How many participants do I need to carry out an four-way Anova?

I am looking at attachment and cyber addiction. I'm carrying out an four-way Anova, attachment patterns being my ivs (secure, preoccupied, fearful and dismissing) with cyber addiction as my dependent variable. I am intending to use 100 participants in my study, I wanted to know if that is an appropraite amount to run a four-way anova?

• You will want to look up resources on power analysis (including the questions on this site tagged power-analysis. Feb 3, 2012 at 13:36
• In addition, many suggest a minimum of 20 participants per cell. Also note that the effect size estimates you get from published studies are likely to be biased upwards, as they do not take account of the file-drawer problem. Feb 3, 2012 at 14:09
• Do you have a continuous measure of cyber addiction? ANOVA is for continuous outcomes (or outcomes that have enough levels that you can treat them as continuous, at least). Feb 3, 2012 at 14:48
• This is a one-way ANOVA, i.e. it has a single factor with four levels. Understanding this terminology should help you to interpret the answers you get and to read the relevant literature. Incidentally, it is much easier to set-up and interpret than an actual four-way design.
– Gala
Feb 3, 2012 at 15:21

I agree with richiemorrisroe: Always use a minimum of at least 20 participants per cell. This was latest uttered in the paper by Simmons et al:

Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant. Psychological Science, 22(11), 1359 -1366. doi:10.1177/0956797611417632

Therefore 100 participants in total should be okay if the four attachment styles are evenly distributed in your sample. However, this is probably not the case. Therefore you should consider getting more participants until the smallest group consists of at least 20 participants (although this strategy, sampling until a certain n is reached in a certain condition, might seem dubious to some, it is not, see Simmons et al., 2011).

As already mentioned, another way of approaching this problem is via power analysis. Following this approach, you would need to find papers with the same/similar question to estimate in advance how big would the effect that you could expect. Based on this estimation you select the sample size for your study. If you find those papers and could make an educated guess on the effect size based on prior studies, simply look at the following paper for an estimate of the desired sample size (if you are unwilling to use GPower):

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. doi:10.1037/0033-2909.112.1.155

Furthermore, as mentioned by Anne Z, four-way ANOVA is not the correct term. You probably mean one-way ANOVA with four factor levels.

• I was not aware of that recommendation of a minimum of 20 participants per cell -- good to know. Also that power primer looks useful and probably easier than downloading and dealing with GPower. Feb 3, 2012 at 15:04

Required sample size depends on the population effect size, the alpha significance level you are planning to use, and the power you want to achieve to detect the effect. If the difference in levels of cyber addiction is very large across attachment pattern levels then you can get by with a smaller sample than if the differences are slight. If you're willing to increase the chance of not finding an effect that is actually there (that is, decrease the power of the analysis), you can do with a smaller sample size. Check out the free G*Power software which allows you to calculate sample size given an estimated population effect size, power, and significance level.

By the way, a "four-way ANOVA" implies you have four different factors (i.e., four different independent variables) not four different levels of a single factor, as it sounds like you may have.