# MSCI 101 Coursework Exercise 2018

```MSCI101 Coursework Exercise
2018
Management report for MSK service
Name: Jason Lam
Library Card Number: 34718397
I have read the coursework declaration form and I accept the University rules on
cheating and plagiarism. I state that the work submitted is my own and does not
contain any unacknowledged work from other sources. As the author of the
submitted work I am prepared to undertake an oral examination of its contents
Executive Summary
The primary purpose of this report is to use the data which have been
analysed, to provide advice to CCG on the five issues identified.
From the results we have recorded and analysed, we can now recommend
the best operational methods to CCG.
Introduction
This report is aiming to help CCG management to have an optimal plan for the
coming years with the MSK services they provide. Providing the analysis we are
constructing, we can then support our conclusion with evidence
Issue 1
Overall Volume (provided)
Physio
Daycase
Inpatient
Total
Area A
6399
1086
402
7887
Area B
6432
1412
465
8309
Total
12831
465
867
16196
Table 1.1
Percentage of different cases in Area A and B
Physio
Daycase
Inpatient
Total
Area A
81.13%
13.77%
5.1%
7887
Area B
77.41%
16.99%
5.60%
8309
Total
12831
2498
867
16196
Table 1.2
From Table 1.2, we can see that main spread of the data for both area A and B is
located under the physio column, approximately 81% and 77% respectively. With
daycare, area A has recorded 13.77% and area B has recorded 16.99% which shows
that area B has more Daycases then area A in terms of their total volume.
Furthermore, in terms of inpatient cases, both areas have approximately the same
percentage which means area B should have more inpatient cases as then area A as it
has a higher total amount of cases.
Expected numbers of different cases in Area A and B
Physio
Daycase
Inpatient
Total
Area A
6248.339
1216.456
422.2048
7887
Area B
6582.661
1281.544
444.7952
8309
Total
12831
2498
867
16196
Table 1.3
Chi-Squared Test
Chi-squared statistic = sum of (observed values– expected values)2 / expected values
= (6399-6248.339)2/6248.339 + (1086-1216.456)2/1216.456 + (402422.204)2/422.204 + (6432-6582.661)2/6582.661 + (1412-1281.544)2/1281.544 +
(465-444.795)2/444.795
= 36.232
The result of the chi-squared test is greater than 5.991 which means we can reject
the null hypothesis as it is statistically significant.
Issue 2
In particular, a course of physio treatment costs on average &pound;200, treatment as a
daycase costs on average &pound;500, and treatment as an inpatient costs on average
&pound;1500.
Overall Volume (provided)
Physio
Daycase
Inpatient
Total
Area A
6399
1086
402
7887
Area B
6432
1412
465
8309
Total
12831
465
867
16196
Table 2.1
Overall Costs of the three types of work in the two areas
Area A
Physio
Daycase
Inpatient
Total
6399*200 =
1279800
1086*500 =
543000 (22%)
402*1500 =
603000 (25%)
2425800
(53%)
Area B
6432*200=
1286400
(48%)
1412*500 =
706000 (26%)
465*1500 =
697500 (26%)
2689900
Total
2566200
1249000
1300500
5115700
Table 2.2
In issue 2, we can see that the total costs of all treatments are &pound;5115700 with the
costs of physio treatments being the biggest portion (&pound;2566200) and then the costs
of inpatient cases (&pound;1300500) and finally the costs of daycases being the least with
only &pound;1249000. If we look at the data in a more detailed ways, we can see that
actually in area A costs for physio treatments are lower than in area B, but the
percentage of the physio treatments are higher which suggests area A spent most in
physio treatments compare to the other two treatments. However, area B also
focuses the most on physio treatments as it has the highest portion of costs out of
the total cost of area B which showes in both areas physio treatments are the ones
that has the highest demand.
Issue 3
Numbers of patients aged under 65 undergoing the three types of MSK service
(provided)
Physio
Daycase
Inpatient
Total
Area A
4371
508
126
5005
Area B
4113
791
187
5091
Total
8484
1299
313
10096
Table 3.1
Numbers of patients aged 65 and over undergoing the three types of MSK service
(provided)
Physio
Daycase
Inpatient
Total
Area A
2028
578
276
2882
Area B
2319
621
278
3218
Total
4347
1199
554
6100
Table 3.2
Percentage of the number of patients aged under 65 undergoing the three types of
MSK service in Area A and B
Physio
Daycase
Inpatient
Total
Area A
87.3326%
10.1498%
2.5174%
5005
Area B
80.7896%
15.5372%
3.6731%
5091
Total
8484
1299
313
10096
Table 3.3
Percentage of patients aged 65 and over undergoing the three types of MSK service
in Area A and B
Physio
Daycase
Inpatient
Total
Area A
70.4166%
20.0555%
9.5766%
2882
Area B
72.0633%
19.2977%
8.6389%
3218
Total
4347
1199
554
6100
Table 3.4
Expected numbers for patients aged under 65
Physio
Daycase
Inpatient
Total
Area A
4205.8656
643.9674
155.1668
5005
Area B
4278.1343
655.0325
157.8331
5091
Total
8484
1299
313
10096
Table 3.5
Expected numbers for patients aged 65 or over
Physio
Daycase
Inpatient
Total
Area A
2053.7793
566.4783
261.7422
2882
Area B
2293.2206
632.5216
292.2577
3218
Total
4347
1199
554
6100
Table 3.6
Patients aged under 65 Chi-squared statistic = sum of (observed values– expected
values)2 / expected values
= (4371-4205.866)2/4205.866 + (508-643.967)2/643.967 + (126-155.167)2/155.167
+ (4113-4278.134)2/4278.134 + (791-655.033)2/655.033 + (187-157.833)2/157.833
=80.662
The chi-squared result is greater than 5.991 which suggests we can reject the null
hypothesis as it is statistically significant.
Patients aged 65 and over Chi-squared statistic = sum of (observed values– expected
values)2 / expected values
= (2028-2053.78)2/2053.78 + (578-566.48)2/566.48 + (276-261.74)2/261.74
+ (2319-2293.22)2/2293.22 + (621-632.52)2/632.52 + (278-292.26)2/292.26
=2.53
The chi-squared result is less than 5.991 which suggests we can’t reject the null
hypothesis as it is not statistically significant.
To see how much money per annum that Area A would save if it were
able to move its pattern of services to the pattern in use in Area B
Patients aged under 65
Observed
Area A
Area B
Total
Physio
4371
4113
8484
Daycase
508
791
1299
Inpatient
126
187
313
total
5005
5091
10096
number
Table3.7a
Percentage of patients aged under 65
Area A
Area B
Total
Physio
87.33%
80.79%
84.03%
Daycase
10.15%
15.54%
12.87%
Inpatient
2.52%
3.67%
3.10%
Total
100.00%
100.00%
100.00%
Table 3.7b
Expected number of patients aged under 65 in area A
Expected number
Physio
5005*80.79%
4043.5395
Daycase
5005*15.54%
777.777
Inpatient
5005*3.67%
183.6835
Total
5005
Table 3.7c
Cost for patients aged under 65 in area A
Expected number
Treatment costs (\$)
Expected total cost
4043.5395
200
808707.9
777.777
500
388888.5
183.6835
1500
275525.25
1473121.65
Table 3.7d
Total Cost
Area A
Physio
Daycase
Inpatient
Observed total cost
874200
254000
189000
1317200
Table 3.7e
Saving=1317200-1473121.65
= (155921.65)
Patients aged 65 and over
Area A
Area B
total
Physio
2028
2319
4347
Daycase
578
621
1199
Inpatient
276
278
554
total
2882
3218
6100
Area A
Area B
total
Physio
70.37%
72.06%
71.26%
Daycase
20.06%
19.30%
19.66%
Inpatient
9.58%
8.64%
9.08%
total
100.00%
100.00%
100.00%
Table 3.8a
Percentage of patients aged 65 or over
Table 3.8b
Expected number of patients aged 65 or over in area A
Expected number
Physio
2882*72.06%
2076.866998
Daycase
2882*19.30%
556.1597265
Inpatient
2882*8.64%
248.9732753
Total
Table 3.8c
Costs for patients aged 65 and over in area A
2882
Expected number
Treatment cost (\$)
Expected total costs
2076.866998
200
415373.3996
556.1597265
500
278079.8633
248.9732753
1500
373459.913
1066913.176
Table 3.8d
Total Costs
Physio
(2028*200)
Area A
Daycase (578*500) Inpatient (276*1500)
405600
289000
414000
Total
1108600
Table 3.8e
Saving= 1108600-1066913.176
= 41686.82411
Area A total saving= 41686.82411+ (-155921.65)
= -114234.8259
Instead of area A being able to save money, it will actually increase its costs by an
extra &pound;114234.83.
From the results shown on all the table above, we can see that age-group is an
important lurking variable.
Issue 4
Relationship between the percentage in
Physio and the percentage in daycase
and Inpatient
10
5
0
0
2
4
6
8
10
12
-5
% increase in physio and
% decrease in daycase
and inpatient
-10
-15
-20
Table 4.1
Percentage in physio treatments
Predicted % increase in
physio and % decrease in
daycase and inpatient
The regression line shown on the graph has the equation of y = 0.7555x –
2.6402. This means that if we are looking into how much daycases and
inpatient services are decreasing by when area A increases its physio
treatments by a 7.5%, we just have to substitute 7.5 into the regression line
equation.
y = 0.7555*7.5 - 2.6402
y = 3.026
This brought us to a conclusion that daycases and inpatient services will
decrease by 3.026% if physio treatments in area A are going to increase by
7.5%.
Number of patients going to be using all 3 services after the increase of 7.5%
in physio treatments in area A
= 6399*(100%+7.5%) + 1086*(100%-3.026%) + 402*(100%-3.026%)
= 6878.925 + 1053.137 + 389.835
= 8321.897 = 8322 patients
Overall costs needed for all the services after the increase of 7.5% in physio
treatments in area A
= 6878.925*200 + 1053.137*500 + 389.835*1500
= &pound;2487106
The saving that CCG could make after the increase of 7.5% in physio treatments in
area A
Total costs stated above is &pound;2425800
New costs after increasing the physio treatments by 7.5% is &pound;2487106
This means that the saving CCG could make after the increase of 7.5% in
physio treatments in area A is 2425800 – 2487106
= (&pound;61306)
This also means that if CCG increase the physio treatments in area A by 7.5%,
they won’t be able to increase its savings, instead it would increase its costs.
However, in this set of data, there is two outliers which suggests the accuracy
and the reliability of the result is questionable and may not be as accurate.
Issue 5
As stated above, the regression line shown on the graph has the equation of y
= 0.7555x – 2.6402. This means that if we are looking into how much daycases
and inpatient services are decreasing by when area A increases its physio
treatments by a 15%, we just have to substitute 15 into the regression line
equation.
y = 0.7555*15 - 2.6402
y = 8.6848
This brought us to a conclusion that daycases and inpatient services will
decrease by 8.6848% if physio treatments in area A are going to increase by
15%.
Number of patients going to be using all 3 services after the increase of 15%
in physio treatments in area A
6399*(100% + 15%) + 1086*(100% - 8.692%) + 402*(100% - 8.692%)
= 7358.85 + 991.602 + 367.057
= 8717.509
Overall costs needed for all the services after the increase of 15% in physio
treatments in area A
= 7358.85*200 + 991.602*500 + 367.057*1500
= &pound;2518156.242
The saving that CCG could make after the increase of 15% in physio treatments in
area A
Total costs stated above is &pound;2425800
New costs after increasing the physio treatments by 15% is &pound;2518156.242
This means that the saving CCG could make after the increase of 15% in physio
treatments in area A is 2425800 – 2518156.242
= (&pound;92356.242)
This also means that if CCG increase the physio treatments in area A by 15%,
they won’t be able to increase its savings, instead it would increase its costs.
However, in this set of data, there is two outliers which suggests the accuracy
and the reliability of the result is questionable and may not be as accurate.
With area A wanted to invest into more physio treatments in order to reduce cost
and the demand of daycases and inpatient we can find out the deficit per person in
respect to increasing physio treatments by 7.5% and 15%.
If physio treatments are to increase by 7.5%:
= -61306.467 / 8321.897376
= (&pound;7.367)
If physio treatments are to increase by 15%:
= -92356.242 / 8717.509
= (&pound;10.594)
When comparing these two results, we can tell that the deficit per person in
area A by increasing the investment of physio treatments by 7.5% is lower.
Therefore I would advise area A to increase by 7.5% instead of 15%. However,
the investment they are making now is better than both of these strategies; It
means they should also put their current plan under consideration before
making any decisions.
Conclusion
To conclude, in issue 1 we can tell that physio treatments are demanded the most by
the audience. The number observed from the chi-squared test shown that it is
statistically significant. In issue 2, two areas spend most of their costs in different
areas. In issue 3, we found out that age-group is an important lurking variable. We
also found out that there is a deficit instead of savings when Area A used the pattern
of service in Area B. In issue 4, we found out that there is a deficit if CCG increased its
physio treatments in Area A by 7.5%; And there would be an even bigger deficit if
CCG increased its physio service in Area A by 15%.
Recommendation
We have found out that operating like area B in area A would not increase area A’s
financially, so I would not advice CCG to use the area B’s operation in area A. We %
and ave also found out that increasing the physio treatments by either 7.5% and 15%
will only increase the overall costs which implies the way area A is working now could
be the optimal solution among the three options. Therefor I would recommend to
put the current plan under consideration as financially it has the best results.
```