Correlation and regression analysis in research methodology

¶ … childhood obesity, which is proving to be a serious concern for policymakers and health administrators in the U.S. It is estimated that the prevalence of overweight and obesity among school-going children has almost tripled over the last decade. This places the generation in question at an extremely high risk for type II diabetes, cardiovascular diseases, and other weight-related complications. My main interest lies in understanding the causes of overweight and obesity among children. I am particularly interested in determining whether there is an association between the level of familial income, and the risk of childhood obesity. The research question guiding my study is:

"How does the risk of developing childhood obesity relate to the level of familial income?"

The simple linear correlation coefficient will be used to provide answers to the research question. The linear correlation coefficient is used to show the direction and strength of an association that exists between two variables; this question lends itself effectively to this test since we are interested in determining i) whether an association indeed exists between the level of familial income and the risk of childhood obesity, ii) the direction of that relationship, and iii) the strength of that association (Lane, n.d.). There are different types of correlation tests that one could use -- linear correlation, multiple correlation, or the logistic correlation. The simple correlation test would suffice in this case because neither of our two variables is dichotomous in nature (Sukal, 2013).

Variables and their Attributes: the level of income is the independent variable for this particular study, whereas obesity is the dependent variable. For this particular study, we will define obesity as a BMI equal to or in excess of 30. BMIs between 26 and 29 will be regarded as healthy. Values for BMI can be expected to take an infinite number of values between any two measures -- between 29 and 30, for instance, we could have an infinite number of BMI values including 29.1, 29.7, 29.34, 29.896, and so on. This would make the dependent variable, obesity, a continuous, interval variable. Level of income, the independent variable would be defined as the total income generated by a child's parents and working siblings in a given month. In this case, we could expect a wide range of figures ranging from 0 to say $30,000. We could take a sample of 20 children in the same grade, but from different neighborhoods; we could then record each child's level of familial income against their BMI levels to determine whether there indeed is an association between the two variables. Measured in this manner, the independent variable, income level, would be evaluated as a continuous, interval variable.

Variable Qualification: the assumptions of the linear correlation test require that both the independent and the dependent variables be measured at the interval level. Our two variables, obesity and income level, both satisfy this requirement as demonstrated in the preceding section. As such, our variables perfectly fit the qualifications for the selected test.

Expectations and Predictions: we would expect the results to yield a negative correlation in this case, implying that the higher the familial income level, the lower the risk of a child developing childhood obesity. This is likely to be the case because children from affluent backgrounds are more likely than their colleagues in less affluent backgrounds to afford healthy diets. If the correlation is found to be significant, I would use the line of best fit generated thereof to predict the obesity levels of children at different levels of income, particularly those not recorded by any of the 20 participating children.

Hypotheses: the statistical notations and theoretical explanations for the null and alternative hypotheses guiding the study are as stated below:

H0: r = 0 There is no significant association (correlation) between the two variables

HA: r ?0 There is a significant correlation between the two variables

Possible Errors: just as is the case with ANOVA, correlation tests are susceptible to both type 1 and type II errors. At the conventional p

Part 2: Case Study

The Stroop Interference Case Study

The case study was based on three distinct research questions:

RQ1: do males and females differ in the time it takes to correctly conduct the stroop tasks?

H0: µ A= µB -- males and females do not differ in the time it takes to conduct the tasks

HA: µ A? µB -- males and females differ in the time it takes to conduct the tasks

RQ2: are there differences in the time it takes to correctly conduct the various stroop tasks -- words, colors or interference?

H0: µ AW = µBW -- there is no difference in the time males and females take to conduct the words task

HA: µ AW? µAW -- there is a significant difference in the time males and females take to conduct the words task

H0: µ AC = µBC -- there is no difference in the time males and females take to conduct the colors task

HA: µ AC? µBC -- there is a significant difference in the time males and females take to conduct the colors task

H0: µ AI = µBI -- there is no difference in the time males and females take to conduct the interference task

HA: µ AI? µBI -- there is a significant difference in the times males and females take to conduct the interference task

RQ3: does the effect of the stroop task type depend on the gender?

H0: C12= 0 -- there is no interaction between factors 1 and 2 (gender and stroop task type)

HA: C12 ? 0 -- there is a significant interaction between factors 1 and 2

Variables: 'task time' is the dependent variable -- it is measured in terms of how long it takes a participant to conduct a particular task. This makes it a continuous, interval variable. The study has two independent variables -- gender and stroop task type. Stroop-task type is the within-subject variable whilst gender is the between-subjects factor. Both gender and stroop task type are measured as categorical, nominal variables.