ANOVA F-Test Calculator

ANOVA F-Test Calculator

Calculate the ANOVA F statistic and one-tailed p-value: $$ F = \frac{SSB/dfB}{SSW/dfW}. $$

* Enter the between-group sum of squares (SSB) with its degrees of freedom (dfB) and the within-group sum of squares (SSW) with its degrees of freedom (dfW).

Step 1: Enter ANOVA Parameters

e.g., 30

e.g., 2

e.g., 90

e.g., 27

Formula: $$ F = \frac{SSB/dfB}{SSW/dfW}. $$

Understanding ANOVA F-Test

An ANOVA F-test is a statistical test that uses the F-statistic to compare variances and determine if group means are significantly different. It's part of Analysis of Variance (ANOVA), a family of statistical methods that compare group means. 

How it works 

  1. Calculate the variance in each group mean
  2. Calculate the overall group variance
  3. Compare the two variances
  4. Calculate the F-statistic
  5. Check if the F-statistic follows an F-distribution
  6. Determine if the F-statistic is statistically significant

When to use

To use an ANOVA F-test, you can assume that: 

  • Observations are independent
  • The response variable is normally distributed
  • The variances are homogeneous
  • Each group is normally distributed
  • The groups have the same variance
  • The samples are randomly selected in an independent manner

Why it's useful

If the variance between groups is larger than the variance within groups, the F-value is higher, which indicates that the difference observed is real. 

History

ANOVA was developed by statistician Ronal

Statistical Significance

A high F-statistic indicates that the differences between groups are statistically significant. This means that the differences are unlikely to be due to chance alone. 

How is the F-statistic calculated?

  • The F-statistic is calculated by dividing the between-group variance by the within-group variance. 
  • The F-statistic is always positive or zero. 
  • The F-distribution curve is positively skewed towards the right. 

How is the F-statistic interpreted?

  • Compare the F-statistic to a critical value from an F-table or a p-value from a statistical software package. 
  • If the F-statistic is significantly large, you can reject the null hypothesis. 
  • If the F-statistic is not significantly large, you must accept the null hypothesis. 

When is the F-statistic used? 

  • The F-statistic is used in various tests such as regression analysis, the Chow test, and the Scheffe Test.

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