Between CEO and Employees? So you are not evaluating a difference between companies?

Each company has n=1 for the CEO score, and an mean score for the employees? Is the sample n=326 for each company or is n=236 the total for all companies?

Yes, between CEOs and employees. The CEO self-assessed their leadership style using a Likert scale (0-4). The employees rated their CEO with the rater version of the leadership style assessment.

For clarification, the CEO scores are not mean scores, they are actual. The employee scores are the mean scores. Only the summative means scores are actual means of both groups.

So you have a sample of n=8 companies. You can compare each self-assessment
with the corresponding aggregated assessment, using Wilcoxon signed rank test
(a dependent samples t-test is not recommended, due to the very small sample size).

So you have a sample of n=8 companies. You can compare each self-assessment
with the corresponding aggregated assessment, using Wilcoxon signed rank test
(a dependent samples t-test is not recommended, due to the very small sample size).

I am not sure if I am following your suggestion. Take company 1 for example, there were 1 CEO and 42 employees. The CEO rated himself 1.8 and the 42 employee ratings were tabulated with a mean of 2.3. Wilcoxon would tell me if there is a significant difference between these two scores

Take company 1 for example, there were 1 CEO and 42 employees. The CEO rated himself 1.8 and the 42 employee ratings were tabulated with a mean of 2.3.

You could find a confidence interval for the employee mean and see if the CEO lies outside it - effectively a one sample t test. Wjth 42 employees there is enough data for a one sample test. However, with 8 companies and 3 styles there are 24 tests so even if there was no real difference anywhere you would be very likely to have a few p values less than 0.05. You would need to set your cutoff for significance very low to protect against these false positives, say 0.005 or less?