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Analysis of crime rate in India

Designs of Experiment

Mentor: Dr. Hemant Kulkarni

Presented By-

Mohneet Sandhu

Rabjot Sethi

Smriti Agrawal

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CONTENTS

  1. Introduction
  2. Problem Statement
  3. Objective
  4. Case Information
  5. General Statistics
  6. Hypothesis
  7. Analysis
  8. The conclusion of the test
  9. References
  10. Acknowledgement
  11. Our Team

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INTRODUCTION

  • The crime rate in India showed a hike of almost 1.6 %, which is approximately 50.7 lakh cases, in a very short span of time, according to the National Crime Records Bureau.
  • More than a fifth of all registered crime were classified as offences affecting the human body, which included violent acts such as murder, kidnapping, assault and death by negligence.
  • The rapid rise in the various crimes has been in talks since a very long time, which actually intrigued our group to take up its analysis as a project.

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PROBLEM STATEMENT

Our problem statement for this project is to show how various crime rates have increased over the years and their dependency on the year before them.

For more comprehensive analysis we have shown how the data behaves both state-wise as well as region-wise.

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OBJECTIVE

The objective of our study is to use various statistical tests and visualisations to determine if -

  • There is a significant difference between crime rates in all the regions in the years 2018, 2019 and 2020.
  • There is a significant difference between crime rates in all the states in the years 2018, 2019 and 2020.

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CASE INFORMATION

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GENERAL STATISTICS OF DATASET

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GRAPHICAL REPRESENTATION OF CASES PER MILLION (Region-Wise)

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GRAPHICAL REPRESENTATION OF CASES PER MILLION (Region-Wise)

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GRAPHICAL REPRESENTATION OF CASES PER MILLION (Region-Wise)

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GRAPHICAL REPRESENTATION OF CASES PER MILLION (Region-Wise)

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GRAPHICAL REPRESENTATION OF CASES PER MILLION (Region-Wise)

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GRAPHICAL REPRESENTATION OF MEDIAN (Yearwise)

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GRAPHICAL REPRESENTATION OF MEDIAN (Yearwise)

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GRAPHICAL REPRESENTATION OF MEDIAN (Yearwise)

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HYPOTHESIS TO BE TESTED

H01 - There is no significant difference between the medians of the crimes in various regions for years 2018, 2019 and 2020.

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H11 - There is a significant difference between the medians of the crimes in various regions for years 2018, 2019 and 2020.

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H02 - There is no significant difference between the medians of the crimes for years 2018, 2019 and 2020 in various states.

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H12 - There is significant difference between the medians of the crimes for years 2018, 2019 and 2020 in various states.

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ANALYSIS

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NON - PARAMETRIC TEST

Why Non-Parametric Test ?

A Non-Parametric (N.P.) Test is a test that does not depend on the particular form of the basic frequency function from which the samples are drawn.

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The dataset used in our study does not follow independence criteria due to the presence of “Time” factor. So, instead of using parametric test models like ANOVA, we have conducted the statistical hypothesis by using non-parametric test models.

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FRIEDMAN TEST

This test is a non-parametric statistical approach with repeated measurements,i.e. replication of each treatment is not independent. The Friedman test is used to compare more than two dependent samples.

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where,

n: number of rows/ subjects.

k: number of columns/ conditions.

Ri: sum of the ranks from column/ condition i.

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The degrees of freedom for the Friedman test is (k-1).

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Region-Wise Analysis

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Human Trafficking

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Since, p-value > 0.05

Therefore, we accept H0 .

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Murder

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Since, p-value > 0.05

Therefore, we accept H0

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Crime Against Women

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Since, p-value > 0.05

Therefore, we accept H0

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Crime Against Senior Citizens

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Since, p-value > 0.05

Therefore, we accept H0

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Crime Against Sc/Sts

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Since, p-value > 0.05

Therefore, we accept H0

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Summary of Region-Wise Analysis

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Year-Wise Analysis

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Human Trafficking

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Since, p-value < 0.05

Therefore, we reject H0

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Murder

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Since, p-value > 0.05

Therefore, we accept H0

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Crime Against Women

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Since, p-value < 0.05

Therefore, we reject H0

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Crime Against Senior Citizens

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Since, p-value > 0.05

Therefore, we accept H0.

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Crime Against SC/STs

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Since, p-value > 0.05

Therefore, we accept H0

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Summary of Year-Wise Analysis

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WILCOXON SIGNED RANK TEST

The Wilcoxon signed rank test is a nonparametric statistical procedures for comparing two samples that are paired or related. Like the sign test , this test is also used for testing population median. In sign test, we consider the sign of (xi - θ0) that is the direction only is considered whereas in the Wilcoxon Test in addition to the direction, magnitude of the xi - θ0 is also considered.

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The paired sample Wilcoxon test is a non-parametric alternative to paired t-test used to compare paired data. It’s used when your data are not normally distributed.

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Human Trafficking

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Since, p-value < 0.05

Therefore, we reject H0

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Since, p-value > 0.05

Therefore, we accept H0

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Crime Against Women

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Since, p-value < 0.05

Therefore, we reject H0

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Since, p-value < 0.05

Therefore, we reject H0

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CONCLUSION

By conducting suitable non-parametric tests on our data related to the crime rates of the various states/regions, we concluded the following -

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  • There is no significant difference between the medians region-wise for all the crimes in the given years, as the null hypothesis were accepted in all the cases .
  • For crime against senior citizens, SC/STs and murders the H0 was accepted which implies that there is no significant difference between the medians of the crimes in various states for years 2018, 2019 and 2020.
  • For human trafficking cases the H0 got rejected by the Friedman Test. Under the Paired Wilcoxon Test:

For the year 2018-19: Accept H0

For the year 2019-20: Reject H0

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CONCLUSION

  • For crime against women, the H0 got rejected by the Friedman Test. Under the Paired Wilcoxon Test:

For the year 2018-19: Reject H0

For the year 2019-20: Reject H0

  • Finally, we were able to conclude that there is not a significant difference between the medians of the Murder Cases , Crimes Against Senior Citizens and Crimes Against SCs/STs in the various states of the country , however that was not true for Crimes Against Women and Human Trafficking .

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REFERENCES

  • www.ncrb.gov.in
  • Fundamentals of Applied Statistics by SC Gupta.
  • Introduction to Statistical Learning by Gareth James.

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ACKNOWLEDGEMENT

We are grateful to our respectable professor, Dr. Hemant Kulkarni & Dr Suresh Pathare, whose insightful leadership and knowledge benefited us to complete this project successfully. Thank you so much for your continuous support and presence whenever needed.

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All in all, we would like to thank everyone involved in this project directly or indirectly and helped us with their suggestions to make the project better

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Our Team

Mohneet Sandhu

S062

75252019138

Rabjot Sethi

S058

75252019132

Smriti Agrawal

S050

75252019079

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THANK

YOU!

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