Inferential Statistics: Decision Modeling Decision Modeling: Inferential Statistics

Decision models are important components of inferential statistics. They are crucial in helping researchers choose the most appropriate statistical test to use for their study. This text presents the various steps involved in decision modeling, and uses two studies to demonstrate how such models can be used to guide the decision on what test to use.

Decision Models in Inferential Statistics

Decision models play a crucial role in inferential statistics; particularly in assisting researchers identify the most appropriate statistical test to use for their study. The decision about what statistical test to use for a study is made in a series of steps laid out in the decision tree or decision model. Each stage requires the researcher to answer a simple question about the investigation. This text summarizes the basic steps of a decision model, and provides a demonstration of how such a model could be used in choosing an appropriate statistical test for a study.

Steps in the Decision Chart

The very first step involves identifying the study variables and categorizing them as either discrete or continuous (Larson-Hall, 2015). This basically involves developing an operational definition for each variable, and determining their scale of measurement -- either nominal or ordinal for discrete variables, or interval/ratio for continuous variables. The basic question to be answered at this stage is, 'What type of variable is your dependent variable'. Developing a good operational definition for the variables so that they measure exactly what they are intended to measure can be quite challenging; it is advisable that one reviews studies that have been done by more experienced researchers involving the same variable to obtain insight on how the same could be measured effectively.

Once the dependent variable has been rightly categorized, the next step is to determine what exactly the study is seeking to measure, that is whether it is interested in determining the kind of relationship that exists between variables, or whether there are differences between groups/samples (Larson-Hall, 2015). This is the easiest of the four steps because the objectives of the study and hypotheses to be measured will usually have been determined beforehand, when the study is being conceptualized. If the study is interested in comparing groups for differences and similarities, and the dependent variable has been identified as categorical, the chi-square test is conducted; however, the chi-square test chosen will depend on the number of categories being compared. On the other hand, if the dependent variable is measured at the continuous level, the researcher will need to determine what exactly the study seeks to measure, and then proceed to the third step, which is determining whether the data is normal or non-parametric. This could be the hardest step of the process because it may not be possible to determine normality manually, and the researcher may, therefore, be forced to use an additional test, specifically the Shapiro-Wilkins test for normality to determine whether their data is normally distributed. If data is continuous in nature, and the study is interested in determining the strength of the relationship between variables, the Pearson correlation is used if the data is normally distributed, and the Spearman Rank correlation is used if the data is non-parametric in nature. On the other hand, if the study is interested in comparing samples/groups to determine whether significant differences exist, and the dependent variable is measured at the continuous level, t-test or ANOVA is used if the data is normally distributed; otherwise, the Kruskal-Wallis test is used. The decision of whether to use ANOVA or the t-test in such a case will be based on the number of samples being compared -- t-test is used when there are only two samples whereas ANOVA is used when the number of samples is greater than two.

The final step of the model is determining whether the samples being compared are dependent or independent (Larson-Hall, 2015). This would help one determine the specific t-test or ANOVA to use -- if there are only two samples and the two are dependent, the dependent samples t-test is used; otherwise, the independent samples t-test is used. Similarly, if the number of samples is greater than two, and the different samples are dependent, the repeated measures ANOVA is used; otherwise, the one-way ANOVA is used.

Using the Model to Choose Appropriate statistical Tests

A decision model is regarded as effective if it is able to lead one to identify the most appropriate statistical test to use for their study. We will test the effectiveness of the developed model using two different studies.

Study 1: Assessing the Relationship between Parenting Style and Childhood Delinquency

Juvenile delinquency has become a serious social concern in the American...

These high rates have attracted the attention of researchers, who are now focusing their effort on determining what the causes of juvenile delinquency are, and potential solutions for addressing the same. In this study, I am interested in examining the role of parents in cases of delinquency. More specifically, I am interested in determining whether there is a relationship between parenting style and the risk of juvenile delinquency. The research question guiding the study is:
"Is there a significant correlation between parenting style and juvenile delinquency?"

The corresponding null and alternative hypotheses are:

H0: r = 0 there is no significant correlation between parenting style and juvenile delinquency

HA: r ?0 there is a significant correlation between parenting style and juvenile delinquency

We could use the decision model presented earlier on to determine what test to use to test the above hypotheses. The first step is to identify the study variables and determine what type of variable the dependent variable is. The independent variable in our case is parenting style whereas the dependent variable is juvenile delinquency. We could select a group of 20 pupils from the same grade to participate in the study. The parental authority questionnaire, which assesses the level of parental strictness or permissiveness based on how a child interacts with their parents, and how decisions are made in the home could be used to measure the independent variable. Participants will indicate their level of agreement or disagreement (on a scale of 1 to 5) with t statements on the questionnaire such as 'my mother does not allow me to question her decisions', 'my mother always used force to get us to behave in a certain way', and so on. Numerical values ranging from 1 to 5 will be attached to each scale, and the total value obtained from all the 13 statements will be taken as the measure of one's parent's authoritativeness. Juvenile delinquency, on the other hand, will be measured using the Self-Reported Delinquency Survey -- participants will indicate their degree of agreement or disagreement on a scale of 1 to 5 with a set of statements designed to measure self-discipline and the risk of committing delinquent acts. Numerical values will be attached and the responses summed up to give the total delinquency score for each individual. These will then be recorded alongside their total for the parental authority questionnaire, which implies that both variables will be measured as continuous, interval variables.

Having categorized the dependent variable as an interval variable, we move to determine what exactly the study is geared at measuring -- in our case, it seeks to determine whether a relationship exists between the two variables, which implies then that we use the correlation test. In order to determine which correlation to use, we will need to subject the data collected to the Shapiro-Wilkins test for normality -- if the data is shown to be normally distributed, we use the Pearson correlation test; otherwise, we use the Spearman Rank correlation test. In this case, the model correctly leads us to the correlation test, which is the most appropriate test for the study.

Study 2: Assessing the Differences between the Health and Service Needs of Homeless Youth and Homeless Adults

Youth homelessness has become a serious concern for policymakers and administrators in America. It is estimated that approximately 407, 996 youths fall homeless every year, with 50% of these remaining chronically homeless (SAMHSA, 2011). Researchers have identified numerous problems faced by these homeless youths, one of the main ones being lack of access to healthcare facilities. Numerous programs have been implemented at the state level to make healthcare more accessible to this group; however, most of these have failed to realize their intended objective. It has been noted that one fundamental reason why these programs fail is because they are usually designed to address the healthcare and service needs of the homeless population as a whole, with no consideration for the fact that the service needs of homeless youth may not necessarily be the same as those of their adult counterparts. For this reason, researchers have shifted their attention to studying the differences that exist between the health needs of homeless youth and those of their homeless counterparts. The current study seeks to add to this line of research.…