Decision Modeling in Inferential Statistics: Choosing Tests

Introduction to Decision Modeling

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 paper presents the various steps involved in decision modeling and uses two studies to demonstrate how such models can be used to guide the selection of the correct test.

Steps in the Decision Chart

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

The first step involves identifying the study variables and categorizing them as either discrete or continuous (Larson-Hall, 2015). This 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 key 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 to review studies conducted by more experienced researchers on the same variable to gain insight into how it can be measured effectively.

Once the dependent variable has been correctly categorized, the next step is to determine what the study is seeking to measure — that is, whether it aims to identify the kind of relationship that exists between variables, or whether it seeks to detect differences between groups or samples (Larson-Hall, 2015). This is typically the easiest of the four steps because the study's objectives and hypotheses will usually have been determined beforehand during the conceptualization phase. If the study is interested in comparing groups for differences and similarities and the dependent variable is categorical, the chi-square test is conducted; however, the specific chi-square test chosen will depend on the number of categories being compared.

If the dependent variable is measured at the continuous level, the researcher must determine what the study seeks to measure and then proceed to the third step: determining whether the data is normal or non-parametric. This can be the most challenging step, as it may not be possible to determine normality manually. The researcher may therefore need to use an additional test — specifically, the Shapiro-Wilk test for normality — to determine whether the data is normally distributed. If the data is continuous and the study aims to determine the strength of the relationship between variables, the Pearson correlation is used when the data is normally distributed, and the Spearman Rank correlation is used when the data is non-parametric. If the study is instead interested in comparing samples or groups to detect significant differences, and the dependent variable is continuous, a t-test or ANOVA is used for normally distributed data; otherwise, the Kruskal-Wallis test is used. The decision between ANOVA and the t-test is based on the number of samples being compared — the t-test is used when there are only two samples, while ANOVA is used when there are more than two.

The final step is determining whether the samples being compared are dependent or independent (Larson-Hall, 2015). This helps determine which specific t-test or ANOVA to use. If there are only two samples and they 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 samples are dependent, the repeated-measures ANOVA is used; otherwise, the one-way ANOVA is used.

Juvenile delinquency has become a serious social concern in American society; the rising numbers of school shooting incidents and homicides perpetrated by juveniles are a clear demonstration of this. These high rates have attracted the attention of researchers, who are now focusing their efforts on identifying the causes of juvenile delinquency and potential solutions. This study examines the role of parents in cases of delinquency — more specifically, whether there is a relationship between parenting style and the risk of juvenile delinquency. The research question guiding the study is:

Study 1: Parenting Style and Juvenile Delinquency

"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.

Applying the decision model, the first step is to identify the study variables and determine the type of dependent variable. The independent variable is parenting style; the dependent variable is juvenile delinquency. A group of 20 pupils from the same grade could be selected to participate. Parenting style could be measured using the parental authority questionnaire, which assesses parental strictness or permissiveness based on how a child interacts with their parents and how decisions are made in the home. Participants would indicate their level of agreement or disagreement on a scale of 1 to 5 with statements such as "my mother does not allow me to question her decisions." Numerical values from 1 to 5 would be assigned to each response, and the total score across all 13 statements would serve as the measure of parental authoritativeness.

Juvenile delinquency would be measured using the Self-Reported Delinquency Survey, in which participants indicate their degree of agreement or disagreement on a scale of 1 to 5 with statements designed to measure self-discipline and the risk of committing delinquent acts. Responses would be summed to produce a total delinquency score for each participant. Both variables would therefore be measured as continuous, interval variables.

Having categorized the dependent variable as an interval variable, the next step is to determine what the study seeks to measure. Since the goal is to determine whether a relationship exists between the two variables, the correlation test is indicated. To determine which correlation test to use, the collected data would need to be subjected to the Shapiro-Wilk test for normality. If the data is normally distributed, the Pearson correlation test is used; otherwise, the Spearman Rank correlation test is used. In this case, the model correctly leads to the correlation test, which is the most appropriate test for the study.