displayed figures or p-values differ slightly?

Sums of squares are computed from your entered decimals, but displayed sums, means and mean squares may round. The displayed total is the sum of the displayed between-group and within-group sums. Standard deviations, F and p-values are numerical approximations. The p-value uses the full F ratio, so calculating p from a rounded F can produce a different answer.

One-Way ANOVA Calculator

Paste raw observations with one independent group per row or column. The tool shows group summaries and the complete one-way ANOVA table, including F, degrees of freedom and p-value. Copy keeps every observation and the results. This is an informational calculation; it does not decide which group differs.

3 groupsIndependentF test

A   5  6  7   mean  6B   8  9 10   mean  9C  11 12 13   mean 12        grand mean  9source   SS  df    MS      Fbetween  54   2  27.0  27.00within    6   6   1.0total    60   8p = 0.001000assumes independent groups and equal variances

F: 27.00

df: 2 and 6

p: 0.001000

Groups: 3

9 values in 3 groups, 2 and 6 degrees of freedom. The mean squares are 27.0 between and 1.0 within.

Sums of squares are computed from your entered decimals. The displayed between-group sum (54) plus the displayed within-group sum (6) equals the displayed total (60). The p-value is the upper tail of the F distribution on 2 and 6 degrees of freedom. It is a numerical approximation. The design is balanced: 3 values in each of the 3 groups. Eta squared is 0.9, the between-group share of the total sum of squares. It describes this sample and estimates nothing about a population. The table reads your groups as independent samples. The classical F model assumes independent observations, normally distributed errors and equal variances. It runs no post-hoc test, so it names no pair of groups.

Your groups

One group per line. A line may start with a name and a colon, as in Control: 5 6 7, and lines may be different lengths: unequal group sizes are ordinary here.

Layout

Group dataValues can be separated by spaces, commas or tabs. Nothing you type leaves the browser.

Group summary

The count, mean, sample standard deviation and within-group sum of squares. Means and sums of squares are calculated from your entered decimals; displayed figures may round. Standard deviations are approximate.

Group	n	Mean	SD	Sum of squares
A	3	6	1	2
B	3	9	1	2
C	3	12	1	2

Worked cases

Three examples show how group sizes and within-group variation affect the table.

[1,2,3] against [4,5,6]two groups
F 13.50, df 1 and 4, p = 0.021312
Default three-group example: 5,6,7; 8,9,10; 11,12,13one-way ANOVA
F 27.00, df 2 and 6, p = 0.001000
Every value identicalno variation within groups
F undefined, said so, not reported as 0

Accuracy. Sums of squares are computed exactly from your entered decimals; displayed values may round. The displayed between-group and within-group sums add to the displayed total. F, standard deviations and p-values are numerical approximations. The p-value is the upper tail of the F distribution at the stated degrees of freedom. The classical assumptions include independent observations, normally distributed errors and equal variances. It runs no post-hoc test and draws no conclusion about which group differs.

Common questions

How do I do ANOVA on this calculator?: Choose Groups in rows and put each independent group on its own line, such as A: 5 6 7, B: 8 9 10 and C: 11 12 13 on three lines. Or choose Groups in columns and paste a spreadsheet table. The results update as you edit. Read F, df and p above the inputs; the full table shows the calculation components. No installation is needed for this browser calculator.
How is the one-way ANOVA table calculated?: The grand mean uses all observations. Between-group SS sums each group's size times the squared difference between its mean and the grand mean. Within-group SS sums squared differences from each group's mean. For 5, 6, 7; 8, 9, 10; and 11, 12, 13, the group means are 6, 9 and 12 and the grand mean is 9. Between-group SS is 54, within-group SS is 6 and total SS is 60. Their degrees of freedom are 2, 6 and 8. The mean squares are 27.0 and 1.0, giving F 27.00 and p = 0.001000.
Where are F, degrees of freedom and mean squares?: F and both degrees of freedom appear in the readout and table. For k groups and N observations, between-group df is k minus 1, within-group df is N minus k and total df is N minus 1. Each mean square is its sum of squares divided by its df. F is the between-group mean square divided by the within-group mean square. Within-group mean square is also called MSE.
What does the p-value mean?: Under the classical model with equal population means, p is the probability of an F ratio at least as large as the observed ratio. The model assumes independent observations, normally distributed errors and equal variances. This page reports the number without a decision about your study.
Can I use only two groups?: Yes. Groups 1, 2, 3 and 4, 5, 6 give between-group SS 13.5, within-group SS 4, F 13.50 and p = 0.021312. For two groups, F equals the square of the pooled two-sample t statistic and gives the same two-sided p-value. This page displays F rather than a signed t statistic.
Does it calculate effect size or eta squared?: Yes. Eta squared appears in the notes and copied results. It is between-group SS divided by total SS. For the three default groups, it is 54 divided by 60, or 0.9. It describes the share of variation between these sample groups; it is not a population estimate. When total SS is zero, that ratio is undefined and no eta squared is reported.
Can groups have unequal sizes?: Yes. For groups 2, 4 and 3, 5, 7, the grand mean is 4.2, between-group SS is 4.8, within-group SS is 10, F is 1.44 and p = 0.316262. Rows may have different lengths. In columns, blank cells are gaps rather than zeros.
Why is F undefined?: The within-group mean square is zero, so F would divide by zero. Groups 0.1, 0.1, 0.1 and 0.7, 0.7, 0.7 give between-group SS 0.54 and within-group SS 0. The table still shows these sums but reports no F or p-value.
Which group differs, and can I use repeated measurements?: The page runs no post-hoc test and names no pair of groups. It computes classical independent one-way ANOVA only. It does not compute two-factor, repeated-measures, mixed, Welch or rank-based ANOVA. Repeated observations of the same participants need a different model.
Can I enter means and standard deviations instead of observations?: No. Paste the raw observations for each group. There are no mean, standard-deviation and sample-size input fields, and the tool cannot fill gaps in a partially completed ANOVA table.
How much data can I paste and copy?: Up to 10,000 values across at most 100 groups, within a 200,000-character paste. Individual values support at most 20 decimal places and magnitude up to 1e15. The stage previews the first ten values per group; Copy includes every value, the full table and assumptions. Nothing you paste leaves the browser. Copy creates text, not a spreadsheet download.
How do I paste a spreadsheet or a number with thousands separators?: Choose Groups in columns and paste cells separated by tabs, commas or spaces. A first row of text can supply group names. Omit thousands separators: for a value of 11,880, enter 11880. A comma can separate observations, so the tool refuses ambiguous grouped numbers rather than guessing.
Why can displayed figures or p-values differ slightly?: Sums of squares are computed from your entered decimals, but displayed sums, means and mean squares may round. The displayed total is the sum of the displayed between-group and within-group sums. Standard deviations, F and p-values are numerical approximations. The p-value uses the full F ratio, so calculating p from a rounded F can produce a different answer.

Sums of squares are computed exactly from your entered decimals; displayed values may round. The displayed between-group and within-group sums add to the displayed total. F, standard deviations and p-values are numerical approximations. The p-value is the upper tail of the F distribution at the stated degrees of freedom. The classical assumptions include independent observations, normally distributed errors and equal variances. It runs no post-hoc test and draws no conclusion about which group differs.