Design-led companies (Apple, Google, Airbnb, etc.) frequently apply design thinking to design new products (Naiman 2020). A/B testing (also known as split testing or bucket testing) is “a method of comparing two versions of a webpage or app against each other to determine which one performs better.” (Optimizly, 2019).
Some people get randomly assigned to group A, some others to group B. Each group is exposed to a different treatment of some underlying variable. This variable could be the discount amount, ad copy, etc. This underlying variable is what gets “manipulated.” Marketing researchers or data scientists then observe some outcome(s) that might be affected by the manipulated variables. We then create a dummy variable for the treatment group and for the control group. ## To evaluate the effect of the 2 different treatments of (A and B), we run the following regression: Y = β0 + β1*XA + ϵ
The coefficient β1 can be interpreted as the additional effect that treatment A has on the outcome variable compared to treatment B. β0 can be interpreted as the average outcome, or the predicted value of Y, for treatment group B. Usually, if one of the treatments is considered a “control” group, the control group would be used as the baseline in the regression. i.e. the group that is left out and absorbed into the intercept β0. In the regression model above, this would be group since is an indicator for whether treatment was applied.
Dummy coding is required for performing experimental research. Since we have dummy variables (i.e., a control/placebo group and a treatment group) in our model, the intercept has more meaning. Dummy coded variables have values of 0 for the reference/control/placebo group and 1 for the comparison/treatment group. Since the intercept is the expected mean value when X=0, it is the mean value only for the reference group (when all other X=0). Dummy coding a way to make the categorical variable into a series of dichotomous variables (variables that can have a value of zero or one only). For more details, please see the UCLA statistics site for more details (available at https://stats.idre.ucla.edu/spss/faq/coding-systems-for-categorical-variables-in-regression-analysis/).
It is suggested that “the effect of advertising appears non-linear, with an optimum between two and three exposures per week (Tellis, 1987).” For our example on the relationship between advertising exposures and product purchase below, we will be testing the relationship between advertising and product purchase using regression analysis. Our null hypothesis (usually denoted as H0) is that there is no relationship between advertising exposures and product purchases using regression analysis. The alternative hypothesis (usually denoted as H1) is that there is a relationship between advertising exposures and product purchases. The hypothesis test can be represented by the following notation:
Null Hypothesis: H0: β1 = 0 Alternative Hypothesis: H1: β1 ≠ 0
First, we will be creating a new variable that has a value of one for each observation at that level and zeroes for all others. In our example using the variable (Ads), the first new variable (Ads1) will have a value of one for each observation in which the consumers are exposed to the 1st ads campaign and zero for all other observations. Likewise, we create Ads2 when the consumers are exposed to the 1st ads campaign, and 0 otherwise, and Ads3 is 1 when the consumers are exposed to the 3rd ads campaign, and 0 otherwise. The level of the categorical variable that is coded as zero in the new variables is the reference level or the level to which all of the other levels are compared. In our example, it is the reference level Ads0. Our objective is to see which ads campaign leads to more product sales.
#setwd("C:/Users/zxu3/Documents/R/abtesting")
#Please install the following package if the package "readr" is not installed.
#install.packages("readr")
library(readr)
data <- read_csv("abtesting.csv")## Rows: 38 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (2): Ads, Purchase
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.ls(data) # list the variables in the dataset## [1] "Ads" "Purchase"head(data) #list the first 6 rows of the dataset## # A tibble: 6 × 2
## Ads Purchase
## <dbl> <dbl>
## 1 1 113
## 2 0 83
## 3 0 52
## 4 1 119
## 5 1 188
## 6 0 99# creating the factor variable
data$Ads <- factor(data$Ads)
is.factor(data$Ads)## [1] TRUE# showing the first 15 rows of the variable "Ads"
data$Ads[1:15]## [1] 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0
## Levels: 0 1#now we do the regression analysis and examine the results
summary(lm(Purchase~Ads, data = data))##
## Call:
## lm(formula = Purchase ~ Ads, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -57.000 -23.250 3.071 22.643 51.000
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 95.429 6.441 14.816 < 2e-16 ***
## Ads1 41.571 9.630 4.317 0.000118 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.52 on 36 degrees of freedom
## Multiple R-squared: 0.3411, Adjusted R-squared: 0.3228
## F-statistic: 18.64 on 1 and 36 DF, p-value: 0.0001184Since the p-value for X is .00018, which is less than .05, we reject the null hypothesis in favor of the alternative hypothesis.
The coefficient for Ads1 in the regression output is 41.57, which indicates that the 1st Advertising campaign is more effective (relative to the group who did not receive any advertising exposure).
Now the estimates for β0 and β1 are 95.43 and 41.57, respectively, leading to a prediction of average sales of 95.43 for the control group (group A) and a prediction of average sales which is 95.43 + 41.57*1 = 137 for the treatment group or the group of consumers who were exposed to the advertising campaign.
You will also find exactly the same coefficients using the Regression Data Analysis Tool in Excel. However, Excel also can’t handle large datasets (hundreds of thousands of records (Gapintelligence, 2020). Additionally, if you would like to perform the analysis and document the whole process (e.g., objectives, methods, hypotheses, results, and discussions), then using Rstudio with RMarkdown is probably one of the best choices.
Reference: Understanding R programming over Excel for Data Analysis https://www.gapintelligence.com/blog/understanding-r-programming-over-excel-for-data-analysis/
note: You can also perform this analysis using Excel We would like to see which campaign lead to more product sales in 2 different ways below.
#now we do an analysis for a predictor with 4 different levels
display <- read_csv("ab_testing.csv")## Rows: 80 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (2): Ads, Purchase
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.ls(display) # list the variables in the dataset## [1] "Ads" "Purchase"head(display)## # A tibble: 6 × 2
## Ads Purchase
## <dbl> <dbl>
## 1 1 152
## 2 0 21
## 3 3 77
## 4 0 65
## 5 1 183
## 6 1 87# creating the factor variable
display$Ads <- factor(display$Ads)
is.factor(display$Ads)## [1] TRUE# showing the first 15 rows of the variable "Ads"
display$Ads[1:15]## [1] 1 0 3 0 1 1 2 2 2 0 3 3 0 2 3
## Levels: 0 1 2 3#now we do a regression analysis for a predictor with 4 different levels
summary(lm(Purchase~Ads, data = display))##
## Call:
## lm(formula = Purchase ~ Ads, data = display)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50.095 -27.891 -0.227 24.773 65.905
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.381 6.472 8.557 9.41e-13 ***
## Ads1 75.714 9.152 8.273 3.31e-12 ***
## Ads2 36.557 9.842 3.715 0.000386 ***
## Ads3 -2.654 9.048 -0.293 0.770096
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.66 on 76 degrees of freedom
## Multiple R-squared: 0.5624, Adjusted R-squared: 0.5452
## F-statistic: 32.56 on 3 and 76 DF, p-value: 1.216e-13#Alternatively, you can also use the factor function within the lm function, saving the step of creating the factor variable first.
summary(lm(Purchase~ factor(Ads), data = display))##
## Call:
## lm(formula = Purchase ~ factor(Ads), data = display)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50.095 -27.891 -0.227 24.773 65.905
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.381 6.472 8.557 9.41e-13 ***
## factor(Ads)1 75.714 9.152 8.273 3.31e-12 ***
## factor(Ads)2 36.557 9.842 3.715 0.000386 ***
## factor(Ads)3 -2.654 9.048 -0.293 0.770096
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.66 on 76 degrees of freedom
## Multiple R-squared: 0.5624, Adjusted R-squared: 0.5452
## F-statistic: 32.56 on 3 and 76 DF, p-value: 1.216e-13The regression model shows that there is a statistically significant relationship between the different advertising campaigns and the number of product purchases. The overall model is significant, with an F-statistic of 32.56 and a p-value of 1.216e-13, indicating that the model fits the data well.
The results indicate that Ads1 and Ads2 are both significant predictors of product purchases, with estimated coefficients of 75.714 and 36.557, respectively. The coefficient for Ads1 is higher than that of Ads2, suggesting that it may be a more effective advertising campaign. The coefficient for Ads3 is not statistically significant, meaning that this advertising campaign is not a significant predictor of product purchases.
The Adjusted R-squared value of 0.5452 suggests that the model explains around 54.5% of the variability in the data, leaving about 45.5% unexplained.
As a marketing implication, the company can use this information to focus on Ads1 and Ads2 as the most effective advertising campaigns for driving product purchases. They may consider investing more resources in these campaigns or adjusting their strategies to optimize their impact. Meanwhile, they may want to re-evaluate the effectiveness of Ads3 or allocate fewer resources to it.
Yes, Example 2.1 and Example 2.2 gave the same results. Both methods resulted in the same coefficient estimates, standard errors, t-values, and p-values.
I prefer Example 2.2 because it saves a step in creating the factor variable, and it is more concise. Using the factor() function within the lm() function avoids the need to create a separate factor variable before running the regression. This makes the code more streamlined and easier to read.
Reference: Understanding R programming over Excel for Data Analysis https://www.gapintelligence.com/blog/understanding-r-programming-over-excel-for-data-analysis/
5 reasons why R programming can add value to your career are: R can handle very large datasets that Excel cannot contain. Excel has a limit to the number of rows and columns that it can handle, whereas R can handle large datasets and run efficiently while doing so. R can automate and calculate much faster than Excel, and does not crash like Excel when handling a large amount of data. This is due to the fact that R can handle huge datasets and still run efficiently while doing so. R source code is reproducible, which means that research conducted using R can be used repeatedly with different datasets. This is because R source codes can be applied to any dataset with only a few changes to code and reference data that can then be reapplied several times over very easily. R has a community of users who contribute to the available packages and libraries, which creates a community of R users who are extending their knowledge easily to other R users who may require a similar solution to their data. R provides more complex and advanced data visualization than Excel, which can take very complicated data and turn it into much easier to understand visual representation. R can provide advanced data visualization for more complex datasets.Additionally, R is free, which is a bonus point in favor of learning R.
The success of companies like Apple, Pepsi, IBM, Nike, Procter & Gamble, and SAP has been attributed to their design-led approach. According to the 2015 Design Value Index, such companies have outperformed the S&P 500 by an incredible 211%. Design thinking has played a critical role in such successes by providing a framework for addressing complex, human-centred challenges and making the best possible decisions regarding organizational change, innovation, and value creation. Design thinking helps to minimize risk, reduce costs, and improve customer experiences while energizing employees. It provides a way for companies to become customer-centric, rather than product or marketing-focused, and to find ideal solutions based on the real needs of real people. https://www.creativityatwork.com/design-thinking-strategy-for-innovation/
A/B Testing: Test Your Own Hypotheses & Prepare to be Wrong - Stuart Frisby
https://www.youtube.com/watch?v=VQpQ0YHSfqM&t=189s
Naiman 2020. Design Thinking as a Strategy for Innovation. https://www.creativityatwork.com/design-thinking-strategy-for-innovation/
Tellis 1987. Marketing Science. https://www.msi.org/reports/advertising-exposure-loyalty-and-brand-purchase-a-two-stage-model-of-choice/
https://stats.idre.ucla.edu/r/modules/coding-for-categorical-variables-in-regression-models/
Create an A/B test, https://support.google.com/optimize/answer/6211930?hl=en Experiments at Airbnb,https://medium.com/airbnb-engineering/experiments-at-airbnb-e2db3abf39e7
Your Step-by-Step Guide to A/B Testing with Google Optimize, https://www.crazyegg.com/blog/ab-testing-google-analytics/
https://firebase.google.com/products/ab-testing
https://www.sitepoint.com/perform-ab-testing-google-optimize/
https://marketingplatform.google.com/about/optimize/features/