I am trying to analyze data based on a sample size of around 50 and would appreciate advice on which statistical test would be most appropriate. Participants, on a single questionnaire, were asked to complete two different sections. Variable 1: rating Likert items on a scale from 1-5 (strongly agree to disagree). Variable 2: rating Likert items of a validated tool on a scale of 1-9, which is averaged to obtain a single number.
My research question is: Do those who 'agree' with the statement in the first section significantly differ in terms of their scores on the variable 2, compared to those who 'disagree'? (ex. Do participants tend to 'agree' with "I like to read books for pleasure." have higher IQs (variable 2) than those who 'disagree'?)
I was advised by a colleague to run a one-way ANOVA with variable 1 (categorical) as IV and variable 2 (continuous) as DV.
Question 1: My independent variable is the three groups: 'agree', 'neutral', and 'disagree.' (I combined strongly agree with agree because of low frequencies and likewise for strongly disagree and disagree.) However, there are many more participants in the 'agree' category than in the 'disagree' category. The distribution is, on average, around 44 agrees, 3 neutrals, and 3 disagrees. Do the (very) unequal sample sizes prevent me from performing ANOVA, or any other tests? Which test would be most appropriate for this analysis?
Question 2: I would like to run analyses on all of the Likert items, which is more than 10 statements. (ex. Seeing how IQs correlate with agreement to many statements including “I like to read books for pleasure,” “I watch a lot of TV,” “I exercise more than 30 minutes each week,” etc.) I was planning to do a Bonferroni correction to adjust for the multiple tests. Would this be correct, and help make my analyses more robust? Note: The continuous data are not normally distributed (there is negative skewness), but I seem to be able to correct the skewness using logarithmic transformation.
Any advice or suggestions for papers to read would be appreciated. Thank you!