Statistical Study


Every study requires statistical tests that give us the relevance of a hypothesis stated or a theory, the statistics can only be done through the use of data and using statistical hypothesis testing methods then we can validate the significance of a theory or a hypothesis.

In the case of identity theft we will consider the theories of crime to help us formulate a hypothesis that will be tested using available data, this data can be collected using interviews with victims of these crimes or even questionnaires, other sources include books and journals. This paper discusses the theories on crime and also shows the independent and the dependent variables that will aid in formulating our model and then test the statistical significance of our theory.

Theories on crime and its prevention:

Identity theft has increased in our societies in the recent past, there has been increased opportunities regarding these crimes, this paper discusses the possible solutions to these problems and how these crimes can be prevented. Some of the supporting theories include the control theory of crime, the situational theory and the rational choice theory. All these theories give a guideline on how these crimes can be stopped. Data on identity crime is available in various data bases and also to test our hypothesis whether indeed the consideration of certain factors there will be decline in the occurrence of these crimes.

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Control theory by Travis Hirsch:

Travis Hirsch in his theory of control regarding crime stated that there exist control mechanisms that can help reduce the rate of crimes; he identified direct control mechanisms, indirect control mechanism, need satisfaction control and the internal control mechanism.

Direct control entails the use of formal threats such as punishments to offenders of these crimes; offenders will not involve themselves in crimes if there is the existence of harsh punishment associated with these crimes. Indirect control according to Travis Hirsch is attained as a result of influence from the superego of the offenders, people will gain control against making offences due to their inner control developed.

Internal control will result from the people who influence a person behavior, these include friends and parents and the nature of the relationship will determine whether a person commits a crime or does not. Finally need satisfaction control results from the result of fulfilling an individuals needs, when the needs of an individual are met then they will be less likely to commit crimes.

Situational theory by Clarke and Hough:

this theory depicts a possible ways by which crime can be prevented through making crimes more difficult, one way to achieve this is through educating the individuals on crimes, crimes will be reduced if the individuals know that there is a high possibility of crime occurrences on certain occasion and if the strategies set by offenders is well known to the individuals it will be less likely for these crimes to occur.

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Rational choice theory by Clarke:

This theory by Clarke depict that crimes will be deterred by the certainty of the occurrence of punishment and fines and not the severity of the punishment, by this Clarke means that the existence of harsh punishments will not deter crimes but it is the certainty that punishments will occur that makes crimes to be reduced by the punishments.

Therefore from the theories given crime will be reduced by the following factors:

– Giving information about the opportunistic crimes

– Harsh and the certainty of punishments

The dependent and independent variables

In our research on crimes we will have use the variables that include the occurrence of the crime, and we will consider control measures which include information about the crime and the existence of harsh crimes in the system that deter crime.

Our dependent variable therefore will be the occurrence of these crimes, this will be given by the data available, and this variable will be a measure of the frequency of these crimes.

The independent variables will include the control measures and at the same time the availability of information regarding these crimes, the independent variables will be those factors that influence these crimes. Our model will take the following form:

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Y = α + b X1 + b X2 + u

Where Y is the crime rate, α is the autonomous value of these crime, X1 will be the existence of control measures, X2 will be the existence of information regarding these crimes and finally the u is the error term.

The reason why we choose these variables is due to the available literature and how they depict how this crime can be stopped, one way in which these crimes can be stopped is the existence of a control measure and the other way is through giving out of information regarding the crimes and the opportunities that lead to this crime.

The other thing to consider after we have specified our model as Y = α + b1 X1 + b2 X2 + u, is the signs expected, we expect that as the level of control increases then the rate of these crimes will reduce, in the same case as the level of information increases then the rate will decrease. Therefore there exist an inverse relationship between the independent variable and the dependent variable.

Therefore the parameters of X1 and X2 will be negative in such a way that when the value of X1 increase then Y decreases, when X2 on the other hand increases then Y decreases. For the autonomous value it must take a positive value meaning that if there existed zero levels of control measure and also information then the level of crime will be at a positive level, therefore the autonomous value is positive.

After getting our data from either a secondary or primary source then there will be a need to estimate the model using the classical linear regression model, this will involve determining the parameters and the autonomous value. After regressing we will first check the signs whether

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they are consistent with our expected signs. After these we will test hypothesis regarding these parameters regarding their statistically significance.

If the parameters are statistically significant and our correlation levels are high then it is clear that our model is appropriate and explains the effects of the existence of the independent variables in crime prevention.

Null and alternative hypotheses

Hypothesis testing involves testing the estimates of a model to check whether the estimates are statistically significant. The steps of a statistical hypothesis test are as follows:

State the null and alternative hypothesis;

We will consider in our case the significance of

Α, b1 and b2

For α

We state the null hypothesis as

Ho: α = 0

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And the alternative hypothesis will be as follows

Ha: α ≠ 0

For b1 and b2 we do the same as follows

null hypothesis

Ho: b1 = 0

alternative hypothesis

Ha: b1≠ 0

Null hypothesis

Ho: b2 = 0

Alternative hypothesis

Ha: b2≠ 0

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After stating the null and alternative hypothesis we have to make a decision regarding their significance by finding the t calculated value and the t critical value

The T critical value;

The T critical value is retrieved from a z table whereby we make a decision on the level of test we would like to test, this include such levels as 95%, 98% and 99% levels.

When the T Critical is retrieved from the table taking into consideration the degrees of freedom we compare them with the t calculated value.

The T calculated;

The T calculated value will be calculated by dividing our estimated parameters with their standard errors, this gives us the t critical value, the decision therefore will be made as follows, if the T calculated value is greater than the T critical value then we reject the null hypothesis, when the t calculated value is less than the t critical value then we accept the null hypothesis. It is important to note that when we reject the null hypothesis we at the same time mean that we have accepted the alternative hypothesis. By rejecting the null hypothesis then this means that our parameter in question is statistically significance. This is because our test shows us that the value is not equal to zero at the given test level.

Data sources

Primary sources:

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These are the sources of data that include the use of interviews and questionnaires to gain data, it is termed as secondary because the person undertaking the research has first hand data collection and does not rely on the use of what others have gathered.


Interviews are reliable source of statistical data, interviews can either be face to face interviews or phone interviews, all these interviews however require the preparation of questions that aid in the collection of data. However interviews are sometimes very difficult to conduct due to the fact that they are time consuming and they are not cost effective. In our case interviews could be conducted on victims of these crimes which will help us get data for testing our hypothesis.


Data can be collected by the use of questionnaires. This involves setting up questions that will aid in the collection of data regarding these crimes. Questionnaires are designed in a way that they give us both quantitive data and at the same time qualitative data. When these questions are set up then they are first tested to check if there exist any biasness in the questions and then they are mailed to the respondents, when the questionnaires are returned then there is data analysis and any incomplete questionnaire is disregarded.

Secondary data:

Secondary data is available regarding the research paper, with the website today it is possible to retrieve data regarding these crimes which will aid in our model estimation. Some of the source that are relevant in this study can be retrieved from websites, books, journals and

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research papers from people who have done similar studies.


Lind and Mason (2003) Statistical Techniques in Business and Economics, McGraw Hill, New York