I want to compare the means of teachers and students perceptions collected from two likert scale questionnaires. I have 112 teacher respondents and 60 student respondents. Should I use all the responses for analysis or take only the first 60 from teachers' to balance with the students' sample of n=60?
Most data analysis programs will deal with unequal sample sizes for you.
I would recommend keeping all 112 teacher surveys. That is a great deal of work on your part and the part of the teacher to just throw out 52 surveys.
As per my information there is no such condition that the no. of observations in various groups should be equal for application of ANOVA. So, you can proceed with unequal size groups. But before that you need to check for normality.
I agree with Bhag. There is no equality of sample size condition.
The normality assumption is normality in the residuals of the ANOVA model, not the dependent or independent variables. You should plot the residuals. I am less concerned about a failed normality test if the residuals look like they are randomly distributed about zero, and do not show some sort of pattern. Generally, if your sample size is large enough you will be able to reject the normality assumption.
Another issue is that I suspect that the assumption of normality is with the underlying distribution. It is quite possible to draw a small number of values from a Normal distribution such that the distribution of the sample is not Gaussian. The other part of this is that if I withdraw a sample of 200 values from some (I won't tell you which one) distribution, there is no way that you will be able to guess which one I chose. In this game I can choose any distribution from https://cran.r-project.org/web/views/Distributions.html, or I could make a custom distribution. At a sample size of 200, you could probably eliminate a few possibilities, especially if you can see several examples (three or four sets of 200 draws each).
sample sizes need not be equal they can have different sizes. Only you have to check for normality and equality of variances between groups. You can use Shapiro wilk to test normality,
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No need to have same sample size in groups. Only check for homogeneity of variance and normal distribution,you can carry out one way ANOVA
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