I'm comparing 1 continuous variable across 36 groups (nurses grouped into 36 hospital units). Several groups have only 1 observation, but most have more, ranging from 1-24 observations per group. Total observations across all groups are 120.
Here are the results and problems with each of the tests I've done (using SPSS 26):
One-way ANOVA: p = 0.002, but a Levene's test yields p=0.002 based on mean (p=0.121 based on median, not sure if that's relevant) indicates heteroscedasticity, which rules out ANOVA since my group sizes are so different.
Welch's ANOVA: Cannot produce results because some groups have only 1 observation. SPSS states, "Robust tests of equality of means cannot be performed because at least one group has the sum of case weights less than or equal to 1."
Kruskal-Wallis: p = 0.006, but some sources indicate that this test is not valid for data with unequal variances, and I've also read that this test should only be done for groups of sample size >=5.
Is there a test appropriate for comparing these groups? Or can I omit the groups with just 1 observation?
Thanks so much!