Quantitative Assessment of Crime Rate Data

This document provides a quantitative assessment of crime rate data, including summary statistics and analysis of various variables. It explores the relationship between crime rate and police expenditure, the difference in crime rates between southern and non-southern states, and the change in crime rates over 10 years. Additionally, it examines the relationship between crime rate and youth unemployment. The document also discusses the concepts of probability and statistical significance, as well as how to choose appropriate statistical tests and the assumptions underlying parametric and non-parametric tests.

Quantitative assessment crime
rate data

Contents
SECTION A.....................................................................................................................................1
Summary Statistics......................................................................................................................1
Do states in the south have a higher crime rate?.........................................................................2
Is there a relationship between crime rate and police expenditure?............................................3
Have crime rates increased in 10 years?......................................................................................4
Is youth unemployment higher in the south?...............................................................................5
SECTION B.....................................................................................................................................7
Probability and statistical significance........................................................................................7
How to choose statistical test and theory about the tests.............................................................7
Assumption underlying parametric and non parametric tests......................................................8
Levels of measurement................................................................................................................8
REFERENCES..............................................................................................................................10

SECTION A
Summary Statistics
The data set which has been given is the US state crime data which includes the crime rate
and other variables of variety of US states. All the variables in the data set are analysed by
presenting their summary statistics below:
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
Crime rate (number of
offences per million
population)
47 45.50 161.80 102.8085 28.89327
Young males (number of
males aged 18-24 per 1000) 47 119 177 138.57 12.568
Southern state 47 0 1 .34 .479
Education time (average
number of years schooling
upto 25)
47 10 15 12.39 1.120
Expenditure (per capita
expenditure on police) 47 45 166 85.00 29.719
Youth labour force (males
employed 18-24 per 1000) 47 480 641 561.19 40.412
Males (per 1000 females) 47 934 1071 983.02 29.467
More males identified per
1000 females 47 0 1 .19 .398
State size (in hundred
thousands) 47 3 168 36.62 38.071
Youth Unemployment
(number of males aged 18-
24 per 1000)
47 70 142 95.47 18.029
Mature Unemployment
(number of males aged 35-
39 per 1000)
47 20 58 33.98 8.445
High Youth Unemployment 47 0 1 .32 .471
Wage (median weekly wage) 47 288 689 525.38 96.491
Below Wage (number of
families below half wage per
1000)
47 126 276 194.00 39.896
1

Valid N (listwise) 47
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
CrimeRate10 47 26.50 178.20 102.0702 39.27807
Youth10 47 120 164 140.53 10.914
Education10 47 10 15 12.40 1.171
ExpenditureYear10 47 41 157 80.23 27.961
LabourForce10 47 497 641 565.53 37.645
Males10 47 935 1079 986.87 29.846
MoreMales10 47 0 1 .21 .414
StateSize10 47 3 180 37.70 39.491
YouthUnemploy10 47 71 143 97.45 17.843
MatureUnemploy10 47 15 59 33.36 8.414
HighYouthUnemploy10 47 0 1 .40 .496
Wage10 47 359 748 594.64 93.750
BelowWage10 47 126 257 192.96 38.756
Valid N (listwise) 47
Above descriptive statistics provides various insights about the data set. One of these
interesting insights is that crime rate in first 10 years was higher than the crime rate of second 10
years as mean value of crime rate is 102.80 and mean of crime rate10 is 102.70.
Do states in the south have a higher crime rate?
In order to identify whether southern states have higher crime rate or not, the SPSS
statistical test of Independent samples T test is selected as crime rate is a continuous variable and
southern is a grouping variable.
Group Statistics
Southern state N Mean Std. Deviation Std. Error Mean
Crime rate (number of
offences per million
population)
No 31 103.9065 31.95755 5.73975
Yes 16 100.6813 22.58823 5.64706
Independent Samples Test
2

Levene's Test
for Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig.
(2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Crime rate
(number of
offences per
million
population)
Equal
variances
assumed
4.139 .048 .359 45 .721 3.22520 8.97957 -
14.86059 21.31099
Equal
variances not
assumed
.401 40.428 .691 3.22520 8.05195 -
13.04304 19.49344
The above results show the significance or p value of .048 which is lower than its alpha
value of .05; this implies that the crime rate in southern and non southern states is significantly
different. As it has identified that southern states have a different crime rate, it is important to
identify whether this crime rate is higher or lower than non southern states. The mean value of
southern states is 100.68 and mean value of non southern states is 103.90; this implies crime rate
of southern states is not higher.
Is there a relationship between crime rate and police expenditure?
In order to identify the relationship between crime rate which is a continuous variable and
police expenditure which is also a continuous variable, the SPSS test of correlation is selected.
Correlations
Crime rate
(number of
offences per
million
population)
Expenditure (per
capita
expenditure on
police)
Crime rate (number of
offences per million
population)
Pearson Correlation 1 .646**
Sig. (2-tailed) .000
N 47 47
Expenditure (per capita
expenditure on police)
Pearson Correlation .646** 1
Sig. (2-tailed) .000
3

N 47 47
**. Correlation is significant at the 0.01 level (2-tailed).
From the above results, it has been seen that the p value is .000 that is lower than the
alpha value of .05, this implies that the relationship between both the variables is significant.
Furthermore, correlation coefficient is .646 which states the nature of this relationship is positive
and strength of this relationship is higher.
Have crime rates increased in 10 years?
As both the variables for this analysis are dependent, the SPSS test of paired sample t test
has been selected.
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 Crime rate (number of
offences per million
population)
102.8085 47 28.89327 4.21452
CrimeRate10 102.0702 47 39.27807 5.72930
Paired Samples Correlations
N Correlation Sig.
Pair 1 Crime rate (number of
offences per million
population) & CrimeRate10
47 .997 .000
Paired Samples Test
Paired Differences
t df
Sig. (2-
tailed)Mean
Std.
Deviation
Std. Error
Mean
95% Confidence
Interval of the
Difference
Lower Upper
4

Pair
1
Crime rate (number
of offences per
million population) -
CrimeRate10
.73830 10.75032 1.56810 -2.41811 3.89471 .471 46 .640
The p value of the correlation is .000 which implies that the relationship between the
crimes rates of 10 years apart is significant. In order to identify whether the crime rates have
increased, the mean value is essential to be evaluated. As the mean value is .738, this concludes
the crime rate of before 10 years is higher by .073 than the crime rate of recent 10 years.
Therefore, no, the crime rate has not increased.
Is youth unemployment higher in the south?
As the variables of high youth unemployment and southern states are categorical, the SPSS
test of Chi square has been selected.
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
High Youth Unemployment *
Southern state 47 100.0% 0 0.0% 47 100.0%
High Youth Unemployment * Southern state Crosstabulation
Count
Southern state
TotalNo Yes
High Youth Unemployment No 17 15 32
Yes 14 1 15
Total 31 16 47
Chi-Square Tests
5

Value df
Asymptotic
Significance (2-
sided)
Exact Sig. (2-
sided)
Exact Sig. (1-
sided)
Pearson Chi-Square 7.353a 1 .007
Continuity Correctionb 5.672 1 .017
Likelihood Ratio 8.700 1 .003
Fisher's Exact Test .008 .006
Linear-by-Linear Association 7.197 1 .007
N of Valid Cases 47
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 5.11.
b. Computed only for a 2x2 table
From the Pearson’s Chi square test, it has been seen that the unemployment rate of youths in
southern and in non southern states are different as the p value of Chi square is .007 which is
lower than the selected alpha value of .005. From the cross tabulation table, it has been observed
that only one out of 15 southern states has higher youth unemployment and on the other hand, 14
out 17 non southern states have high youth unemployment. So, youth unemployment in South is
not higher.
6

SECTION B
Probability and statistical significance
The concepts of probability and statistical significance are similar but are not same.
Statistical significance is the p value which is calculated against a data set that helps to show
statistical significance between two variables. As analysed in section A, the p value of
independent samples t test was lower than its alpha value which implied in statistical difference
in two variables. This p value is the probability value of obtaining the difference in the sample. It
must be noted that p value is directly related to the confidence interval. For example, if the
confidence interval is 95% then the alpha value will be .05 and the p value will be compared to
this alpha value (McShane and Gal, 2017).
On the other hand, probability is an extent of a situation which is likely to happen. The
probability significance is different from statistical significance as the probability significance is
not certain and it only showcases the likelihood between the relationships of two variables.
How to choose statistical test and theory about the tests
Statistical tests are the command tests in SPSS which are conducted in order to fulfil
certain research objectives. In order to choose a valid statistical test, there are certain steps which
are analysed below:
 Firstly, it is important to check the normality of data as if the data set is not normal then
instead of parametric tests, non parametric tests must be used.
 Second step in the selection of appropriate statistical test is to check the type of variables
that are being used. Different types of tests are used for continuous and categorical
variables. For example, in Section A when both the variables were categorical, the chi
square test was used and when both the variables were continuous, the correlation test
was used.
 Lastly, it is important to identify whether the objective requires regression, correlation or
comparison analysis as all these objectives will be evaluated with different test (Bhui,
2019).
7

Assumption underlying parametric and non parametric tests
Parametric tests are the ones which are used to test group means. This type tests are used
when the data is normal and there are few assumptions which are taken while conducted such
tests. These assumptions involve:
It has been assumed in parametric tests that population variances are equal. These tests
also assume interval scale of measurement along with random sampling from a defined
population. All parametric tests also assume that the populations from which samples are taken
have some specific features and these characteristics are normally distributed in the population.
On the other hand, non parametric tests are used to check the variation and relationship between
the median of groups. These tests are distribution free due to which these can be used for non
normal variables. These non parametric tests make assumptions about random sampling and the
dependence of the samples. The non parametric tests do not make any assumptions regarding
population due to which they are considered as more reliable (Derrick, White and Toher, 2020).
All the tests which are conducted in Section A are parametric tests due to which
assumptions regarding data normality are made for each objective.
Levels of measurement
Data levels of measurements are the way by which a specific data set is measured. There are
only four types of measurements which are nominal, ordinal, interval and ratio. All these levels
of measurement are analysed below:
Nominal – This level is a scale level measurement which measures the data set that is
qualitative. This level is used for data where scope of values is lower such as colour, names, food
and many more. The data must be in alphabets or symbols rather than numbers as it scale s for
qualitative data and not for quantitative data (Wildemuth, 2016).
Ordinal – This is also a scale level measurement which is similar to nominal scale with a
minor difference. This level is also used for qualitative data but the scale can be ordered and can
be amended. For example, Likert scale analysis is an example of ordinal level of measurement.
Interval – This type of level does not only classifies and orders the measurement but also
capable of specifying the distance between each interval. For example, in the Section A crime
rates of 10 years apart was the level of interval.
8

Ratio – This level has the scale with equal differences values (Cumming and Calin-Jageman,
2016).
9