## Statistical Methods Essay

A graph is a pictorial representation of data / information. This is important because it is easy to understand and therefore has strong impact on the audience, besides it is concise form of data presentation as a big dataset can be effectively presented as a meaningful graph. It is said that “A picture is worth a thousand words”. Therefore, in statistics graphical representation of data is a usual practice.

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Figure 1, below presents base lending rate of the Bank of England over a period of time (An unshocking increase, May 10th 2007, The Economist print edition)
Figure 1: Base lending rate of the Bank of England over time (January 2000 to January 2007)

This is essentially a scatte diagram with data point connected by straight lines. This is giving changes in the basic lending rate of the Bank of England over a period seven years starting January 2000 upto January 2007. The basic lending rate (in percentage terms) is marked over the y-axis and the time is on the x-axis. Every time there is a change in the base lending rate, there is a vertical down (for decrease in base lending rate) or verical up (for increase in base lending rae) line. The graph has been able to convey the message it wanted to. The shape of the graph is also a very good match with the title of the graph i.e. “Turn of the screw” as it looks like a screw.

However, there are some poor aspects of this graph. Some of these are

1.      The title of graph, no matter how fancy it is, is not telling the readers as to what is presented in the graph. Therefore, though an well educated reader will find no problem in getting what is contained in the graph, a not so well educated person will have to work hard to understand that and that defeats the very perpose of graphical representation, which is “ a graphical representation is easy to understand by just anybody”.

2.      Axes are not marked. In this graph the axes (x and y) are not marked. In a good graph the axes should be marked properly so that just anybody can understand, without putting any pressure on his head, as to what the axes represent.

Besides, these two faults everything else appears to be alright with this graph.

Introduction:

People do suffer from injuries during automobile accidents and many times the injury leads to brain damage. Those suffering from damages due to automobile accidents seek compensation. This compensation depends on age, sex, extent of damage etc. In this study a sample of sixty subjects of both sexes – male and female across different age groups, who suffered brain damage during automobile accidents, were selected to make a statistical study to establish whether or not there is significant difference in the amount of compensation claimed by victims of the two sexes and also those of different age groups.

There are six variables in this study, which are listed below:

Variable Name
Description
Gender
0 = male and 1 = female
ID
Subject identification number
Age Group
1 = 0 – 11; 2 = 12 – 20; 3 = 21 – 35; 4 = 35 – 60; 5 = over 60
Mental 1
Mental performance before injury
Mental 2
Mental performance after injury
Amount (\$)
Compensation claimed by the subjects
Subsequently statistical analysis was done to establish whether or not the compensation claimed is significantly different for males and females. Besides, it was also established whether or not the compensation claimed is significantly different for those of different age groups. This was done on the significance level of 0.05.

Statistical Report

Statistics of the Sample:

From a large sample of 200 subjects a small sample of 60 subjects was randomly selected using a random number generator macro. The original sample of 200 hundred subjects as well as the small sample of 60 subjects is presented in Data_Injury_with_random_row_generator.xls. All the statistical analysis was performed on the small sample of sixty subjects.

Statistical analysis of the sample results in following statistics of the sample:

Mean Compensation  : \$23181

Standard Deviation    : \$12446

Maximum                   : \$56736

Minimum                    : \$500

Sample Size                : 60

Analysis of Distribution

Subsequently, the compensation data was analyzed for normality. For this purpose, the compensation values were fixed at an interval of \$2000 across the range and frequency of the compensation was recorded and plotted as a histogram. Over this histogram, a normal distribution curve was super imposed. From the figure 1, below, it can be seen that the compensation values are normally distributed around the mean, with the exception of a few values at the extremes. The values at the extreme incorporate some error in statistical analysis, as the analysis is based upon the assumption, that the distribution is normal. However, the deviation from the normality is very small and accordingly, the errors will also be negligible.

Comparison of the different Groups:

Statistical analysis was performed to examine presence or otherwise of the significant difference in the compensation amount of different groups. Statistics of the compensation amounts of the different sexes is presented below, table 1:

Table1: Statistics of the compensation claimed by males and females

Sex
Sample Size (n)
Mean Compensation (\$) ( )
Standard Deviation (\$) (S)
Both
60
23181
12446
Male
37
26017
13040
Female
23
18618
10094
To examine whether there is significant difference in amount of compensation claimed by the two sexes, a 95% confidence interval (i.e. 0.05 significance level or z = 1.96) was established, for both sexes, for the mean compensation amount.

For Males:

30218]

For Females:

22743]

As the two ranges are overlapping, one can conclude that there is no significant difference in compensation claimed by males and females.

Similar analysis was made for the compensation claims of the subjects across the different age groups. The results are presented in table 2, below:

Table 2: Statistics of the compensation claimed by subjects across the different age groups

Age Group
Sample Size (n)
Mean Compensation (\$) ( )
Standard Deviation (\$) (S)
95% Confidence Interval (\$)
All
60
23181
12446
[20032, 26330]
0-11
8
33350
15712
[22462, 44238]
12-20
11
32283
8222
[27424, 37142]
21-35
19
26167
8257
[22454, 29880]
35-60
12
13046
7078
[9041, 17051]
60+
10
10612
7407
[6022, 15202]
From the 95% confidence interval on the mean compensation amount claims following conclusions can be drawn:

1.      There is no significant difference in compensation claimed by 0-11 and 12-20 and 21-35 age groups.

2.      There is no significant difference in compensation claimed by 35-60 and 60+ age groups.

3.      The compensation claimed by 35+ age group is significantly lower than that by 35- age groups.

Mental Health Before and After the Accident

The plot of mental health of the subjects after the accident vs. the same before the accident is presented below, in figure 2.

One can notice a linear trend in the plot. This linear trend implies that a better mental health before the accident has resulted in better mental health after the accident and vice versa. However, slope of the trend line is less than one; this is because the accidents lead to drop in mental health.

Mental health of the subjects before and after the accident is shown below in figure 3:

What one can notice in this plot is that mental health of the subjects before the accidents is maximum in the 20-35 age groups, which represents the most mature age group. Besides, another important observation is that the loss in mental health due to the accidents has been the minimum in the less than 11 years age group, which is indicative of the better recovery in children than in grown ups.

Conclusions:

Statistical analysis was made on the sample having compensations claims made by victims of automobile accidents leading to loss of mental health. The sample comprised of males as well as female in the age group from 11- to 60+. Following conclusions can be drawn from this analysis:

1.      There is no significant difference in amount of compensation claimed by males and females at 0.05 significance interval.

2.      There is no significant difference in compensation claimed by 0-11 and 12-20 and 21-35 age groups.

3.      There is no significant difference in compensation claimed by 35-60 and 60+ age groups.

4.      The compensation claimed by 35+ age group is significantly lower than that by 35- age groups.

5.      The mental health after the accident shows a linear relationship with that before the accident.

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