Abstract

Inferential statistics refers to a branch of statistics that is used to assist researchers in testing hypotheses and making inferences from sample data to a larger sample or population. It consists of procedures used to make inferences about population characteristics from information contained in a sample drawn from the same population. Statistical tests such as t test, analysis of variance or f test, or chi square test are used to see whether two or more groups of participants tend to differ on some variable of interest. However, due to the complexity and number of inferential statistical tests available, it becomes a difficult decision for a researcher to decide on which statistical tool to employ for a particular study. Therefore, there arises a need for a matrix or model that facilitates the decision making by a researcher. This matrix can take the form of a decision tree, outline or model that encompasses a series of questions that guide a researcher to decide on which statistical test in most appropriate for a particular study. This paper presents such as model.

Introduction

The importance of inferential statistics in research cannot be over emphasized. It facilitates the acquisition of information that would otherwise not have been obtainable about a particular population. It is less costly, practical, and saves on time and labor. However, and most importantly, inferential statistics provides reliable information which is accurate and of high quality and whose margin of error can be specified. This paper presents a tabulated statistical decision model that can guide a researcher on deciding on which statistical test to use for a particular research study.

Steps Involved In the Model and the Easiest and Most Difficult Parts of the Process

When trying to make a decision with regards to which statistical test to use, one needs to ask oneself questions such as:

1. Am I interested in….?
2. Description (Association)- Factor Analysis, Correlation, Path Analysis
3. Intervention (Group Differences)- T-Test, ANOVA, MANOVA, Chi-Square
4. Explanation (Prediction)- Regression, Discriminant Analysis, Logistic Regression
5. Is my Dependent Variable Nominal, Ordinal, Interval, or Ratio…?
6. Nominal- Chi-Square
7. Dichotomous-Logistic Regression
8. Ordinal-Chi-Square
9. Interval/Ratio – Correlation, Multiple Regression, T-Test, ANOVA, MANOVA,
10. Other questions a researcher needs to ask is: Do differences exists between groups?; Do the differences exists between 2 groups or more on one DV, or on multiple DVs?; How strongly and in what direction are the IV and DV related?; and finally, What is the likelihood of the dependent variable occurring as the values of the independent variables change?.

These guiding questions, together with considerations such: what form the research question took such as to investigate group differences, degree of relation ship and predictions of group membership; number and type of the dependent variables and independent variables; covariate; and finally, the goal of the research question

 

 Statistical Decisions Model

Research Question?	Number And Type Of DV?	Number and Type Of IV?	Covariates	Test	Goal Of Analysis
Group Differences	Nominal Or Higher	1 Nominal Or Higher		Chi Square	To Determine Whether there are Differences between Groups
	Continuous	1 Dichotomous		T-Test	To Determine Significance of Mean Group Differences
		1 Categorical		One-Way ANOVA
			1+	One-Way ANCOVA
		2+ Categorical		Factorial ANOVA
			1+	Factorial ANCOVA
	2+ Continuous	1 Categorical		One-Way MANOVA	To Create Linear Combo of DVs to Maximize Mean Group Differences
			1+	One-Way MANCOVA
		2+ Categorical		Factorial MANOVA
			1+	Factorial MANCOVA
Degree Of Relationship	Continuous	1 Continuous		Correlation	Determine Relationship/ Prediction
		2+ Continuous		Regression	Linear Combination to Predict The DV
	1+ Continuous	2+ Continuous		Path Analysis	Estimate Causal Relations among Variables
Prediction Of Group Membership	Dichotomous	2+ Nominal Or Higher		Regression	Create Linear Combo of IVs of the Log Odds of Being in one Group

The most difficult and challengingpart in the construction of the statistical decision tree was in finding the broad and umbrella differentiating characteristics of the statistical tools so as to broadly group the tests, as well as finding the unique distinguishing attributes of each tool which makes them distinct from the other tools. This required keen scrutiny and examination of each statistical tool and necessitated the spending of a lot of time noting down the differences.

RESEARCH QUESTIONS IN THE AREA OF CRIMINOLOGY

Research Question 1: What is the impactof contemporary police strategies in reducing crime rates?

Hypotheses

The research study wants to investigate whichcontemporary police strategy between Geographic Policing and Geographic Profiling reduces community crime rates more. The following are the null hypothesis and alternative hypothesis for the research study:

H₀: µ_{Geographic Policing} = µ_{Geographic Profiling}

H₁: µ_{Geographic Policing} ≠ µ_{Geographic Profiling}

The null hypothesis for this research question supposes that the two police approaches to addressing crime; geographic policing and geographic profiling, have equal impact in reducing crime levels. The alternative hypothesis supposes that at least one of the police approach to reducing crime is more effective than the other

Variables

The contemporary police strategies that include Geographic Policing and Geographic Profiling form the independent variables of the study, while level of crime rates form the dependent variable.

The contemporary police strategies,the effectiveness of geographic policing and effectiveness of geographic profiling can be measured by use of proxies such as the perception of the law enforcement officers and the community towards their effectiveness, and or through the use of official statistics that reflect a change in crime levels since the introduction of geographic policing or geographic profiling into the community.  They are categorical variablesthatare measurable using ordinal scale.Crime levels can be measured using the number of reported cases to law enforcement establishments. It is a continuous variable.

Utilization of the statistical decisions model to make a decision

Using the statistical decision model to decide on an appropriate statistical test to use in the study, I would first look at the umbrella characteristics of the study such as the nature and number of independent variables as well as number of dependent variables, their attributes and scales of measurement and finally the goal of the analysis.The research study has one independent variable which is categorical in nature and one dependent variable which is continuous in nature.Additionally, the two variables in the research question do not covary.Lastly, the study aims at determining significance of mean group differences. Therefore, using the decision model, the study will employ the use of a One-Way ANOVA. The model guidedme to the correct statistical tool, this is because, aOne-Way ANOVAwould be the most appropriate tool for drawing conclusions for this study.

Research Question2: What is the correlation between choice of forensic tools employed and the number of solved criminal cases (clearances) and crime rates?

Hypotheses

The objective of the study is to establish whether there exists any relationship between the choice of forensic investigation tool by the police and the number of solved criminal cases and crime rates. Following are the statistical notations of the null hypothesis and alternative hypothesis;

H₀: µ_(x) = µ_(y)

H₁: µ_(x) ≠ µ_(y)

The null hypothesis supposes no significant relationships exists between the choice of forensic investigation tool (X) and the number of solved criminal cases and crime rates (Y), while the alternative hypothesis supposes that significant relationships exists between the choice of forensic investigation tool and the number of solved criminal cases and crime rates.

Variables

The variables for the study were the different forensic investigation tools available on one hand and the number of solved criminal cases (Clearances) and crime rates. The forensic investigation tools are nominal variables, and so are the number of solved criminal cases and crime rates. Both of these variables are categorical or nominal variables since they can take two or more categories that have no intrinsic ordering.

Utilization of the Statistical Decisions Model to Make Decisions

To choose an appropriate tool for the study, we look at the broad characteristics of the research question such nature and number of variables, their attributes and scales of measurement, goal of the analysis and nature of research question. This research question has two variables, both of which are continuous variables and do not covary, and its goal is to establish whether there are differences between groups. Based on the statistical decision model, the statistical tool to use is a chi-square. As a researcher, I would also have used the chi-square statistical tool. Therefore, I consider the decision model to have given chosen the correct tool.

Limitations and Usefulness of Statistical Decision Models in Statistics and Research Methods

Statistical decision models play an important role in statistics and research methods. They are useful as they provide a direct and often simpler approach to deciding which statistics tool to employ for a particular research question. Statistical decision models also have the advantage that they are self-explanatory and easy to follow and can easilybe grasped by non-professional users. Additionally, they can handle both nominal and numeric input attributes thereby making them more accepting to statistical tools with various differentiating attributes.However, these decision models have disadvantages, the key ones being; firstly, they predominantlyemploy the use the “divide and conquer” method, thus they tend to perform well only when a small number of highly relevant characteristics exist, but less so if numerous composite correlations are present. Secondly, considerable time is necessary to make a summary of the various statistical tools characteristics and attributes to create the statistical decision model, thus it is tiresome in its construction.

What Was Learnt From Creating the Model and Applying It to the Study of Interest and How It Might Be Used the Future

Creating this statistical decision model necessitated me to keenly examine the characteristics and attributes of each of the statistical tools so as to note the unique differentiating qualities and elements of each tool. Therefore, I can consider myself to be more conversant with the various statistical tools more than before, and I can now easily identify a particular tool to use for a particular research question without referring back to a textbook or to the decision model. The model will be important in future especially in times when a decision with regards to which statistical tool to use is needed. Indeed, it was an eye-opening exercise that summarized all that I have learnt in this class.

 

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