Step 1: Design the experiment

Traditional brand research argues that successful logos are ones that are highly relevant to the product they represent. However, a market research firm recently reported that nearly 20% of all table wine brands introduced in the last three years featured an animal on the label. Since animals have little to do with the product, why are marketers using this tactic? Some researchers have proposed that consumers who are “primed,” have thought about the image earlier in an unrelated context, process visual information easier and might have different preferences from non-primed consumers.

Taken from Sample.Exam1.pdf written by Professor Carver

Step 2: Collect Data

preference <- read.csv("preference.csv")
preference
##    preference primed
## 1         1.8      0
## 2         0.1      0
## 3         4.0      0
## 4         2.1      0
## 5         2.4      0
## 6         3.4      0
## 7         1.7      0
## 8         2.2      0
## 9         1.9      0
## 10        1.9      0
## 11        0.1      0
## 12        3.3      0
## 13        2.1      0
## 14        2.0      0
## 15        1.4      0
## 16        1.6      0
## 17        2.3      0
## 18        1.8      0
## 19        3.2      0
## 20        0.8      0
## 21        1.7      1
## 22        1.7      1
## 23        4.2      1
## 24        3.0      1
## 25        2.9      1
## 26        3.0      1
## 27        4.0      1
## 28        4.1      1
## 29        2.9      1
## 30        2.9      1
## 31        1.2      1
## 32        4.0      1
## 33        3.0      1
## 34        3.9      1
## 35        3.1      1
## 36        2.5      1
## 37        3.2      1
## 38        4.1      1
## 39        3.9      1
## 40        1.1      1
## 41        1.9      1
## 42        3.1      1

Step 3: Describe the Data

In the preference data set, we have 42 rows and 2 columns. The rows of the preference data set represents the subjects of the test (the people seeing whether they like the logos). While the column represents the variables of the study. Overall, the variables represent the ratings the subject gave to the wine logo, and if the subject has been primed or not. The first variable (preference) is the score that each subject gave in the test. The ratings given by the subjects ranges from 0 - 6 with six being the highest score. In other words, whether the subject liked the logo or not. The second column is a variable labeled “primed”, where placing each subject into the group of primed or not primed, with a primed subject being labeled 1 and a not primed one labeled with a 0. There are 22 primed subjects and 20 not primed subjects, with a total of 42 subjects.

Step 4: Purpose of the Study

The purpose of this study is to determine whether a subject being “primed” to an animal logo beforehand makes them like different wine logos more.

Step 5: Visualize data

library(ggplot2)
## Warning: package 'ggplot2' was built under R version 3.4.3
ggplot (data=preference, mapping=aes(x=as.factor(primed), y=preference)) + geom_point()

Step 6: Interpret the plot

According to the plot, we can estimate that most of the subjects who are primed to the animal logo beforehand enjoy the wine logos more than the subjects who aren’t primed to an animal logo beforehand.

*Step 7: Formulate the null hypothesis

The null hypothesis of this study is that the mean preference of primed subjects is equal to the mean preference of not primed subjects.

Step 8: Formulate the alternative hypothesis

The alternative hypothesis is that the mean preference of primed subjects is higher than the mean preference of not primed subjects. This means primed subjects prefer wine logos more than not primed subjects.

Step 9: The type of test

We are allowed to choose from two types of tests, proportion tests and T-tests. Since proportion tests tests hypotheses about proportions of catergorical variables, the better option is to choose T-test. T-tests tests hypotheses about means of quantitative varaibles.

Step 10: Choose the number of samples

We should use a two sample T-test because we have two samples, the preference of primed and not primed subjects.

Step 11: Check assumptions of the test

With this graph, we can assume that subjects primed to a logo beforehand prefer the logos more

ggplot(data=preference) + geom_qq(mapping=aes(sample=preference, color=primed))

Step 12: Decide on a level of significance of the test

It is always safe to use the traditional level of significance of 0.05

Step 13: Perform the test

t.test(formula=preference~primed, data=preference)
## 
##  Welch Two Sample t-test
## 
## data:  preference by primed
## t = -3.2072, df = 39.282, p-value = 0.002666
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.577912 -0.357543
## sample estimates:
## mean in group 0 mean in group 1 
##        2.005000        2.972727

Step 14: Interpret the P-Value

The P-value of the test is 0.002666, since this is lower than our level of significance of 0.05, we reject our null hypothesis.

Step 15: Interpret the confidence interval

The 95% confidence interval is between -1.577912 to -0.357543. Since the 95% confidence interval does not mention the number 0, 0 is not a possible difference in the means. This suggests that there IS a difference in the means, which in turn suggests that the null hypothesis is false.

Step 16: Interpret the sample estimates

According to the sample estimates, the mean of preferences for not primed subjects (2.005000) is not as high as the mean of preferences for primed subjects (2.972727)

Step 17: State your conclusion

It is clear that primed subjects prefer logos more than a not primed subject.