Descriptive Statistics for Medical Malpractice Claims

This article provides descriptive statistics and estimation analysis for medical malpractice claims. It includes hypothesis testing and relationship analysis between factors such as speciality of physician involved, severity of the claim, and average amount of insurance claim.

Running head: DESCRIPTIVE STATISTICS
Descriptive Statistics
Name of the Student:
Name of the University:
Author’s Note:

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Table of Contents
Introduction:...............................................................................................................................3
1. Descriptive Statistics:.............................................................................................................3
2. Estimation:.........................................................................................................................3
2.a)......................................................................................................................................3
2. b)....................................................................................................................................4
Answer 3................................................................................................................................4
3.a)......................................................................................................................................4
3. b)....................................................................................................................................4
3.c)......................................................................................................................................5
3.d).....................................................................................................................................5
3. e).....................................................................................................................................6
Answer 4................................................................................................................................6
4. a).....................................................................................................................................6
4.b).....................................................................................................................................7
References:.................................................................................................................................9
Appendix:.................................................................................................................................10

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Table of Tables
Table 1......................................................................................................................................12
Table 2......................................................................................................................................12
Table 3......................................................................................................................................12
Table 4......................................................................................................................................13
Table 5......................................................................................................................................14
Table 6......................................................................................................................................15
Table 7.1...................................................................................................................................17
Table 7.2……………………………………………………………………………………...18
Table 8......................................................................................................................................20
Table 9......................................................................................................................................22
Table 10.1.................................................................................................................................23
Table 10.2……………………………………………………………………………………24
Table of Figures
Figure 1....................................................................................................................................13
Figure 2....................................................................................................................................14
Figure 3....................................................................................................................................15
Figure 4....................................................................................................................................16
Figure 5....................................................................................................................................19
Figure 6....................................................................................................................................21
Figure 7....................................................................................................................................24
Figure 8....................................................................................................................................26

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To: You
From: Edmond Kendrick
Subject: Analysis of Claims
As per earlier discussion, I have cleaned and simplified the undertaken dataset to eight
variables for your convenience. The cleaned dataset contains information about 200 randomly
selected claims promised this year.
Introduction:
The medical malpractice of United States is a severe problem these days as reported
in US News and World report. It consumes a significant segment of total expenditure of the
USA households. The physicians who are mal-practicing are claiming unjustified amount
from the patients. The struggling people not only contribute a high cost of healthcare, but also
contribute a high premium for medical insurance due to malpractices.
The preliminarily collected data is under inspection to justify the true scenario of
medical situations (Pearson 2013). In the followings, descriptive and inferential analysis is
carried out in the surveyed data.
1. Descriptive Statistics:
The descriptive statistics of “Amount” of the Claim payment indicates that-
 The average amount of the claim payment is 73457.49 Australian dollar.
 The claim payment has highest frequency for the amount 5400 Australian dollar.
 The lowest amount of claim payment is 1547 Australian dollar.
 The highest amount of claim payment is 228724.8 Australian dollar.
 The range of amount of claim payment is 227177.8 Australian dollar.
 The 95% of the observations lies in the interval (73457.49±4486.92) Australian dollar
= (77944.41, 68970.58) Australian dollar (Weiss and Weiss 2012).

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2. Estimation:
Answer 2.a)
It is observed that-
The calculated average age of the claimants is 44.49 years. In the dataset of 200 samples, the
interval lower limit of 95% confidence interval is calculated as (44.49-2.4669) = 42.02 years.
The interval upper limit of 95% confidence interval is calculated as (44.49 + 2.4669) = 46.96
years. Therefore, it is estimated that average age of 200 samples lie in the interval of 42.02
years and 46.96 years with 95% probability. Therefore, 95% of the ages of total claimants are
estimated to lie in the interval of 42.02 years and 46.96 years.
Answer 2. b)
Out of 200 samples, the number of claimants with the insurance level “No Insurance” is 18.
The calculated proportion is 0.09. The upper limit of the proportion of claimants with “No
Insurance” is given by 12.97%. The lower limit of the proportion of claimants with “No
Insurance” is 5.03%. Hence, it is 95% evident that the proportion of claimants with “No
insurance” lies in the range of 5.03% and 12.97%. Therefore, it is 95% evident that the
estimated proportion of claimants who do not have insurance would lie in the interval of
5.03% and 12.97% (Montgomery, Runger and Hubele 2009).
Answer 3.
Answer 3.a)
We assume the null hypothesis (H0) as the average paid claim amount is greater than or equal
to $77,500 Australian dollar. The alternative hypothesis (H1), the average amount of paid
claim is less than $77,500 Australian dollar.
The calculated sample average is $73457.49 with the sample size 200. The level of
significance is 0.05. Therefore, the null hypothesis is rejected with 95% probability. The
alternative hypothesis is accepted. Hence, it could be concluded that average amount of paid
claims has dropped below $77,500. It could be concluded that there is no evidence that the
average paid claim amount is greater than or equal to the hypothesised amount.
Answer 3. b)
A study had reported that 3 out of 4 claims are either “MILD” or “MEDIUM” severity
conditions. The calculated count of success is 154 and sample size is 200. Sample proportion
is 0.77. The sample proportion is greater than 75% (3 out of 4). Here, the null hypothesis is

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failed to be rejected with 95% probability. Hence, it could be concluded that the proportion of
severity conditions of “MILD” and “MEDIUM” is at least 75% with respect to all the
severity conditions. Therefore, it could be interpreted that according to all the severity
conditions, the proportion of insurance claimants of “MILD” and “MEDIUM” severity is
greater than or equals to 75%. The inference has enough evidence about severity
measurement.
Answer 3.c)
Now, we would like to find the significant difference between the proportions of “MILD”
and “MEDIUM” insurance claims in accordance to the gender of the patients. The difference
in proportion of “MILD” or “MEDIUM” claims by female patients compared to the male
patients is calculated.
Out of 154 samples whose severity conditions are either “MILD” or “MEDIUM”, 60 are
males and 94 are females. The sample proportions of males and females are 38.96% (Π1) and
61.04% (Π2). The null hypothesis of equality of proportions of frequencies of males and
females is rejected at 5% level of significance. Hence, the difference of proportions is
prominent with 95% probability (Olive 2014). There is a difference in proportion of “MILD”
and “MEDIUM” insurance claims by genders of patients. Therefore, gender has an effect on
the proportions of severity conditions alike “MILD” and “MEDIUM” severity according to
the insurance claimant.
Answer 3.d)
As per the standard of industry, it could be hypothecated that the insurance payment amounts
are related to the private attorney of the claimants. The average claim amount for the private
attorney is greater than the average claim specifically at no involvement of private attorney.
The average of payment amount of private attorney is $80501.07 for 137 samples (Abbott
2017). The average of payment amount of non-private attorney is $58140.51 for 63 samples.
Null hypothesis assumed that the average payment amount of private attorney and the
average payment amount associated to the non-private attorney are equal. The alternative
hypothesis conversely states that the difference of average payment amount of private
attorney and average payment amount related to non-private attorney is unequal to 0. The null
hypothesis of equality of payment amounts is rejected at 5% level of significance (Abbott 2017). It is

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95% evident that the higher average paid claim amount of the private attorney and the non-
private attorney are equal. Therefore, the testing entirely supports the proposition that there is
sufficient evidence of having greater insurance claim amount in case of non-private attorney
than the average payment amount of the claimants who has private attorney.
Answer 3. e)
The industry stakeholders suspect that the private attorney representation is greater in case of
insurance claims of “SEVERE” severity rather than for the insurance claims of “MEDIUM”
severity. The statement is validated by testing of hypothesis. The null hypothesis is assumed
as the proportion of private attorney in case of “SEVERE” claims is equal to the claims with
a “MEDIUM” severity. The alternative hypothesis assumes the proportion of private attorney
for “SEVERE” claims and claims with “MEDIUM” severity is unequal.
The number of private attorney representation for “SEVERE” severity condition is 36. The
frequency of private attorney representation for “MEDIUM” severity condition is 93. The
proportions of these two severities with respect to fixed private attorney are 78.26% and
72.66% (De Winter 2013).
At 5% level of significance, we fail to reject the null hypothesis. It could be concluded that
the proportions of private attorney in “SEVERE” severity is equal to the proportions of non-private
attorney in “MEDIUM” severity. Hence, the assertion that the number of private attorney is
higher for “SEVERE” claims than for claims with “MEDIUM” severity is invalid (Efron
2012). The proposition is proved to be absolutely authentic.
Answer 4.
Answer 4. a)
It would be an interesting fact to find the relationship between the factors – “Speciality of
physician involved”, “severity of the claim” and “average amount of insurance claim”. I think
you consider that the percentage of claims in “SEVERE” severity for Orthopaedic surgeon is
greater than other specialists involved.
The null hypothesis assumed that the difference between the percentage of Orthopaedic
surgeon and the other specialists in the “SEVERE” severity is 0. The alternative assertion

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assumed that the percentage of Orthopaedic surgeon is lower than other specialists in the
“SEVERE” severity.
It is observed the 46 patients of “SEVERE” severity condition, 8 patients consult with
Orthopaedic surgeons and 38 patients consult with other types of specialists. The sample
proportions are respectively 17.39% and 82.61%. Here the basic assertion is rejected at 5% level
of significance. Therefore, the null hypothesis of the equal proportions of insurance claim in
“SEVERE” severity under treatment of an Orthopaedic surgeon and other specialists is
accepted (Brandt 2014). Hence, the belief that the percentage of “SEVERE” severity that
claims with the involvement of an Orthopaedic surgeon is lower than other types of
specialists is accepted.
Answer 4.b)
It regarded that the average amount of insurance claim for “SEVERE” severity is greater
when an Orthopaedic surgeon is considered rather than involvement of other specialists.
The null hypothesis is that the of average claim amount for “SEVERE” severity for
Orthopaedic surgeon and the average claim amount for “SEVERE” severity for the other
specialists is different. The alternative hypothesis is assumed that the average claim amount
in “SEVERE” severity for Orthopaedic surgeon and the average claim amount in “SEVERE”
severity for the other specialists are different.
The number of patients in “SEVERE” severity is 46. Among them 8 patients consulted
Orthopaedic surgeon and 38 patients consulted other types of surgeon. The average claim
amount of 8 patients is $118944.27. The average claim amount of 38 patients is $108466.41. The
null hypothesis is accepted here. With 95% probability, it could be said that the average claim
amount for “SEVERE” severity is not higher for the involvement of Orthopaedic surgeon
than other specialisations. Therefore, it could be concluded that the average claiming amount
in “SEVERE” severity is not higher for the involvement of Orthopaedic surgeon than
involvement of other specialisations.
I look forward to your response.
Sincerely,
Edmond Kendrick

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Chief Data Scientist – United Health Group.

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References:
Abbott, M.L., 2017. Independent Sample T Test.
Brandt, S., 2014. Testing Statistical Hypotheses. In Data Analysis (pp. 175-207). Springer,
Cham.
De Winter, J.C., 2013. Using the Student's t-test with extremely small sample sizes. Practical
Assessment, Research & Evaluation, 18(10).
Efron, B., 2012. Large-scale inference: empirical Bayes methods for estimation, testing, and
prediction (Vol. 1). Cambridge University Press.
Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., Gümüs, Z.H., Harding, S.T.,
Klepeis, J.L., Meyer, C.A. and Schweiger, C.A., 2013. Handbook of test problems in local
and global optimization (Vol. 33). Springer Science & Business Media.
Olive, D.J., 2014. Testing Statistical Hypotheses. In Statistical Theory and Inference (pp.
183-213). Springer, Cham.
Pearson, H., 2013. Science and intuition: do both have a place in clinical decision
making?. British Journal of Nursing, 22(4), pp.212-215.
Weiss, N.A. and Weiss, C.A., 2012. Introductory statistics. London: Pearson Education.

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Appendix:
Table 1
Table 2
Table 3

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Figure 1
Table 4

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Figure 2
Table 5

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Figure 3
Table 6

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Figure 4

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Table 7.1

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Table 7.2

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Figure 5

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Table 8

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Figure 6

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Table 9

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Table 10.1

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Figure 7

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Table 10.2

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Figure 8

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