Decisions Involving Probability

Independent and Dependent Variables

Ideally, the two main variables in an experiment include the independent and dependent variables. By definition, an independent variable is a variable that is controlled in the experiment to test the impact on the dependent variable (Gratton & Jones, 2004). Usually, the variable is not affected by the other variables within the experiment. On the other hand, the dependent variable is the variable that is tested or measured in an experiment. The variable depends on the independent variable and as the experiment changes; the impact is visible on the dependent variable. Viewed in terms of a cause and effect, when the independent variable changes, then the effect is recorded in the dependent variable. In the scenario described, the variables are the brightness of the moon and the burglars breaking into the house. The presence of a bright moon is the independent variable (cause) because it causes a change in the dependent variable, which is burglars breaking into the house and stealing (effect). 

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Relationship between the Variables

Virtually, it is critically important to understand the relationship between the two variables to be able to come up with the correct conclusion from a statistical viewpoint. According to Mitchell and Jolley (2010), the relationship between the two variables helps achieve the right conclusions, and without this understanding, it is possible to fall into the pitfall of inferring wrong results. In this case, the relationship between the two variables is an illusory correlation. Practically, in an illusory correlation, the perception of a relationship between the two variables is present when a minor or no relationship exists. More particularly, an illusory relationship occurs when people assume that because two events occurred at one point in the past, then one is the cause of another. In this case, three of the women at the PTO meeting had their houses broken into while they were asleep and there was a bright moon. The women then assumed that the presence of a full moon caused the burglars breaking into their houses. The relationship between these two variables is illusory and based on a basic assumption that the presence of a bright moon caused the theft. 

Is the data presented Sufficient?

No, the data provided was not sufficient to determine a relationship between the two variables. More specifically, the data was not enough because there is no sufficient information indicating whether the theft occurred on another night when there was no bright moon. Besides, the sample size is significantly small to determine a relationship between the two variables.

What additional Data that would be required

Ideally, in research, the central goal is the identification of a causal relationship or demonstrating that an independent variable affects the dependent variable. In order to have a causal relationship, an association, time ordering, and non-spuriousness must be present (Abrahamson, 2017). The first step, the association involves establishing the relationship between independent and dependent variables. In this case, to make a causal relationship, the statistical inference should be able to make an observation and establish a connection between the two variables. In time ordering, the researcher should carefully control the exposure to treatment then measure the outcome of the interest. This means, although the bright moon might have caused the theft incidents, it could also be possible that the burglary occurred during the night without a bright moon. The third criteria, which is also the most difficult requires ruling out alternative explanations in relationships. In light of this, before concluding that the presence of a bright moon causes burglary, the research should be able to rule out the possibility of another cause of the theft apart from the bright moon. 


Abrahamson, M. (2017). Studying cities and city life: An introduction to methods of research. London: Routledge, Francis & Taylor Group.

Gratton, C., & Jones, I. (2004). Research Methods for Sports Studies. London: New York; Routledge; Taylor & Francis Group. 

Mitchell, M. L., & Jolley, J. M. (2010). Research design explained. Australia: Wadsworth.

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