In doomlab/learnSTATS: Introduction to Statistics (ANLY 500)

library(learnr)
library(learnSTATS)
library(faux)

##simulated data
between <- list(where_bought = c(online = "Online",
                                 store = "Store"),
                who_bought = c(different = "Different", 
                               same = "Same"))
within <- list(rm_var = c("money", "time"))

##pattern is money, then time, so keep the numbers larger in the first one
mu <- data.frame(
  online_different = c(25, 10),
  online_same = c(25, 10),
  store_different = c(35, 15),
  store_same = c(35, 20), 
  row.names = within$rm_var)

more_data <- sim_design(within, between, 
                        n = sample(25:50, 1), 
                        mu = mu, 
                        sd = 3, 
                        r = .10,
                        interactive = FALSE,
                        empirical = FALSE, 
                        plot = FALSE)

knitr::opts_chunk$set(echo = FALSE)

Introduction to More Statistics

In this example, we will begin to build our first statistical models. You will learn how to use apply family of functions to calculate our descriptive statistics. The learning objectives include:

Know what a statistical model is and why we use them
Measures of central tendency, dispersion, frequency distributions
Know what the 'fit' of a model is and why it is important
Distinguish models for samples and populations

Exercises

In this next section, you will answer questions using the R code blocks provided. Be sure to use the solution option to see the answer if you need it!

Please enter your name for submission. If you do not need to submit, just type anything you'd like in this box.

question_text(
  "Student Name:",
  answer("Your Name", correct = TRUE),
  incorrect = "Thanks!",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

Experiment Design

Title: Consumer Pseudo-Showrooming and Omni-Channel Product Placement Strategies

Abstract: Recent advances in information technologies (IT) have powered the merger of online and offline retail channels into one single platform. Modern consumers frequently switch between online and offline channels when they navigate through various stages of the decision journey, motivating multichannel sellers to develop omni-channel strategies that optimize their overall profit. This study examines consumers' cross-channel search behavior of "pseudo-showrooming," or the consumer behavior of inspecting one product at a seller's physical store before buying a related but different product at the same seller’s online store, and investigates how such consumer behavior allows a multichannel seller to achieve better coordination between its online and offline arms through optimal product placement strategies.

Participants in the study were grouped into the following categories:

Where_bought: Where they ended up purchasing an item: bought at the store, bought online.
Who_bought: If they bought from the same or a different retailer.

Each participant was then measured on:

Money: how much money they spent in dollars on the product.
Time: how much time (in minutes) they spent looking at the product online.

question_text(
  "What would be one possible null hypothesis based on this study?",
  answer("Many right answers.", correct = TRUE),
  incorrect = "Hint: remember that your null hypothesis should indicate how the IV relates to the DV AND says that there is NO effect.",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

question_text(
  "What would be one possible alternative hypothesis based on this study?",
  answer("Many right answers.", correct = TRUE),
  incorrect = "Hint: remember that your alternative hypothesis should indicate how the IV relates to the DV AND says that there IS an effect.",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

question_text(
  "Give an example of type 1 error based on this study (do not just define, explain in context how it might have happened here).",
  answer("Many right answers.", correct = TRUE),
  incorrect = "Hint: you could say something like we said there was a difference in time spent based on where they bought the item, but in reality there was no time difference (type 1 = say there is an effect, when there actually is not)",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

question_text(
  "Who are they sampling in this study?",
  answer("Consumers.", correct = TRUE),
  incorrect = "Hint: you could say shoppers, consumers, clients, etc.",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

Build Models

Here's the head() and summary() of our example data:

head(more_data)
summary(more_data)

question_text(
  "For the where bought variable, what are the groups tested?",
  answer("online, store", correct = TRUE),
  incorrect = "Hint: look at the summary output to see the groups examined.",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

Often, groups for each individual variable in a study are called levels. When you combined two variables, you create conditions. For our study, we have four conditions by combining where_bought and who_bought:

Bought online, different retailer
Bought in store, different retailer
Bought online, same retailer
Bought in store, same retailer

We can use the tapply() to calculate the means, standard deviations, and standard errors for each group. The code is started for you below, and you should fill in each comment (#) with the code to get the means for the money dependent variable when where_bought and who_bought variable.

M <- tapply(
  #dependent variable
  list(more_data$where_bought, more_data$who_bought),
  #function name
)

M

M <- tapply(
  more_data$money,
  list(more_data$where_bought, more_data$who_bought),
  mean
)

M

Modify the tapply() code from above to calculate the standard deviation for each condition.

SD <- tapply()

SD

SD <- tapply(
  more_data$money,
  list(more_data$where_bought, more_data$who_bought),
  sd
)

SD

question_text(
  "Which condition appears to have the best model fit using the mean as the model (i.e. smallest error) for money spent?",
  answer("online, same", correct = TRUE),
  incorrect = "Hint: look for the smallest standard deviation to see which model fits best. ",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

Effect Sizes and Confidence Intervals

Use the MOTE library to calculate the effect size for the difference between money spent for store versus online when bought at the same retailer. Your M and SD are printed how to help you figure out how to grab the right numbers. We've also included sample size N like the lecture example to allow you to complete the question.

M <- tapply(more_data$money, 
             list(more_data$where_bought, more_data$who_bought),
             mean)

SD <- tapply(more_data$money, 
             list(more_data$where_bought, more_data$who_bought),
             sd)

M
SD
N <- tapply(more_data$money, 
             list(more_data$where_bought, more_data$who_bought),
             length)
N

For the MOTE library, we need to grab only one value at a time to fill in. By saving M, we can treat it like a small dataframe or matrix. Therefore, M[1,1] is the mean score for bought online at a different retailer. In the code below, fill in the [] with the numbers for store, same retailer as the first mean, sd, and sample size. Then fill in online, same retailer for the second mean, sd, and sample size.

The effect size and confidence intervals will print out once you've filled it in correctly!

M <- tapply(more_data$money, 
             list(more_data$where_bought, more_data$who_bought),
             mean)

SD <- tapply(more_data$money, 
             list(more_data$where_bought, more_data$who_bought),
             sd)

N <- tapply(more_data$money, 
             list(more_data$where_bought, more_data$who_bought),
             length)

library(MOTE)

effect <- d.ind.t(m1 = M[], m2 = M[],
                  sd1 = SD[], sd2 = SD[],
                  n1 = N[], n2 = N[], a = .05)
effect$d

effect$M1low #lower confidence interval
effect$M1 #mean
effect$M1high #upper confidence interval

library(MOTE)

effect <- d.ind.t(m1 = M[2,2], m2 = M[1,2],
                  sd1 = SD[2,2], sd2 = SD[1,2],
                  n1 = N[2,2], n2 = N[1,2], a = .05)
effect$d

effect$M1low #lower confidence interval
effect$M1 #mean
effect$M1high #upper confidence interval

question_text(
  "What can you determine about the effect size in the experiment - is it small, medium or large?",
  answer("large", correct = TRUE),
  incorrect = "Hint: small is .2, medium is .5, and large is .8.",
  try_again_button = "Modify your answer",
  allow_retry = TRUE
)

Submit

On this page, you will create the submission for your instructor (if necessary). Please copy this report and submit using a Word document or paste into the text window of your submission page. Click "Generate Submission" to get your work!