# What statistical test should be performed in this setting?

I am analyzing a dataset. There I have 3 different "Lab test report findings" and 1 "clinical findings" which is obtained by the clinical examination of the patient (most of the time this clinical examination is not done by the health professionals).

To diagnose a specific disease, Each of the 3 lab tests can independently be used to diagnose the disease. What I am trying to establish is that these clinical findings of the patient can also be one of the most important diagnostic methods of this disease as like other Lab tests.

So, what statistical test should I be used to prove and compare the effectiveness of this clinical examination findings? Also, suggest me some graphs, that can visualize with this case) N.B. All 4 tests had a dichotomous answer. The findings of these tests can either be positive or negative.

## 1 Answer

Two-by-two table of counts. From what you say, I assume that you have a finding for each patient Y or N on the clinical exam and then a final determination Y or N on actual presence of the disease. Then you have a 2-by-2 table such as the one below for 125 patients:

               Final Diagnosis
Clinical       Yes          No        Total
-------------------------------------------
Yes             50          13           63
No              15          47           62
-------------------------------------------
Total           65          60          125


Fisher exact test. Then you could do a Fisher exact test to see if there is a significant association between clinical findings and final diagnosis, using R statistical software as shown below. For my fake data the P-value is very small, which leads to rejection of the null hypothesis that Clinical and Final are independent.

TBL = rbind(c(50,13), c(15,47))
fisher.test(TBL)

Fisher's Exact Test for Count Data

data:  TBL
p-value = 4.889e-10
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
4.822488 30.644986
sample estimates:
odds ratio
11.74651


Notice that this test uses counts, not proportions. An analysis for only 25 patients with roughly the same proportions, is still significant at the 5% level of significance, but not at the 1% level.

TBL2 = rbind(c(10,3), c(3,9))
fisher.test(TBL)\$p.val
[1] 0.01693172


About barplots. One kind of graphical presentation of such data is a barplot in R. Several styles are in common use. Many other statistical programs are available for making barplots.

It is important to make sure that information about actual counts is displayed on a barplot. (Proportions or percentages are not sufficient.) Without clearly marked axes showing counts of patients, barplots for TBL and TBL2 will look a lot the same.

Note: if you want to test whether the results of the clinical exam are useful mainly along with (or only along with or notwithstanding) the results of lab tests, please provide more detail so someone can help you with that more complicated inference.