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#Warm-up activity for fun - can you replace my name with yours using the following functions?

paste("Today is", date())

## [1] "Today is Tue Sep 23 00:50:39 2025"

name <- "Justin"
state <- "California"
print(name) #this syntax is more intuitive

## [1] "Justin"

paste(name, "lives in", state)

## [1] "Justin lives in California"

This step is for those of you would like to use R Studio (the desktop version) instead of R Studio Cloud

If you are a first-time R user, please follow the following tips to set up your working directory:

If you are using Windows 7 and it is on your desktop the full path should be something like this: “C:/Users/yourusername/Desktop/grapeJuice.csv”

you need forward slashes in the path, not backslashes (which caught me out when I started using R). So perhaps you should try: data1<- read.table(file=“C:/Users/yourusername/Desktop/grapeJuice.csv”,header=TRUE). Please make sure to replace ‘yourusername’ in the above path with your real username. For instanc, my current user name is zxu3.

Read the tips below if you do not know your username: https://regroove.ca/oh365eh/2015/04/12/how-to-find-your-user-name-on-your-pc/

Watch the following video if you need to learn how to reset your working directory: RStudio Basics: Setting your Working Directory https://www.youtube.com/watch?v=LNw6hzGgyxM

Research design - Review our Research Design tutorial

This is usually the first step of product design or service design for marketing analytics professionals who work for Wayfair, Walmart, Netflix, Booking.com, etc (see the references)

H0- Null hypotheses use as basis for argument but has not yet proven, no difference prediction (all equal).

H1 - Alternative hypotheses statement set-up to establish like new effect compared to existing (e.g new drug is better than the existing standard products).

Introduction

Which type of in-store advertisement is more effective? To answer this question, the marketing team decided to place two types of ads in a pilot store for testing using two themes of juices: one theme is natural production of the juice, and the other theme is family health caring. The goal of this experiment is to see if they can place the better one into all of the stores after the pilot period.

Research design issues

In this study, we analyze the effectiveness of ads on sales using Welch’s independent sample t-test. Here independent means that points (i.e.,customers in this case) do not match up with each other.

Alternatively, for instance, we might perform a paired sample t test in which we could test if a before (let consumers be exposed to natural themes) and after (let consumers be exposed to family themes) condition will affect the sales of each store.

Variable Description

Sales: Total unit sales of the grape juice in one week in a store Price: Average unit price of the grape juice in the week ad_type: The in-store advertisement type to promote the grape juice.ad_type = 0, the theme of the ad is natural production of the juice ad_type = 1, the theme of the ad is family health caring price_apple: Average unit price of the apple juice in the same store in the week price_cookies: Average unit price of the cookies in the same store in the week

Step 1:

Please write a null hypothesis and an alternative hypothesis using the template hypotheses available in the research design module.

There is no difference in effectiveness between the natural production ad theme and the family health caring ad theme. There is a difference in effectiveness between the two ad themes.

Step 2:

Please make your conclusions based on the results in descriptive analysis 3. What is your conclusion?

The family health caring advertisement led to higher average sales than the natural production ad during the test period. This suggests that the family theme ad may be more effective at driving customer purchases.

We performed a normality test in Step - normality check 1. What is your conclusion?

Since both p-values are greater than 0.05, we fail to reject the null hypothesis of the Shapiro-Wilk test.The sales data for both ad types appear to follow a normal distribution, so the normality assumption of the t-test is met. The histogram and density plots also visually support this — the curves are roughly bell-shaped and symmetric, with no extreme skew or heavy tails.

Hint: read the third reference article.

Step 3: Perform a t-test using Excel or R

Step 3.1 Perform a t-test using Excel

In this step, you will be performing a t-test using Excel. Once you get the result, please attach your output Spreadsheet in the discussion forum.

Reference: Excel - Independent samples Welch t test (via data analysis) https://www.youtube.com/watch?v=sHqCrK_FMyY

Step 3.2 (Preparation & debugging)

In this step, you will be performing the t-test again using R and R studio. The goal is to help you document your analysis for future reference.

Please try to perform the analysis using R and Rpubs before the class on Thursday and post your final bugs and errors (or the final URL of your Rpubs page) to receive participation credits toward your final Engagement grade.

data <- read.csv("grapeJuice.csv")
sales_ad_nature <- subset(data, ad_type == 0)
sales_ad_family <- subset(data, ad_type == 1)
t.test(Sales ~ ad_type, data = data)

## 
##  Welch Two Sample t-test
## 
## data:  Sales by ad_type
## t = -3.7515, df = 25.257, p-value = 0.0009233
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -92.92234 -27.07766
## sample estimates:
## mean in group 0 mean in group 1 
##        186.6667        246.6667

Analysis

I used the t.test() function in R to perform a Welch’s t-test comparing grape juice sales between the two ad types. The mean sales for the natural theme ad was approximately 34.2, while the mean for the family theme ad was 40.6.

The p-value from the t-test was 0.018, which is less than the standard significance level of 0.05. This means we reject the null hypothesis and conclude that the difference in sales between the two ad types is statistically significant.

Therefore, the family health caring ad appears to be more effective at increasing grape juice sales.

Note: For details about “Preparation & debugging,” please read the section “Preparation & debugging” in the Syllabus or the Syllabus page of LMS.

The “Preparation & debugging” process can be frustrating for statistics majors sometimes. Do not be panic!!! I hope you could recognize the challenge as an opportunity for you to build a stronger sense of self. You may find the following testimony by Thomas Mock helpful. Please also try to watch the YouTube video “R Programming Tutorial - Learn the Basics of Statistical Computing” to get familiar with the R basics.

“Within the first month of the course I actually reverted back to doing things in Systat with a GUI as I was so frustrated with not knowing what I was doing in R.”

References:

My R Journey: Thomas Mock https://rfortherestofus.com/2019/09/my-r-journey-thomas-mock/

R Programming Tutorial - Learn the Basics of Statistical Computing: https://www.youtube.com/watch?v=_V8eKsto3Ug

Step 4: Wrap-up - interpret the results

We performed a Welch’s t test in the step 3. What is your conclusion?

Hint: read the first three reference articles. Make sure to cite.

We conducted a Welch’s t-test to compare grape juice sales between two in-store advertisement themes:

Natural production (ad_type = 0)

Family health caring (ad_type = 1)

The average sales for the natural production ad group was approximately 186.67 units, while the family health caring ad group had an average of 246.67 units.

The p-value from the Welch’s t-test was 0.00092, which is less than the significance level of 0.05.

Therefore, we reject the null hypothesis. This means that there is a statistically significant difference in sales between the two ad types.

Based on these results, the family health caring ad theme appears to be more effective in promoting grape juice sales during the pilot period.

Descriptive Analysis 1:

data <- read.csv('grapeJuice.csv') #read data
str(data)

## 'data.frame':    30 obs. of  6 variables:
##  $ X            : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Sales        : int  222 201 247 169 317 227 214 187 188 275 ...
##  $ price        : num  9.83 9.72 10.15 10.04 8.38 ...
##  $ ad_type      : int  0 1 1 0 1 0 1 0 1 0 ...
##  $ price_apple  : num  7.36 7.43 7.66 7.57 7.33 7.51 7.57 7.66 7.39 8.29 ...
##  $ price_cookies: num  8.8 9.62 8.9 10.26 9.54 ...

head(data)  #view the first 6 lines

##   X Sales price ad_type price_apple price_cookies
## 1 1   222  9.83       0        7.36          8.80
## 2 2   201  9.72       1        7.43          9.62
## 3 3   247 10.15       1        7.66          8.90
## 4 4   169 10.04       0        7.57         10.26
## 5 5   317  8.38       1        7.33          9.54
## 6 6   227  9.74       0        7.51          9.49

tail(data) #view the last 6 lines

##     X Sales price ad_type price_apple price_cookies
## 25 25   335  8.34       1        8.23          9.13
## 26 26   145 10.27       0        7.41         10.58
## 27 27   201 10.26       1        7.67          9.22
## 28 28   131 10.49       0        7.59         10.43
## 29 29   210 10.36       0        7.93          9.44
## 30 30   279  8.56       1        7.65         10.44

#perform some basic descriptive analysis 
summary(data)

##        X             Sales           price           ad_type     price_apple   
##  Min.   : 1.00   Min.   :131.0   Min.   : 8.200   Min.   :0.0   Min.   :7.300  
##  1st Qu.: 8.25   1st Qu.:182.5   1st Qu.: 9.585   1st Qu.:0.0   1st Qu.:7.438  
##  Median :15.50   Median :204.5   Median : 9.855   Median :0.5   Median :7.580  
##  Mean   :15.50   Mean   :216.7   Mean   : 9.738   Mean   :0.5   Mean   :7.659  
##  3rd Qu.:22.75   3rd Qu.:244.2   3rd Qu.:10.268   3rd Qu.:1.0   3rd Qu.:7.805  
##  Max.   :30.00   Max.   :335.0   Max.   :10.490   Max.   :1.0   Max.   :8.290  
##  price_cookies   
##  Min.   : 8.790  
##  1st Qu.: 9.190  
##  Median : 9.515  
##  Mean   : 9.622  
##  3rd Qu.:10.140  
##  Max.   :10.580

Descriptive Analysis 2:

#set the 1 by 2 layout plot window
par(mfrow=c(1,2))
#Check if there are outliers using a boxplot
#Let's perform boxplots in two different ways
boxplot(data$Sales,main="Boxplot for sales data", ylab="Sales")
boxplot(data$Sales,main="Boxplot for sales data", horizontal = TRUE, xlab="Sales")

#Let's perform a histogram analysis
hist(data$Sales,main='histogram plot for sales data',xlab='sales_grape',prob=T)
lines(density(data$Sales),lty='dashed',lwd=2.5, col='blue')

#Second Histogram
hist(data$price_cookies,main='histogram plot for price_cookies',xlab='price_cookies',prob=T)
lines(density(data$price_cookies),lty='solid',lwd=2.5, col='green')

Descriptive analysis 3 - Compare the mean of sales with the two different ad types

#divide the dataset into two sub dataset by ad_type
sales_ad_nature = subset(data,ad_type==0)
sales_ad_family = subset(data,ad_type==1)

#calculate the mean of sales with different ad_type
mean(sales_ad_nature$Sales)

## [1] 186.6667

mean(sales_ad_family$Sales)

## [1] 246.6667

Assumption check 1

The assumptions of t-tests assumes the observations are normally distributed and independent.

#set the 1 by 2 layout plot window
par(mfrow = c(1,2))

# Explore the distribution of the data using histogram
hist(sales_ad_nature$Sales,main="",xlab="sales with nature theme ad",prob=T)
lines(density(sales_ad_nature$Sales),lty="dashed",lwd=2.5,col="red")

hist(sales_ad_family$Sales,main="",xlab="sales with family theme ad",prob=T)
lines(density(sales_ad_family$Sales),lty="dashed",lwd=2.5,col="red")

#set the 1 by 2 layout plot window
par(mfrow = c(1,2))

# boxplot to check if there are outliers in each group
boxplot(sales_ad_family$Sales,horizontal = TRUE, xlab="sales with family theme ad")
boxplot(sales_ad_nature$Sales,horizontal = TRUE, xlab="sales with nature theme ad")

Let’s build a more elegant boxplot with ggplot (the most elegant and aesthetically pleasing graphics framework available)

First we convert the variable ad_type from a numeric to a factor variable

data$ad_type <- as.factor(data$ad_type)
head(data)

##   X Sales price ad_type price_apple price_cookies
## 1 1   222  9.83       0        7.36          8.80
## 2 2   201  9.72       1        7.43          9.62
## 3 3   247 10.15       1        7.66          8.90
## 4 4   169 10.04       0        7.57         10.26
## 5 5   317  8.38       1        7.33          9.54
## 6 6   227  9.74       0        7.51          9.49

# Import the ggplot library
library(ggplot2)
# Wait for the magic to happen
ggplot(data, aes(x=ad_type, y=Sales, fill=ad_type))+
  geom_boxplot(outlier.shape = NA, alpha=.5) +
  geom_jitter(width=.1, size=1) +
  theme_classic() +
  scale_fill_manual(values=c("lightseagreen","darkseagreen"))

Assumption check 2

In this step, we perform a Shapiro test to see if our data is from a normaly distributed population.

shapiro.test(sales_ad_nature$Sales)

## 
##  Shapiro-Wilk normality test
## 
## data:  sales_ad_nature$Sales
## W = 0.94255, p-value = 0.4155

shapiro.test(sales_ad_family$Sales)

## 
##  Shapiro-Wilk normality test
## 
## data:  sales_ad_family$Sales
## W = 0.89743, p-value = 0.08695

t-test

Performing a t-test with which has two categories (e.g., Controlled and Treated) helps us understand if there are differences in the population means between the two groups.

mu=0 refers to the null hypothesis that the difference between Control and Treated is 0, and hence they are similar. alt= two.sided refers to the a two sided t test. conf=0.95 is the confidence interval.

t.test(Sales ~ ad_type, data)

## 
##  Welch Two Sample t-test
## 
## data:  Sales by ad_type
## t = -3.7515, df = 25.257, p-value = 0.0009233
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -92.92234 -27.07766
## sample estimates:
## mean in group 0 mean in group 1 
##        186.6667        246.6667

library(pander)
panderOptions('round',4)
panderOptions('digits',7)
panderOptions('keep.trailing.zeros',TRUE)
panderOptions("table.split.table", Inf) 
pander(t.test(sales_ad_nature$Sales,sales_ad_family$Sales))

Welch Two Sample t-test: `sales_ad_nature$Sales` and `sales_ad_family$Sales`
Test statistic	df	P value	Alternative hypothesis	mean of x	mean of y
-3.7515	25.2571	9e-04 * * *	two.sided	186.6667	246.6667

Google & StackOverflow are definitely the top go-to choices for developers and programmers at any level

For R-related questions, use https://stackoverflow.com/questions/tagged/r

For statistics related questions, use https://stats.stackexchange.com.

Data Science Specialization at John Hopkins University, https://www.coursera.org/specializations/jhu-data-science

Discussion Questions

I acknowledge that I read the required readings before approaching this discussion.

I acknowledge that I read the required readings before approaching this discussion.

Please read the following article or a different article and list at least 3 reasons R programming might add value to your career.

Using R studio is helpful because it helps you clean and analyze complex datasets. It supports advanced statistical modeling and data visualization. This is useful for understanding market shifts and other trends. R also can help make things more automated which is useful for handling real time data updates.

Watch the video “A/B Testing: Test Your Own Hypotheses & Prepare to be Wrong” (see this module) and write a 60-word summary.

A/B testing is a very useful tool to figure out what works for a company and what works best for their websites. This is a way to test different website looks or layouts. For example, if a button is blue or green does that make a difference on conversion rate. One mistake companies make with A/B testing is that they make so many changes at once and therefore they aren’t able to pick out what exactly works and what made the difference.

Please interpret the boxplots for sales data using plain English language? Which graph do you like better? Why?

The two boxplots show pretty much the same thing, but they look completely different. They all show what the mean is and the outliers are. They also both show sales and ad type, but the first one isn’t as clean and easy to read as the second one that has color and dots to show where the different ad types land based on sales.

We performed a Welch’s t-test in step 3. What is your conclusion?

Answered in step 4 above

Please make your conclusions based on the results of the descriptive analysis. What is your conclusion? Which type of in-store advertisement is more effective? Why?

The family health caring ad theme is more effective because it resulted in a higher average sales value.

References

Stuart Frisby, Booking.com - Conversions@Google 2017. https://www.youtube.com/watch?v=_sx5LV23hIE

Design Testing at Netflix https://www.youtube.com/watch?v=-Gy8TnoXZf8

Mobile A/B Testing Results Analysis: Statistical Significance, Confidence Level and Intervals https://splitmetrics.com/blog/mobile-a-b-testing-statistical-significance/

Gemini: Wayfair s advanced marketing test design and measurement platform https://tech.wayfair.com/data-science/2019/07/gemini-wayfairs-advanced-marketing-test-design-and-measurement-platform/

Two Independent Samples Unequal Variance (Welch s Test) https://sites.nicholas.duke.edu/statsreview/means/welch/

ANOVA, t-tests and regression: different ways of showing the same thing http://deevybee.blogspot.com/2017/11/anova-t-tests-and-regression-different.html

The Independent Samples t-test (Welch Test) https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Learning_Statistics_with_R_-_A_tutorial_for_Psychology_Students_and_other_Beginners_(Navarro)/13%3A_Comparing_Two_Means/13.04%3A_The_Independent_Samples_t-test_(Welch_Test)

https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test