Preference
Sarah Elizabeth Bellatti
12/1/2017
STEP 1: Design the experiment
This step is already completed for me.
STEP 2: Collect (or load) 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 1STEP 3: Describe data
We have a data set with 21 rows and 2 columns. The rows represent the subjects of the study (participants) and the columns represent variables. The first variable is preference toward a product (a bottle of pet shampoo with a picture of a collie on the label). Participants used a rating scale from 0 (dislike very much) to 6 (like very much). The second variable is primed. A 0 in this column means that the participant was assigned a non-primed condition. A 1 in this column means that the participant was assigned a primed condition. Primed conditions involved a short word find before indicating preference toward the product. The primed condition word find included 4 words related to pets, whereas the non-primed condition involved a world find with 4 conflicting words. There were 20 subjects in the non-primed group and 22 in the primed group (42 responses total).
STEP 4: Identify the purpose of the study
The purpose of the study is to understand why almost 20% of all table wine brands in the last three years have featured an animal on their labels, when traditional brand research argues that successful logos are those relevant to the product they represent. Thus, the study seeks to confirm/reject one hypothesis that consumers who are “primed” (have thought about the image in an unrelated context) have different preferences from non-primed consumers.
STEP 5: Visualize data
library(ggplot2)
ggplot(data=preference, mapping=aes(x=as.factor(primed), y=preference)) + geom_point()
STEP 6: Interpret the plot
The plot suggests that on a scale of 0 (dislike very much) to 6 (like very much), the primed group’s preference toward the product tended to be higher than the non-primed group’s preference. Most of the primed group answers were between 2.45 to 4.5, while most of the non-primed group answeres hovered between 1.5 to 2.5. This suggests that primed inidivudals have greater preference toward the product. However, there is a lot of variability in the plot and the sample sizes are rather small. Thus, I cannot determine if this trend is due to chance or not. I will conduct a test of significance and analyze a p-value for solid evidence that there is (or isn’t) a slight difference in the preference answers for primed and non-primed groups.
STEP 7: Formulate the null hypothesis
Null hypothesis: The two populations are people primed before exposure to new a product and people who are not primed before exposure to a new product (non-primed). The samples are drawn from these populations. The parameter is mean. The null hypothesis is that the population mean for primed individuals’ preferences is equal to the population mean of non-primed individuals’ preferences. The difference in means is zero.
STEP 8: Identify the alternative hypothesis
Alternative hypothesis: There is a difference in the population means for primed individuals’ preferences v. non-primed individuals’ preferences.
STEP 9: Decide on type of test
Type of test: A t-test will be conducted because we are testing two population means of a quantitative variable.
STEP 10: Choose one sample or two
A two sample test will be conducted, since we have samples for primed preferences and unprimed preferences.
STEP 11: Check assumptions of the test
The major assumption for the t-test is that the data will represent a normal distribution, which has a bell shape. The following plot checks the normality and assumptions of the t test.
gg <- ggplot(data=preference)
gg + geom_qq(mapping=aes(sample=preference, color=as.factor(primed)))
If the data are normal, they will lie on the line. This graphs shows that the data more or less lie on the line, and thus the data are normal.
STEP 12: Decide on a level of significance of the test
The level of significance of the test is 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 2.972727STEP 14: Interpret the p-value
Since the p-value is 0.002666, making it less than the level of significance (0.05), I reject the null hypothesis that the means are equal. I accept the alternative hypothesis that the true difference in means is not equal to 0.
STEP 15: Interpret the confidence interval
The 95 percent confidence interval is -1.577912 -0.357543. Since zero is not in this interval, zero is not a plausible value for the difference in means, so it is not plausible that the means are the same. The result of step 15 is consistent with the result of step 14.
STEP 16: Interpret the sample estimates
I have concluded that the means are not equal, but I really want to know: Do consumers who are “primed” (have thought about the image in an unrelated context) have different preferences from non-primed consumers? Knowing that the means are unequal I can answer this question by looking the sample estimates that state that on average, the non-primed group has a mean of 2.005000, while the primed group has a mean of 2.972727. Thus, the primed group has a higher mean for preference for the product than the non-primed group does. These findings support the conclusions of both step 14 and step 15.
STEP 17: State your conclusion
I have evidence that primed individuals have greater preference for a product than non-primed individuals. Thus, I conclude that priming individuals before exposing them to a product will result in higher preference toward the product.