Significant difference/ANOVA test when some values occure only once

Question

I have fake dataframe with neighbrhood codes and prices of houses in those neighbrhoods, with this amount of values for each negihborhood:

df['neighb'].value_count()

>>>
a    17
b    5
c    3
d    2
e    2
f    1
g    1
f    1

I need to check if there is significant difference in the prices between the neighbrhoods. The problem is that some neighbrhoods have price of only one house, so I don't have group of values as I only have data regard this one house specifically.

Assuming that I cannot get more data regard house prices, (in this task)

Is there any way I can calcualte if there is significant difference in the prices between the different groups? I wanted to use ANOVA but as the groups are really little I find it problematic (also regard the assumption of normal distribution etc).

*clarification : my real database is not prices of houses, is somethiing that I cannot get more data then what I want but I do need to check if there is significant differences between different neighbrhoods when some have alamost no observations.

Answer 1

Consider the following simulated data. Notice that standard deviations differ by group, so I use the oneway.test procedure, which uses a Saterthwaite approximation to give a reasonable P-value.

set.seed(2021)
a = rnorm(17, 1000, 10)
b = rnorm( 5, 800,  10)
c = rnorm( 3, 2000, 15)
d = rnorm( 2,  500,  8)
e = rnorm( 2, 1100, 10)
fgh = rnorm( 3, 800, 20)
x = c(a,b,c,d,e,fgh)
g = rep(1:6, c(17,5,3,2,2,3)) 

This one-way ANOVA procedure works fine, and finds a highly significant difference among groups in my simulated data.

oneway.test(x ~ g)

    One-way analysis of means 
    (not assuming equal variances)

data:  x and g
F = 2317.8, num df = 5.0000, denom df = 5.1515, p-value = 1.298e-08

Using the Bonferroni method to protect against 'false discovery' in ad hoc tests on these data, you might reject two-sample Welch t tests only for P-values below 1%.

It is not surprising to find a sigificant difference ad hoc between a and b because of the difference in sample means and 'reasonable' sample sizes of 17 and 5.

t.test(a,b)$p.val
[1] 5.717784e-09

But some pairs of groups with very small sample sizes are also significantly different. For example,

t.test(c,e)$p.val
[1] 0.0001867002

Of course, I cannot say what will happen with your real data, but at least we know that oneway.test with ad hoc comparisons using Welch t tests is not automatically doomed to failure. I would say that comparisons of the group fgh of 'leftovers' might be difficult to interpret, but you really don't have meaningful data there.