# Confused. What type of ANOVA to use?

A Food Technology student ask me to determine if there is a significant difference between the formulations in his product, denoted by Lot A, Lot B, and Lot C.

I read about ANOVA and decided to use ANOVA Single Factor, BUT, I read previous BS thesis and found out that they all use ANOVA Two-way Factor. Now I got confused whether I will use single factor or two-way.

Sample data:

panelist lotA lotB lotC 1 6 7 8 2 8 9 7 3 8 8 7 4 8 8 7 5 7 8 6 6 8 7 7 7 7 9 8 8 8 8 7 9 8 9 7 10 7 9 6 11 8 9 7 12 7 8 9 13 9 7 8 14 7 9 5 15 8 9 7

Edit (10142016): He wanted to know which product is better (if there is a significant difference) based on the ratings of 15 panelists for each products. By the ways, it is only a product with different formulations: Lot A has a 25% extract of x, Lot B has 50%,whereas Lot has 75%.

I will be using R in my analysis.

• Does this mean 15 people each rated all three products? Some more detail might help. Commented Oct 12, 2016 at 8:53
• Are we simply wanting to compare lotA, lotB and lotC to each other? If so, why not use a pairwise wilcoxon test?
– Jon
Commented Oct 12, 2016 at 15:38
• @mdewey Yes, 15 panelist rated each three products.
– user134390
Commented Oct 13, 2016 at 0:03
• @Jon Sorry to mention but he said that ANOVA must be used because it is the commonly used method in their school. I don't know why but he said it is better to"stick to the rules".
– user134390
Commented Oct 13, 2016 at 0:06
• @Jon why would it make sense to make three pairwise comparisons when a single omnibus test for differences can be performed? Commented Oct 13, 2016 at 16:05

I'm pretty rusty when it comes to Design of Experiments jazz, but sounds like you want to use a balanced ANOVA with repeated measures. Not sure what software you're using to perform the analysis, but I'll link you to some R/SAS material.

ANOVA Repeated Measures (for SAS but applies to R as well):

When to Use Repeated Measures ANOVA

As with any ANOVA, repeated measures ANOVA tests the equality of means. However, repeated measures ANOVA is used when all members of a random sample are measured under a number of different conditions. As the sample is exposed to each condition in turn, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: the data violate the ANOVA assumption of independence. Keep in mind that some ANOVA designs combine repeated measures factors and nonrepeated factors. If any repeated factor is present, then repeated measures ANOVA should be used.

http://www.ats.ucla.edu/stat/sas/library/repeated_ut.htm

Here is an example using R:

https://ww2.coastal.edu/kingw/statistics/R-tutorials/repeated.html

Best of luck!

• I edited my post. I will be using R. I am just confuse why they are using two-way since there is only one variable, the product, correct me if I am wrong.
– user134390
Commented Oct 14, 2016 at 0:57