**Analysis of Variance** (**ANOVA**) is an extension of the two sample hypothesis testing for comparing means to more than two samples. The following topics are described in greater detail.

Topics:

- One-way ANOVA
- Factorial ANOVA
- ANOVA with Random Factors and Nested Models
- Design of Experiments
- ANOVA with Repeated Measures
- Analysis of Covariance (ANCOVA)

how do you calculate f ratios for interactions?

See Two Factor ANOVA with Replications

Charles

Hi Charles!

I have an RCBD experiment testing 7 treatments with 3 replications each. I am trying to find out which treatment generates the highest yield. Is two-way ANOVA an appropriate test for this? If so, then can I use Tukey’s HSD test after it when significant differences are detected?

Hi L.A.

I will be addressing these sorts of problems in the next release of the Real Statistics Resource Pack.

Charles

Hi Charles,

Can you explain to me why when we test shapiro-wilks in excel using your calculations versus shapiro-wilks in SAS we get different results?

Thanks!

Kim

Kim,

I don’t know how SAS calculates Shapiro-Wilk. What was the p-value you got from SAS and what was it in Excel? How big is your sample?

Charles

Hi Charles, thanks a lot for your website. I twice arrived at your website over a period of 2 years. Thought I might try asking you this question I’ve long had.

What’s the difference between ANOVA and regression? I get the impression regression analyses variance, and thereby reaches the line of regression. So isn’t that “Use ANOVA to regress”? Thanks. So isn’t ANOVA and regression really just the same thing, start with ANOVA, end with line of regression.

Would appreciate some clarification please. Thanks.

George,

In a very real sense they are the same things. You can perform Anova via regression (using dummy variables) as described in the webpages http://www.real-statistics.com/multiple-regression/anova-using-regression/ and http://www.real-statistics.com/multiple-regression/unbalanced-factorial-anova/.

To carry out regression you use an F test to compare two variables, which is essentially an ANOVA. See Figure 3 of the webpage of http://www.real-statistics.com/multiple-regression/multiple-regression-analysis/.

Charles