Are these the right tests for my data?

Question

So I am a med student writing up results for a research project which was conducted in the form of a survey. I have no prior training with stats so I am very much struggling, I have collected all data, run a few tests but upon further reading, I am wondering whether the tests I did are appropriate or not. I know there's differences of opinion in the stats worlds as to which test is the best and that might be why I am having doubts.

In this question I will inlcude real numbers but the questions will be different in order to keep my topic private.

1) How would you classify your medical condition? Acute? Chronic? or Don't Know?
2) How would you rate being called by your first name by doctors? (Likert item) Strongly dislike , dislike, neutral, like, Strongly like

In my analysis I want to see whether the condition being acute or chronic has any association with the opinion of patients on the likert scale (q2) so I made this table

I ran a chi-square test on this website (https://www.socscistatistics.com/tests/chisquare2/default2.aspx) and got chi value as 9.0368 and p=.34 (no significant association)

OK SO my questions:
1) Is this test appropriate for this data? If it's not the best is it still valid? By valid I mean can it still be used to make a point in a paper, I'm not concerned with finesse and using the best possible test (although I am interested), I care more about not using the wrong test which is completely inapproariate for the data
2) I read somewhere that chi square isn't appropriate for ordinal data like mine? How true is this?
3) If the test yielded a significant result p less than .05, how would i describe the association? Would I just go by percentages for example: For acute conditions 40% of patients said the strongly liked being called by xxx whereas for those with chronic conditions only 20% strongly liked to be called by xxx? This is very confusing for me because even for some of the other data similar to this in format I get significant results but I have no idea how to describe it.
4) Does anything change for data where there is only 2 rows for example if there was only (acute/chronic, without Don't know)?

Thanks!!!

Answer 1

I put your table into R and ran a chi-squared test of homogeneity, which gave the same results as in your question. If this test had rejected the null hypothesis, then you would have evidence that profiles of Likert scores across categories A, C, D are significantly different. Also, you would have the job of seeing which Likert scores accounted for the difference(s) among categories.

You are correct that this chi-squared test ignores the ordinal aspect of the Likert data. A controversial alternative is to treat Likert scores as if they are numerical, so that it makes sense to add and average them.

Pretending that Likert scores are numerical (and not far from normal) would lead to a one-way ANOVA with three levels A, C, D of the factor. We are treating Likert categories as if they corresponded to numbers 1 through 5.

Here is how to run such an ANOVA in R.

a = c(10,12,25,8,7)
c = c(10,14,58,22,15)
d = c(7,5,24,14,4)
x1 = rep(1:5, a)
x2 = rep(1:5, c)
x3 = rep(1:5, d)
x = c(x1,x2,x3)
g = rep(1:3, c(62, 119, 54))
oneway.test(x ~ g)

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

data:  x and g
F = 1.5024, num df = 2.00, 
   denom df = 117.44, p-value = 0.2268

Controversial or not, this test shows no significant differences in the averages of A, C, D categories. The Likert responses in the three groups are too similar to use them to say anything about categories.

Average Likert scores and standard deviations at the three levels are as follows:

mean(x1); mean(x2); mean(x3)
[1] 2.83871
[1] 3.151261
[1] 3.055556
sd(x1); sd(x2); sd(x3)
[1] 1.190034
[1] 1.062765
[1] 1.088823

One difficulty trying to find differences among A, C, D groups is that all groups had very high proportions of 'Neutral' choices among the five Likert responses.