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?
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.
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.