Abstract

This report will explore the correlation between cuts in the UK Police Force over the last decade with the general crime rate in the UK over the same time period. The report will explore the effect of reducing the number of frontline police officers on violent crime rates in particular. Statistical analyses/methods will be used in order to come to a conclusion by accepting or rejecting the null hypothesis. Following on from this, a brief literature review on existing research, and a proposed methodology to obtain more conclusive results will also be included.

Contents

Abstract

Introduction

Potential research outcomes

Literature Review

Mathematical Equations

Methodology and analysis

Proposed future methodology

Conclusion

Bibliography

Figures

Appendix

A recurring theme often seen in the news relates to budget cuts in the UK, particularly within the UK Police Force. Many news outlets including Sky [1], The Guardian [2] and The Independent [3] have published alarming articles highlighting how these budget cuts have impacted crime rates using headlines such as “Police cuts ‘likely’ factor in serious crime rise” [1] and “Police budget cuts driving violent crime” [3]. These articles contain a few statistics such as “official statistics revealed a 22 per cent rise in knife crime across England and Wales” [3] however, the articles failed to include in-depth statistics which provide a direct correlation to compare how police cuts have affected these crime rates. Along with this, references for where they obtained the data were difficult to get to if at all possible. The main theme throughout these articles is that there are numerous factors which are affecting the crime rate with the main culprit being the budget cuts. As with all things however, there are various other contributing factors such as the rise and fall of the drug market, changes in financial and economic circumstances, and the ‘glamorisation’ of crime and violence on social media and within music.

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For the purpose of this research assignment, we will mainly be focusing on how a reduction in the number of police officers has had an impact on violent crime in the UK. We will take data from the government’s official crime statistics page [4] and use statistical analysis such as Pearson’s r test in order to statistically accept or reject the null hypothesis.

The results from this research paper would fall into one of 3 main categories.

Accepting the null hypothesis (below) – This would mean that there is no significant correlation between police numbers and crime rates.

The null hypothesis (appendix 1.1): There is no statistically significant relationship between the fall in patrol police officers and level of crime rates in the UK.

The second of these would be rejecting the null hypothesis and accepting the alternative hypothesis.

The alternative hypothesis (appendix 1.2): There is a statistically significant relationship between the fall in patrol police officers and level of crime rates in the UK.

Finally, the results could prove to be inconclusive, meaning that further investigation would be required, perhaps with more in-depth data/statistics. This could also be the case if multiple factors have a significant effect on crime rates (on top of just the number of police officers).

As mentioned in the introduction, a lot of the publications/text on this subject seem to be coming from news outlets. Even after trawling through various online scholarly article diaries, there were very few which go into the depth of the data as would be required. Many of the better articles are published around 1980-1990 which makes the results a little outdated. The few articles which were found were more of blog posts etc.

Below are the main articles which were used as a reference.

https://www.justiceinspectorates.gov.uk/hmicfrs/media/police-numbers-and-crime-rates-rapid-evidence-review-20110721.pdf [5]Ben Bradford (July 2011), Police numbers and crime rates – a rapid evidence review This paper was written in 2011, only a year after the 2010 budget cuts, which we are using as the starting point for our research. The summary from this article states “there is very little evidence that increasing the number of officers might result in a reduction in crime” (and vice versa). It does mention however, that more recent studies have suggested there is a link. This article goes on to explore the relationship between police numbers and property crime in particular. An excellent table within the paper can be found in the appendix which contains a summary of 13 pieces of research with the method and findings. (appendix 1.8) 

http://cep.lse.ac.uk/pubs/download/CP190.pdf [6]CentrePiece (Winter 2005/2006), Can more police resources reduce crimes? (A summary of ‘Crime and Police Resources: The street crime initiative’ by Stephen Machin and Olivier Marie, CEP Discussion Paper No. 680)Another older paper, this paper follows a similar mindset to other papers published on the subject. One of the key points made in this is “there is little hard evidence showing that more police do in fact reduce crime.” It goes on to say the reason behind this is it is difficult to disentangle the causal relationship between the two. According to the paper, higher crime usually means more police.  

https://www.jstor.org/stable/10.1086/666614?seq=1#page_scan_tab_contents [7]Ben Vollard, Joseph Hamed (November 2012), Why the Police Have an Effect on Violent Crime After All: Evidence From the British Crime Survey.This findings from this paper suggest that higher numbers of police not only lower the crime rates but also increase the share of crime, and in particular violent crime. 

The issue with the literature above is that there is nothing current. The latest of these articles was published in 2012, which is still early on in the police cuts. Upon reading through these, many of them fail to use statistical methods to statistically back up their statements. I believe this is due to the lack of statistical tests which can be used for this. As we are only focused on one of the various factors affecting crime rates, the range of statistical tests we can use is extremely narrowed down. Due to this, the articles do all agree on the difficulty of proving causality for this scenario.

As part of the research for this article, various statistics for police numbers and crime rates were gathered which will be explored below.

r=nxy–(x)(y)nx2–x2[ny2–(y)2]

Equation 1 – Pearson’s r formula
df=N–2

Equation 2 – Degrees of Freedom

Currently, officers are categorised as either frontline (like response teams, neighbourhood policing, front desk roles), frontline support (such as intelligence), business support (such as training) or not coded (such as national policing). [8]

For the purpose of this report, we will be using frontline police officers as this includes patrol officers which would act as the main visible deterrent for crimes.

Figure 1 – Total police officers        Figure 2 – Frontline police officers graph

As can be seen from figure 1 above, the number of police officers has been falling since 2010. Figure 2 displays the change in frontline police officers which we are using for our analysis. Frontline police officers have decreased from 124,000 in 2010 to 104,000 in 2018 which is a reduction of just over 16%.

In the same time period, crime stats were affected as below. These tables include overall crime rates as well as for more specific crimes/categories of crimes.

Figure 3 – Homicide rates graph         Figure 4 – CSEW Graph

     Figure 5 – Police recorded violent offences   Figure 6 – volume of violent crime

Extracting the data from the graphs above give us the table below.  For the purpose of this paper, the bulk of the crime data was extracted from Figure 6 – which depicts the total violence (appendix 1.3).  These figures were then collated into a table which could be used for further statistical analysis – The raw data can be found in the appendix (appendix 1.4).

Because we are working with an independent variable and a dependant variable, the type of analysis we will be using is regression analysis. This is used when the two fields display a slightly linear relationship [9]. The regression analysis we are using in particular is Pearson’s correlation [12]. This is used to calculate the correlation coefficient, r which is then used to calculate the coefficient of determination. The linear regression can be seen on the graph which is a plot of the table (appendix 1.4). The graph contains a regression line (line of best fit) which indicates the general trend. It is important to note however, that with regression analysis, correlation is not the same as causality.

Figure 7 – Graph of table below with regression line

Calculating r in Pearson’s test (Equation 1) gives us a value of -0.7522 (appendix 1.9 shows calculation). This shows a strong negative correlation (appendix 1.5), which means that high X variable (Number of Police Officers) scores go with low Y variable (Total Violence) scores.

The value of R2, the coefficient of determination, is 0.5658. This means that ~57% of the variance in total violence is predictable from the number of officers.

For the decision rule, we can look at the r table for the critical value. Using a 0.05 level of significance and inputting our degrees of freedom (appendix 1.6), we get a value of 0.666.

Using the above value, we can see that our value of R is greater than 0.666 (ignoring the negatives). This means we can reject the null hypothesis, therefore concluding there is a relationship between the number of officers and total violence.

These results however, do not paint an entirely accurate picture, and this is due to a few reasons. One of the main reasons, as mentioned earlier is that proving causality for the number of officers on total violence is extremely difficult. There is a high chance that they are correlated as can be seen above, however, the results are not conclusive enough. The r and r2 values are not close enough to 1/-1 to say for certain whether it is the police numbers that are causing this change.

Another issue is in the way that crimes are recorded. Many of the other articles touch on this also as inconsistencies in different crime recording agencies make it difficult to get accurate results. It is worth noting also that the above figures are solely for the effect of police numbers on total violence (number of violent offences). This is not indicative of the effect on overall crime rates.

Below you can see an example using the overall crime rates in the UK.

Figure 8 – Graph to show the volume of police recorded crimes.

The graph above was used to extract the number of police recorded crime each year. This gives us a good estimate for the total number of crimes in the UK for this time period. These figures were then collated into a table which could be used for further statistical analysis – The raw data can be found in the appendix (appendix 1.7). It is worth noting that police recorded crime data are not designated as national statistics.

These numbers can then again be used in Pearson’s correlation.

Calculating r in Pearson’s test gives us a value of -0.6173. This shows a moderate negative correlation (appendix 1.5), which means that high X variable scores go with low Y variable scores (and vice versa).

The value of R2, the coefficient of determination, is 0.3811. This means that ~57% of the variance in total violence is predictable from the number of officers.

For the decision rule, we can look at the r table for the critical value. Using a 0.05 level of significance and inputting our degrees of freedom (appendix 1.6) we get a value of 0.666.

Using the above value, we can see that our value of R is smaller than 0.666 (ignoring the negatives). This means we can accept the null hypothesis, therefore concluding there is no statistically significant relationship between the number of officers and total crime.

Proposed future methodology

In order to obtain conclusive results, a much wider and deeper investigation needs to be pursued. My proposed plan for this would be to research into the top 5 factors affecting crime in the UK. An independent analysis would then be undertaken for each of the factors working out the impact/relationship they have with the crime rates. It would also be possible to find scenarios where other factors are mitigated or taken in to account. This would provide a more accurate picture with how much each of the factors are affecting the crime rates. This would however, be very difficult as can be seen by the lack of comprehensive/conclusive evidence available online.

An alternative methodology would be to approach the problem slightly differently. Instead of asking does the number of police officers affect the crime rate, we can ask “How does a reduction in the number of police officers affect different sectors of crime”. This would enable us to compare between the groups due to having nominal/qualitative data and also enable us to carry out the chi-squared test as we would be able to use observed and expected values. This in turn would give you a level of error/certainty indicating which types of crime were increasing due to the budget cuts.

As this research was mainly focused on how the number of frontline police officers affect the crime rates. Research would also need to be carried for other areas of the police force and how reductions/cuts in these areas (non-frontline) affect the crime rate.

Finally, it is worth mentioning that the data taken was for the UK as a whole. Many individual cities/towns/areas could be of an opposing verdict to the null hypothesis as variations in the police force could affect seperate areas differently. This could be affected by other factors such as employability rates in the area, average salary, population and even cost of living coming into effect. Running the tests on smaller areas within the UK such as borough’s or districts would provide more comprehensive results as we could understand how the cuts affect each area individually and factor in the other influences.

Despite what the media may portray, we can quite surely say that regardless of the strong correlation shown, the results are far too inconclusive for us to confidently accept or reject the null hypothesis without investigating further. From the results we obtained, we could accept the null hypothesis (as mentioned in the analysis section) for the rise in violent crimes, however, crime we must reject the null hypothesis for crime as a whole. Looking through the summaries/findings on Appendix 1.8, we can really see the mixed signals and results obtained throughout various papers which are no doubt due to the issues highlighted throughout this text. 

It is likely possible that a decrease in the number of patrol officers may play a part in increasing certain crimes such as violent crimes or burglaries. It is worth noting however, that this is more likely to be the other way around, where an increase in the number of patrol police officers would result in a decrease in certain crime rates which makes sense as they would act as a physical deterrent.

In order to continue the research, further statistical tests could be undertaken, however, this would be for exploring multiple areas of crime and comparing them to each other. This would give a good indication of which types of crime were affected the most from the reduction in patrol officers. This would also mean that a wider range of statistical analyses could be used. As we only had 1 dependant and 1 independent variable, the graph with the regression line and Pearson’s correlation were the best choices to show the statistical significance.

To conclude, as the budget cuts affected the entire police force, the impact of losing ~20 000 frontline officers since 2010 was not significant on the overall crime rate in the UK with many reports even showing how overall crime rates have decreased since 2010. They key issue, which has been picked up by the media is how the reduction has impacted specific areas of crime, most of which would be done out in public. These are then mis portrayed with the headlines mentioned in the introduction.

[1] – https://news.sky.com/story/police-cuts-likely-factor-in-serious-crime-rise-leaked-report-reveals-11323603

[2] – https://www.theguardian.com/uk-news/2018/apr/08/police-cuts-likely-contributed-to-rise-in-violent-leaked-report-reveals

[3] – https://www.independent.co.uk/news/uk/crime/uk-police-cuts-violent-crime-london-stabbings-met-police-chief-cressida-dick-a8357796.html

[4] – https://www.ons.gov.uk/peoplepopulationandcommunity/crimeandjustice/bulletins/crimeinenglandandwales/yearendingjune2018

[5] – Ben Bradford (July 2011), Police numbers and crime rates – a rapid evidence review [online]

Available at: https://www.justiceinspectorates.gov.uk/hmicfrs/media/police-numbers-and-crime-rates-rapid-evidence-review-20110721.pdf

[Accessed 10th December]

[6] – CentrePiece (Winter 2005/2006), Can more police resources reduce crimes? (A summary of ‘Crime and Police Resources: The street crime initiative’ by Stephen Machin and Olivier Marie, CEP Discussion Paper No. 680)

http://cep.lse.ac.uk/pubs/download/CP190.pdf

[Accessed 10th December]

[7] – Vollard, B., Hamed, J., 2012. Why the Police Have an Effect on Violent Crime After All: Evidence From the British Crime Survey.

[8] – https://fullfact.org/crime/police-numbers/

[9] – https://dss.princeton.edu/online_help/analysis/regression_intro.htm

[10] – https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide-2.php

[11] – https://study.com/academy/lesson/what-is-a-null-hypothesis-definition-examples.html

[12] – http://psych.unl.edu/psycrs/350/unit2/gallery/sq3.doc

Additional reads

[13] – https://www.ons.gov.uk/peoplepopulationandcommunity/crimeandjustice/articles/thenatureofviolentcrimeinenglandandwales/yearendingmarch2017#what-are-the-long-term-trends-in-violent-crime

[14] – https://www.independent.co.uk/news/long_reads/police-numbers-crime-rates-uk-law-order-theresa-may-tories-link-a8399001.html

[15] – https://www.bbc.co.uk/news/uk-44397532

[16] – https://www.theguardian.com/uk-news/2018/oct/18/homicide-rate-in-england-and-wales-highest-since-2008

Figure 1 – https://fullfact.org/crime/police-numbers/

Figure 2 – https://fullfact.org/crime/police-numbers/

Figure 3 – https://www.theguardian.com/uk-news/2018/oct/18/homicide-rate-in-england-and-wales-highest-since-2008

Figure 4 – https://www.ons.gov.uk/peoplepopulationandcommunity/crimeandjustice/bulletins/crimeinenglandandwales/yearendingjune2018

Figure 5 – https://www.ons.gov.uk/peoplepopulationandcommunity/crimeandjustice/bulletins/crimeinenglandandwales/yearendingjune2018

Figure 6 – https://www.ons.gov.uk/peoplepopulationandcommunity/crimeandjustice/bulletins/crimeinenglandandwales/yearendingjune2018

Figure 8 – https://www.ons.gov.uk/peoplepopulationandcommunity/crimeandjustice/bulletins/crimeinenglandandwales/yearendingjune2018

1.1   Null Hypothesis – “A null hypothesis is a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove.” [11]

Definition taken from https://study.com/academy/lesson/what-is-a-null-hypothesis-definition-examples.html

1.2   Alternative Hypothesis – “An alternative hypothesis is simply the inverse, or opposite, of the null hypothesis.” [11]

Definition taken from https://study.com/academy/lesson/what-is-a-null-hypothesis-definition-examples.html

1.3   Total Violence – The number of offences of: violence with injury + violence without injury + stalking and harassment

1.4   Table to show total violence against number of officers

Year

Number of officers

Total Violence

2010

124000

699011

2011

120000

665486

2012

117000

626720

2013

113000

601141

2014

111500

634625

2015

110500

778221

2016

106000

992805

2017

105000

1232929

2018

104000

1469200

1.5 Table to show interpretation of values of r

Value of R

Interpretation

Exactly -1.0

A perfect downhill (negative) linear relationship

-0.70

 A strong downhill (negative) linear relationship

-0.50

 A moderate downhill (negative) linear relationship

-0.30

 A weak downhill (negative) linear relationship

0

No linear relationship

+0.30

A weak uphill (positive) linear relationship

+0.50

A moderate uphill (positive) relationship

+0.70

A strong uphill (positive) linear relationship

Exactly + 1

A perfect uphill (positive) linear relationship

1.6   Degrees of Freedom – degrees of freedom (df) is the number of data point minus 2. (N-2) [10](See equation 2)

1.7   Table to show police recorded crimes against number of officers

Year

Number of officers

Police Recorded Crime

2010

124000

4338295

2011

120000

4150916

2012

117000

4379984

2013

113000

4063571

2014

111500

4028463

2015

110500

4167310

2016

106000

4509531

2017

105000

5164448

2018

104000

5620155

1.8   Extract of table from [7]

1.9 – Pearson’s r calculation for number of police officers against violent crime