Lurking Variables - Statistics Project Example

Statistics Lurking Variables Statistics is a technique that involves data collection, analysis, and making appropriate conclusions from collected information (Gupta 20). The technique calls for either complete enumeration where every population unit is studied or sample surveys where a representative portion of a population is studied. In sample surveys, sample observations are used to estimate population parameters and test appropriate characteristics. In either way, statistical analysis involves computation of both descriptive and inferential statistics. Descriptive statistics fully characterize all population parameters. Inferential statistical analysis, on the other hand, entails investigating causes of any observation made on a population. Before analyzing any set of data, a statistician must identify all variables in his/her study design. There is also need to assess how these variables correlate. Peck et al. (p. 72) warns that data analysts should not omit or ignore effects of some factors because there is no direct relation with study variables. These factors that indirectly affect both dependent and independent variables are called lurking variables (Peck et al. 73). This paper uses an example to explore the concept of lurking variables in statistics. Meaning and Significance of Lurking Variables A lurking variable, according to Brase and Brase (p. 33), is a variable that has a significant, but hidden, effect on study variables. The variable is, in most cases, not considered as a predictor variable in a study. Starnes et al. (p. 28) explains that a lurking variable, also known as confounding or hidden variables, is an extraneous factor in a statistical model that correlates with both dependent and independent variables. The correlation is either positive or negative. This type of association is called spurious relationship (Gupta 101). In any assessment, it is important to control and isolate effects of lurking variables. Because of hidden nature of the variables, Peck et al. (p. 41) observes that control of confounding factors is a challenge in many studies. To understand the concept of lurking variables, let X and Y be independent and dependent variables respectively. A lurking variable affects both X and Y such that the two variables appear as if they are related when, in fact, there is no correlation between X and Y. Consider the example below A soccer coach wanted to improve the teams playing ability, so he had them run two miles a day. At the same time the players decided to take vitamins. In two weeks the team was playing noticeably better, but the coach and players did not know whether it was from the running or the vitamins. In this example, both the coach and the players are not aware of any hidden factor that might have influenced the daily running and vitamins intake. In other words, there could be an invisible factor that makes either running everyday or vitamin intake look like it is related with performance of players. It, therefore, implies that if the hidden variable(s) is/are eliminated or controlled, then performance of players will deteriorate. Though not visible, may be the players positively changed their attitude and commitment levels. In any activity, attitude and interest an individual has towards the activity directly influence his/her performance in the same event. In the example, a change in attitudes of the players could have improved skills of the players. Types of Lurking Variables Depending on a study design or the type assessment in a study, various lurking variables exist. Confounding by indication, as one type of lurking variables, is common in studies that evaluate effects of a treatment from observational data. In these studies, certain prognostic factors influence treatment decisions and thus, producing biases. Lurking variables are also classified according to their source. An operational confound, for instance, occurs in both experimental and non-experimental study designs. This factor occurs when a device or a model designed to measure a specific construct unintentionally measures other factor(s). Procedural lurking variables are associated with situational characteristics. In other words, the factors appear when a researcher mistakenly allows a change in another variable while manipulating an independent variable. Inter-individual differences may also be forms of lurking variables. In the example, the existing lurking variable(s) could be situational lurking variable(s). May be within the two weeks, the coach accidentally or mistakenly changed or improved practice methods the players. Apart from unknowingly improving practice techniques, may be the coach motivated his players within the two weeks, resulting to overall performance increase. However, if during the two weeks the coach and the players practiced as before, computation of correlation coefficients can be used to determine cause of the improved performance. The coefficients should be between players’ output and amount vitamin intake and between players’ output and daily running. We, therefore, need to explore the concept of correlation coefficient. Meaning and Computation of Correlation Coefficient Correlation coefficient is a measure of linear dependence between any two variables. The coefficient takes values between +1 and -1, with boundaries inclusive. A positive correlation implies that there exists a positive relationship between two variables, such that an increase in one variable causes an increase in the other variable. On the other hand, a negative correlation implies that an inverse relationship exists between two variables. Absence of any linear correlation between any two variables is revealed by a zero coefficient. Interpretation of correlation coefficients depends on the purpose of analysis and quality of a measuring instrument or level. The table below, however, generalizes interpretation of a correlation coefficient; Correlation Positive Negative Strong 0.5 to 1.0 −1.0 to −0.5 Medium 0.3 to 0.5 −0.5 to −0.3 Small 0.1 to 0.3 −0.3 to −0.1 None 0.0 to 0.09 −0.09 to 0.0 Existence of a correlation coefficient, irrespective of the sign, indicates that there is a linear dependence between the two variables in question. A linear equation connecting two variables, say X and Y, is given by; Y = α + βX + ε Where, α is a constant β is a constant that specifically determines existence of linear dependence ε is an error term Statistical inferences about correlation coefficient involves testing a null hypothesis that β is zero. Accepting the null hypothesis implies that the two variables, X and Y are linearly independent. Also, correlation tests are important in constructing confidence intervals for correlation coefficients. Correlation coefficient (r), α, and β are computed using the formulas below: r = Correlation Coefficient in the Example In the example, performance of the players is the dependent variable, while either distance ran or vitamin intake is the independent variable. Now, assuming all factors or conditions remain the same as they were before the two study weeks, except in the two independent variables, we denote the dependent variable by Y and independent variable by X. To determine whether daily running or vitamin intake is a cause of increased performance in players, two correlation coefficients are computed as mentioned before. Decision is then made based on the size of the coefficients. If the coefficient between running and performance of players is bigger than the coefficient between vitamin intake and performance, it implies that daily running is a possible cause of improved performance of players and vice versa. Strength of the correlation is determined using the table above. Advice to the Coach The coach can reduce effects of lurking variables using three different ways. As one method, the coach can increase the number and types of comparisons in his analysis. That is, the coach should not limit his independent variables to only vitamin intake and daily running. By considering other factors that possibly increase performance of the players, the coach will certainly know whether the improvement is attributed to running of vitamin intake. Lurking variables are unlikely to occur in multiple analysis or studies of different types. The coach can also ensure that environmental factors remain uniform during the test period. Environmental variations are, according to Starnes et al. (p. 61), possible sources of lurking variables. The coach should, therefore, determine if there is any environmental change in the training and playing site before and during the two study weeks. As a third method, the coach should explore the type of relationship between environmental variables and studied parameters. Possible study factors, which are used in evaluating performance of players, include: completeness of passes, goals scored, and ball possession among others. Apart from the three methods of decreasing effect of lurking variables, the coach can also do double blinding. This method requires the coach not to inform his players about why he includes daily running and vitamin intake. The players will, thus, run daily and take vitamins blindly. Alternatively, double blinding can involve blocking effect of one variable while varying the other. For instance, the coach can study effects of daily running while withholding vitamin intake and vice versa. Conclusion In sum, lurking variables, in any study or analysis, are hidden factors that affect both dependent and independent variables. Lurking variables make two or more variables appear as if they are correlated. Depending on design of a study or type measurements a study does, various types of lurking variables exist. Effect of lurking variables is controlled by increasing the number of statistical analysis or type of measurements in a study. Understanding environmental factors influencing outcome of a study is also an important step in preventing effects of lurking variables. In the example, the coach can determine whether daily running or vitamin intake improves performance of players by computing separate correlation coefficients. Alternatively, the coach can determine effects of the two factors by studying one variable at a time. However, in either way, the coach must ensure that similar environmental conditions exist. Works Cited Brase, C. Henry and Brase, C. Pellillo. Understanding Basic Statistics. 5th Edition. Brooks Cole Press, 2008. Gupta, S. K. Statistical Methods. New Delhi: Sultan Chand & Sons Publishers,1989. Peck, Roxy et al. Introduction to Statistics and Data Analysis. 4th Edition. Brooks Cole Press, 2011. Starnes, S. Daren et al. The Practice of Statistics. 4th Edition. W. H. Freeman Press, 2010. Read More