Calculation of measures of association using case control
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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 taking 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.
The odds ratio in this study is used to determine the target group during advertisement of cola drinks. 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 after divided by the likelihood that none will buy after the advertisement.
Data
|
Preference |
Teenagers |
Adults |
Total |
|
Taking Cola |
50 |
80 |
130 |
|
Not taking cola |
80 |
50 |
130 |
|
Total |
130 |
130 |
260 |
Odds of
Exposure(teenagers) =number of cases taking cola =50/80=62.5%
Number of case not taking cola
Odds of
Exposure(Adults) = number of cases taking cola =80/50=160%
Number of case not taking cola
Odds ratio = Odds of exposure (teenagers) =50/80 × 50/80 = 2500/6400 =0.390625=39.0625
Odds of exposure (Adults)
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.
Effect on advertising strategy
The cola company should target the adults when advertising for the cola drink.
Q2. Scatter plot
Introduction
This is a graph of a set of point such as x and y that are plotted to show the relationship between them. It shows how one variable, the y value is affected by the other, the x value. This effect is referred to as the correlation.
The following data was used to draw the scatter plot below
|
X |
Y |
|
3 |
6 |
|
6 |
10 |
|
9 |
15 |
|
12 |
24 |
|
15 |
21 |
|
18 |
20 |
Y values
X values
When x=10 y=18.5
When x=17 y=20
Q3. Relationship between correlation and causation
Introduction
Correlation does not automatically imply causation. Just because two or more events or variable are occur together, have a relationship or are correlated does not necessary imply that one even caused the other. In this case, definition of these term are given then shared with specific hypothetical examples. Correlation refers to a relationship between things, events, statistical values that occur unexpectedly through chance. Causation is the act of causing something to happen. It claims that, two or more variables are tied to each other directly.
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.
Examples
Regarding correlation, a good example is a person who has set to be having meals thrice a day. Breakfast at 7:00 a.m, 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.
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.