Measures of Association, Scatter plot and Relationship between Correlation and Causation

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Q1. Measures of association

Introduction

Calculation of measures of association using case control involves odds ratio. In this case study, a research team conducted a survey on soft-drink preferences in a market. The sample comprised of 260 participants where 130 were teenagers and the rest adults. The research findings showed that 50 teenagers took Cola drink while 130 did not. Teenagers in this study were used as the case while the adults were considered as the controls. The findings showed that 80 adults preferred cola to other soft drinks while 50 did not (Cooper & Schindler, 2014).

The odds ratio in this study is used to determine the target group during advertisement of cola drinks (Cooper & Schindler, 2014). The odds ratio has been used to compare the odds of exposure of advertisement to the factor of interest among teenagers to the odds of exposure of advertisement to the adults. The term odds in this analysis refers to the likelihood that the target group will buy the cola drink divided by the likelihood that none will buy after the advertisement (Sean, 2012).   

Data

Odds of Exposure (teenagers) =number of cases taking cola/ Number of case not taking cola                    

=50/80=62.5%

Odds of Exposure (Adults) = number of cases taking cola/ Number of case not taking cola             

 =80/50=160%

Odds ratio  = Odds of exposure (teenagers)/ Odds of exposure (Adults) 

 =50/80 × 50/80

 = 2500/6400

=0.390625=39.0625

Conclusion

The odds ratio is less than 1.0 meaning the odds of exposure of advertisement among teenagers are lower than the odds of exposure of advertisement among adults (Sean, 2012).

Effect on advertising strategy

The cola company should target the adults more when advertising for the cola drink.

Q2. Scatter plot

Introduction

This is a graph of a set of points such as x and y that are plotted to show their relationship. It shows how one variable, the y value, is affected the x value. This effect is referred to as the correlation (Mack, 2014). The correlation manifests itself by non-random structure in the graph. The Y values take the vertical-axis while the x-values take the horizontal-axis. The technique in drawing the scatter plot below used both spreadsheet and statistical software program (Mack, 2014).

The scatter plot

The following data was used to draw the scatter plot below

                                    Y values

                                                                                           X values

The least-squares line

This method gives the line that gives the summary of the correlation between two variables. For instance, given x and y variables (Heath & Mantange, 2011).

Formula

Y= a+bx

Where

b= r (SDY/ SDX)       

A= Ȳ-b X̄

Where

Where,

b = the slope of the regression line

a = the intercept point of the regression line and the y-axis.

X̄ = Mean of x values

Ȳ = Mean of y values

SDx = Standard Deviation of x

SDy = Standard Deviation of y

r = (NΣxy - ΣxΣy) / sqrt ((NΣx² - (Σx)²) x (NΣy)² - (Σy)²)

The number of X values=N=6

Substitute the above values in the slope formula, Slope (b) = (NΣXY - (ΣX)(ΣY)) / (NΣX² - (ΣX)²)

= (6*1176-63*96)/ (6*819-63*63)

=7056-6048/4914-3969

=1008/945

=1.06666667

This value substituted in the intercept formula

Intercept (a) = (ΣY – b (ΣX)) / N

= (1176-(1.06666667*63))/ 6

= (1176-67.2000002)/ 6

=1108.8/6

=184.8

When the values of a and b are substituted in the equation

Y=a+bx

=184.8+1.06666667x

When x=10, Y= 184.8+1.06666667*10 = 184.8+10.6666667 = 195.466667

When X= 17, Y = 184.8+1.06666667*17 = 184.8+18.1333334 = 202.933333

Conclusion

                   A scatter plot is an important tool to diagnose if a relationship exists. However, the plot is not a conclusive way of determining existence of cause-effect-relationship. Only the researcher can prove the cause-effect-mechanism using the underlying science (Heath & Mantange, 2011).

Q3.  Relationship between correlation and causation

Introduction

Correlation does not automatically imply causation. Just because two or more events or variables occur together, have a relationship or are correlated does not necessary imply that one event caused the other. In this case, definition of this term are given then shared with specific hypothetical examples (Cheryl & Kutner, 2008).

Correlation and causation

Correlation refers to a relationship between things, events or statistical values that occur unexpectedly through chance. Causation is the act of causing something to happen and claims that, two or more variables are tied to each other directly (Anderson, Bergen & Grimes, 2008).

Examples

Regarding correlation, a good example is a person who has set to be having meals thrice a day, Breakfast at 7:00 am, lunch meal at 1:00 pm and super at 6:30 pm through the year. Chances are there are many times when the sun will be setting at the same time when this person is having super. Observation on the eating trend of this individual is likely to lead the observer concluding that the person is classically conditioned to be hungry whenever he notices the sun setting as with the Pavlov’s dog. This would tempt the observer to conclude that the sunset causes hunger for this individual. This is obviously not true even though sunset and super correlate (Careau & Garland, 2012).

Causation on the other hand can be explained using an example of a man hurriedly walking down the road busy texting on phone and suddenly steps on an open ground breaking his leg. Obviously, texting does not cause breaking of the leg although it happens the same time when the man broke his leg. In this case, there is correlation in that stepping on the open ground is the direct cause of breaking the leg (Dochtermann & Roff, 2010).  

Conclusion

Causation is the act of causing something to happen.  It claims that, two or more variables are tied to each other directly (Careau & Garland, 2012).

Correlation does not mean that one variable cause the other to occur but rather events occurring together statistically through random chance. This can be viewed as consistent coincidence of events (Amiram, Donahue-Turner & Psy, 2010).