Empirical Project 3 Working in R
Rspecific learning objectives
In addition to the learning objectives for this project, in this section you will learn how to use the piping technique to run a sequence of functions.
Getting started in R
For this project you will need the following packages:
tidyverse
, to help with data manipulationreadxl
, to import an Excel spreadsheetmosaic
, to help create frequency tablesreadstata13
, to read in a Stata datafile.
You will also use the ggplot2
package to produce accurate graphs, but that comes as part of the tidyverse
package.
If you need to install any of these packages, run the following code:
install.packages(c("readxl","tidyverse","mosaic","readstata13"))
You can import these libraries now, or when they are used in the R walkthroughs below.
library(readxl)
library(tidyverse)
library(mosaic)
library(readstata13)
Part 3.1 The treatment group: beforeandafter comparisons of retail prices
We will first look at price data from the treatment group (stores in Berkeley) to see what happened to the price of sugary and nonsugary beverages after the tax.
 Download the data from the Global Food Research Program’s website, and select the ‘Berkeley Store Price Survey’ Excel dataset. Then upload the dataset into R.
 The first tab of the Excel file contains the data dictionary. Make sure you read the data description column carefully, and check that each variable is in the Data tab.
R walkthrough 3.1 Importing the datafile into R
The data is in
.xlsx
format, so we use thereadxl
package to import it. We also load thetidyverse
library as this includes packages that we will use later for piping and graphing. There are two worksheets: one containing some information on the variables (Data Dictionary), and the other containing the data (Data). It is useful to import both into R, so that you have the additional data information available while you are working without having to refer to Excel.library(readxl) library(tidyverse) var_info < read_excel("sps_public.xlsx",sheet="Data Dictionary") dat < read_excel("sps_public.xlsx",sheet="Data")
Let’s look at the datatypes this import process has assigned to the respective variables.
str(dat)
## Classes 'tbl_df', 'tbl' and 'data.frame': 2175 obs. of 12 variables: ## $ store_id : num 16 16 16 16 16 16 16 16 16 16 ... ## $ type : chr "WATER" "TEA" "TEA" "WATER" ... ## $ store_type : num 2 2 2 2 2 2 2 2 2 2 ... ## $ type2 : chr NA NA NA NA ... ## $ size : num 33.8 23 23 33.8 128 64 128 64 63.9 144 ... ## $ price : num 1.69 0.99 0.99 1.69 3.79 2.79 3.79 2.79 4.59 5.99 ... ## $ price_per_oz : num 0.05 0.043 0.043 0.05 0.0296 ... ## $ price_per_oz_c: num 5 4.3 4.3 5 2.96 ... ## $ taxed : num 0 1 1 0 0 0 0 0 0 1 ... ## $ supp : num 0 0 0 0 0 0 0 0 0 1 ... ## $ time : chr "DEC2014" "DEC2014" "DEC2014" "DEC2014" ... ## $ product_id : num 29 32 33 38 40 41 42 43 44 50 ...
All numerical variables are correctly classified as numerical, but there are some variables that may be useful to have as categorical variables (factor variables in R terminology). Specifically,
type
,taxed
,supp
,store_id
,store_type
,type2
andproduct_id
have been expressed as numbers, but are actually categorical (factor) variables. So let’s use thefactor
function to convert them to factor variables.dat$type < factor(dat$type) dat$taxed < factor(dat$taxed, labels=c("not taxed","taxed")) dat$supp < factor(dat$supp,labels=c("Standard","Supplemental")) dat$store_id < factor(dat$store_id) dat$store_type < factor(dat$store_type,labels=c("Large Supermarket", "Small Supermarket", "Pharmacy", "Gas Station")) dat$type2 < factor(dat$type2) dat$product_id < factor(dat$product_id)
We use the
labels
option to specify the names of different categories (where they are clearly defined).There is another variable,
time
, which is characterized as achr
variable (chr
stands for characters, meaning letters and numbers). It may be useful to changetime
into a factor variable. Before we do this, we use theunique
command to check the values this variable takes.unique(dat$time)
## [1] "DEC2014" "JUN2015" "MAR2015"
If you look at the timeline in the Silver et al. (2017) paper, you will notice that the third survey was not in March 2015 but in March 2016, so the data has been labelled incorrectly. We shall therefore change all the values
MAR2015
toMAR2016
.dat$time[dat$time == "MAR2015"] < "MAR2016" # [dat$time == "MAR2015"] selects all observations for which the value of “time” is equal to "MAR2015".
We can now change
time
into a factor variable.dat$time < factor(dat$time)
 Read ‘S1 Text’, from the journal paper’s supporting information, which explains how the Store Price Survey data was collected.
 In your own words, explain how the product information was recorded, and the measures that researchers took to ensure that the data was accurate and representative of the treatment group. What were some of the data collection issues that they encountered?
 Instead of using the name of the store, each store was given a unique ID number (recorded as store_id on the spreadsheet). Verify that the number of stores in the dataset is the same as that stated in the ‘S1 Text’ (26). Similarly, each product was given a unique ID number (product_id). How many different products are in the dataset?
R walkthrough 3.2 Counting the number of unique elements in a variable
We use two functions here:
unique
to reduce a list (dat$store_id
anddat$product_id
) to its unique elements, thenlength
to count how many unique elements we have. We store the number of stores and products in the two variablesno_stores
andno_products
respectively.no_stores < length(unique(dat$store_id)) no_products < length(unique(dat$product_id)) paste("Stores:", no_stores)
## [1] "Stores: 26"
paste("Products:", no_products)
## [1] "Products: 247"
Following the approach described in ‘S1 Text’, we will compare the variable price per ounce in US$ cents (price_per_oz_c
). We will look at what happened to prices in the two treatment groups before the tax (time = DEC2014
) and after the tax (time = JUN2015
):
 treatment group one: large supermarkets (
store_type = 1
)  treatment group two: pharmacies (
store_type = 3
).
We will create frequency tables containing the summary measures that we are interested in.
 Create the following tables:
 A frequency table showing the number (count) of store observations (store type) in December 2014 and June 2015, with ‘store type’ as the row variable and ‘time period’ as the column variable. For each store type, is the number of observations similar in each time period?
 A frequency table showing the number of taxed and nontaxed beverages in December 2014 and June 2015, with ‘store type’ as the row variable and ‘taxed’ as the column variable. (‘Taxed’ equals 1 if the sugar tax applied to that product, and 0 if the tax did not apply). For each store type, is the number of taxed and nontaxed beverages similar?
 A frequency table showing the number of each product type (type), with ‘product type’ as the row variable and ‘time period’ as the column variable. Which product types have the highest number of observations and which have the lowest number of observations? Why might some products have more observations than others?
R walkthrough 3.3 Creating frequency tables
Frequency table for store type and time period
We use the
tally
function, which allows us to produce frequency tables using theformat = "count"
option. We start with the frequency table that shows the number of stores of different types in each time period.library(mosaic) tally(~store_type+time, data=dat, margins = TRUE, format = "count")
## time ## store_type DEC2014 JUN2015 MAR2016 Total ## Large Supermarket 177 209 158 544 ## Small Supermarket 407 391 327 1125 ## Pharmacy 87 102 73 262 ## Gas Station 73 96 75 244 ## Total 744 798 633 2175
There are fewer observations taken from gas stations and pharmacies and more from small supermarkets.
Frequency table for store type and taxed
Now we repeat the steps above to make the frequency table with
store_type
as the row variable andtaxed
as the column variable. Since we also want separate values for each time period, we add+time
to the specification.tally(~store_type+taxed+time, data=dat, margins = TRUE, format = "count")
## , , time = DEC2014 ## ## taxed ## store_type not taxed taxed Total ## Large Supermarket 92 85 177 ## Small Supermarket 196 211 407 ## Pharmacy 44 43 87 ## Gas Station 34 39 73 ## Total 366 378 744 ## ## , , time = JUN2015 ## ## taxed ## store_type not taxed taxed Total ## Large Supermarket 111 98 209 ## Small Supermarket 192 199 391 ## Pharmacy 52 50 102 ## Gas Station 44 52 96 ## Total 399 399 798 ## ## , , time = MAR2016 ## ## taxed ## store_type not taxed taxed Total ## Large Supermarket 88 70 158 ## Small Supermarket 154 173 327 ## Pharmacy 36 37 73 ## Gas Station 31 44 75 ## Total 309 324 633 ## ## , , time = Total ## ## taxed ## store_type not taxed taxed Total ## Large Supermarket 291 253 544 ## Small Supermarket 542 583 1125 ## Pharmacy 132 130 262 ## Gas Station 109 135 244 ## Total 1074 1101 2175
Frequency table for product type and time period
Now we make a frequency table showing the number of each product type (type), with product type (
type
) as the row variable and time period (time
) as the column variable.tally(~type+time, data=dat, margins = TRUE, format = "count")
## time ## type DEC2014 JUN2015 MAR2016 Total ## ENERGY 56 58 49 163 ## ENERGYDIET 49 54 35 138 ## JUICE 70 64 52 186 ## JUICE DRINK 19 17 6 42 ## MILK 63 61 53 177 ## SODA 239 262 215 716 ## SODADIET 128 174 127 429 ## SPORT 11 16 12 39 ## SPORTDIET 2 2 0 4 ## TEA 52 45 41 138 ## TEADIET 6 6 8 20 ## WATER 48 38 34 120 ## WATERSWEET 1 1 1 3 ## Total 744 798 633 2175
This table shows that there were no observations for the category
Sportdiet
in March 2016. As this is a drink which even in the other months has very few observations, it may be a product that is offered only in one shop, and it is possible that this shop was not visited in March 2016. Or the product may be a seasonal product that is not available in March. It is also likely thatWatersweet
is offered in only one shop.
 conditional mean
 An average of a variable, taken over a subgroup of observations that satisfy certain conditions, rather than all observations.
Besides counting the number of observations in a particular group, we can also calculate the mean by only using observations that satisfy certain conditions (known as the conditional mean). In this case, we are interested in comparing the mean price of taxed and untaxed beverages, before and after the tax.
 Calculate and compare conditional means:
 Create a table similar to Figure 3.1, showing the average price per ounce (in cents) for taxed and untaxed beverages separately, with ‘store type’ as the row variable, and ‘taxed’ and ‘time’ as the column variables. To follow the methodology used in the journal paper, make sure to only include products that are present in all time periods, and nonsupplementary products (
supp = 0
).
 Without doing any calculations, summarize any differences or general patterns between December 2014 and June 2015 that you find in the table.
 Would we be able to assess the effect of sugar taxes on product prices by comparing the average price of untaxed goods with that of taxed goods in any given period? Why or why not?
Nontaxed  Taxed  

Store type  Dec 2014  Jun 2015  Dec 2014  Jun 2015 
1  
3 
The average price of taxed and nontaxed beverages, according to time period and store type.
R walkthrough 3.4 Calculating conditional means
Calculating conditional means is not a straightforward task to achieve (in R or in any other statistical program). It is, however, a common data cleaning operation you will encounter. Here is one way to do this.
In order to identify products (identified by
product_id
) that have observations for all three periods (DEC2014
,JUN2015
andMAR2016
), we will first create a new variable calledperiod_test
, which takes the value 1 (orTRUE
) if we have observations for all periods for a product in a particular store, and 0 (FALSE
) otherwise. We call true/false variables like this ‘boolean variables’.Creating this variable is not straightforward, but the easiest way to achieve this is with a loop.
dat$period_test < NA sid_list = unique(dat$store_id) # List of all store IDs pid_list = unique(dat$product_id) # List of all product IDs for (s in sid_list) { for (p in pid_list) { temp < subset(dat, product_id == p & store_id == s) temp_time < temp$time test < (any(temp_time == "DEC2014") & any(temp_time == "JUN2015") & any(temp_time == "MAR2016")) dat$period_test[dat$product_id == p & dat$store_id == s] < test } }
Now we can use the
period_test
variable to remove all products that have not been observed in all three periods. We define a new dataframe,dat_c
, containing only products that are observed in all three periods in a particular store.dat_c < subset(dat,(period_test == TRUE & supp == "Standard"))
Now we can calculate the price averages (for
price_per_oz
) by grouping the data according tostore_type
,taxed
, andtime
. One way to achieve this is to use a technique called piping:table_res < dat_c %>% group_by(taxed,store_type,time) %>% summarize(n = length(price_per_oz),avg.price = mean(price_per_oz)) %>% spread(time,avg.price) %>% print()
## # A tibble: 8 x 6 ## # Groups: taxed, store_type [8] ## taxed store_type n DEC2014 JUN2015 MAR2016 ## <fct> <fct> <int> <dbl> <dbl> <dbl> ## 1 not taxed Large Supermarket 36 0.112 0.115 0.117 ## 2 not taxed Small Supermarket 70 0.137 0.138 0.134 ## 3 not taxed Pharmacy 18 0.152 0.161 0.154 ## 4 not taxed Gas Station 12 0.169 0.170 0.170 ## 5 taxed Large Supermarket 36 0.156 0.169 0.167 ## 6 taxed Small Supermarket 101 0.159 0.160 0.155 ## 7 taxed Pharmacy 18 0.182 0.191 0.186 ## 8 taxed Gas Station 22 0.194 0.203 0.192
Piping is a very useful technique in R for data analysis. In words, what we did in the line above is: Take the data in
dat_c
, group them according to the variablestaxed
,store_type
, andtime
, and then summarize the data by calculating the mean ofprice_per_oz
(and calculate the number of observations in each group). Then, rearrange the results table so that the time variable shows across the columns and theavg.price
variable gives the values inside the table.The University of Manchester’s Econometric Computing Learning Resource provides a more detailed introduction to piping.
Use the S3 Table in the journal paper to check how closely your summary data match those in the paper.^{1} You should find that your results for Large Supermarkets and Pharmacies match, but the other store types have discrepancies. In R walkthrough 3.5 we will discuss these differences in more detail.
In order to make a beforeandafter comparison, we will make a chart similar to Figure 2 in the journal paper, to show the change in prices for each store type.
 Using your table from Question 3:
 Calculate the change in the mean price after the tax (price in June 2015 minus price in December 2014) for taxed and untaxed beverages, by store type.
 Using the values you calculated in Question 4(a), plot a column chart to show this information (as done in Figure 2 of the journal paper) with store type on the horizontal axis and price change on the vertical axis. Label each axis and data series appropriately. You should get the same values as shown in Figure 2.
R walkthrough 3.5 Making a column chart to compare two groups
Calculate price differences by store type
Let’s calculate the price differences for June 2015 minus December 2014 and March 2016 minus December 2014, and store them as
D1
andD2
respectively:table_res$D1 < table_res$JUN2015  table_res$DEC2014 table_res$D2 < table_res$MAR2016  table_res$DEC2014 print("Group Means")
## [1] "Group Means"
table_res
## # A tibble: 8 x 8 ## # Groups: taxed, store_type [8] ## taxed store_type n DEC2014 JUN2015 MAR2016 D1 D2 ## <fct> <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 not taxed Large Supermar~ 36 0.112 0.115 0.117 2.88e3 0.00510 ## 2 not taxed Small Supermar~ 70 0.137 0.138 0.134 1.46e3 0.00304 ## 3 not taxed Pharmacy 18 0.152 0.161 0.154 8.80e3 0.00240 ## 4 not taxed Gas Station 12 0.169 0.170 0.170 2.90e4 0.00106 ## 5 taxed Large Supermar~ 36 0.156 0.169 0.167 1.31e2 0.0107 ## 6 taxed Small Supermar~ 101 0.159 0.160 0.155 1.44e3 0.00359 ## 7 taxed Pharmacy 18 0.182 0.191 0.186 8.97e3 0.00448 ## 8 taxed Gas Station 22 0.194 0.203 0.192 9.25e3 0.00174
Plot a column chart for average price changes
It is these two new variables we want to display in a column chart. We will use the
ggplot2
package for graphs (which is part of thetidyverse
package we loaded for R walkthrough 3.1). Let’s start with displaying the average price change from December 2014 to June 2015 (which is stored inD1
):ggplot(table_res, aes(fill=taxed, y=D1, x=store_type)) + geom_bar(position="dodge", stat="identity") + labs(y = "Price change (US$/oz)", x = "Store type") + # Add the axes labels scale_fill_discrete(name="Beverages", # Add the title and legend labels labels=c("Nontaxed", "Taxed")) + ggtitle("Average price change from Dec 2014 to Jun 2015")
Now we do the same for the price change from Dec 2014 to Mar 2016:
ggplot(table_res, aes(fill=taxed, y=D2, x=store_type)) + geom_bar(position="dodge", stat="identity") + labs(y = "Price change (US$/oz)", x = "Store type") + # Add the axes labels scale_fill_discrete(name="Beverages", # Add the title and legend labels labels=c("Nontaxed", "Taxed")) + ggtitle("Average price change from Dec 2014 to Mar 2016")
It is important to know whether the difference in means is statistically significant or not. According to the journal paper, the pvalue is less than 0.05 for large supermarkets, but greater than 0.05 for pharmacies.
 Based on a cutoff (significance level) of 5%, what can we conclude about the difference in means? (Hint: You may find the discussion in Part 2.3 helpful.)
Extension R walkthrough 3.6 Testing for significant differences in price changes
In this walkthrough, we show the calculations required to obtain the pvalues above. As the pvalues are already provided, this walkthrough is only for those who want to replicate where these pvalues come from. For the categories of Large Supermarkets and Pharmacies, we conduct a hypothesis test which tests the null hypothesis that the price difference between June 2015 and Dec 2014 (and Mar 2016 and Dec 2014) for the taxed and untaxed beverages in the two store types are actually zero.
We are interested in whether for one group (say, Large Supermarket and taxed), the difference in average price between
JUN2015
andDEC2014
(orMAR2016
andDEC2014
) is statistically significant. Note that we are dealing with paired observations (recall that we only allowed observations for products that were observed in all periods in the same store type).Let’s use the price difference between June 2015 and December 2014 in Large Supermarkets for taxed beverages as an example. First, we extract price vectors for both periods (
p1
andp2
) and then calculate their difference (d_t
).p1 < dat_c$price_per_oz[dat_c$store_type=="Large Supermarket" & dat_c$taxed == "taxed" & dat_c$time=="DEC2014"] p2 < dat_c$price_per_oz[dat_c$store_type=="Large Supermarket" & dat_c$taxed == "taxed" & dat_c$time=="JUN2015"] d_t < p2p1 # Price difference for taxed products
All three new variables are vectors with 36 elements. For
d_t
to correctly represent the price difference for a particular product in a particular store, we need to be certain that every element in both vectors corresponds to the same product in the same store. To check that the elements match, we will extract the store and product IDs along with the prices, and compare the ordering inp1_alt
andp2_alt
.p1_alt < dat_c[dat_c$store_type=="Large Supermarket" & dat_c$taxed == "taxed" & dat_c$time=="DEC2014",c("product_id","store_id","price_per_oz")] p2_alt < dat_c[dat_c$store_type=="Large Supermarket" & dat_c$taxed == "taxed" & dat_c$time=="JUN2015",c("product_id","store_id","price_per_oz")]
You can see that the ordering matches, since the original datafile was ordered in a way (first according to
time
, thenstore_id
and thenproduct_id
) that in this instance guarantees identical ordering.
 standard error
 A measure of the degree to which the sample mean deviates from the population mean. It is calculated by dividing the standard deviation of the sample by the square root of the number of observations.
The average value of the price difference is 0.0131222, and our task is to evaluate whether this is statistically significantly different from 0. To calculate the respective test statistic (), we will need this value’s standard error (). Manually the hypothesis test is calculated as follows:
t < mean(d_t)/sqrt(var(d_t)/(length(d_t)))
Alternatively, we can use the available
t.test
function in R, which gives exactly the same results but has the advantage of directly obtaining pvalues and confidence intervals.t.test(p2,p1,paired=TRUE) # Recognize that the differences come from paired samples.
## ## Paired ttest ## ## data: p2 and p1 ## t = 4.7681, df = 35, pvalue = 3.226e05 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## 0.007535221 0.018709202 ## sample estimates: ## mean of the differences ## 0.01312221
# t.test(d) # Or use the function directly on d, which delivers identical results.
To compare this result to the journal paper, look at the extract from Table S3 (the section on Large Supermarkets) shown in Figure 3.4 below. The cell with ‘**’ shows the mean price difference of 1.31 cents ($0.0131).
Large supermarkets
(n = 6)Taxed beverage price
(36 sets)Untaxed beverage price
(36 sets)Taxed – untaxed difference cents/oz 95% CI cents/oz 95% CI cents/oz 95% CI Round 1: December 2014 15.62 10.15 21.08 11.19 7.45 14.93 Round 2: June 2015 16.93 11.29 22.57 11.48 7.64 15.32 Round 3: March 2016 16.68 11.26 22.10 11.70 7.79 15.61 Mean change
(March 2016–Dec 2014)1.07*
(p=0.01)0.22 1.91 0.51*
(p=0.01)0.16 0.86 0.56
(p=0.22)−0.35 1.46 Mean change
(June 2015–Dec 2014)1.31**
(p<0.001)0.75 1.87 0.29
(p=0.08)−0.03 0.61 1.02^{‡}
(p=0.002)0.39 1.66 Table S3 in Silver et al. (2017), showing means and confidence intervals.
n = number of stores of each type; ** denotes statistically significant difference between prices in March 2016 compared to earlier round (December 2014 or June 2015) at p < 0.01 using paired ttests. * denote statistically significant difference between prices in March 2016 compared to earlier round (December 2014 or June 2015) at p < 0.05 using pairedttests. ‡ denotes statistically significant difference of price of taxed beverages compared to untaxed beverages at p < 0.05 (unpaired ttests since taxed and untaxed beverage items are different).
In our test output we get a very small pvalue (0.0000323) which in the table is indicated by the double asterisk. Our test output also automatically delivers the confidence interval for the mean of price differences: [0.0075, 0.0187].
Tests for other store types are calculated similarly, by changing the data extracted to
p1
andp2
. Let’s do that for one more example: the price difference between June 2015 and December 2014 in Large Supermarkets for untaxed beverages.p1 < dat_c$price_per_oz[dat_c$store_type=="Large Supermarket" & dat_c$taxed == "not taxed" & dat_c$time=="DEC2014"] p2 < dat_c$price_per_oz[dat_c$store_type=="Large Supermarket" & dat_c$taxed == "not taxed" & dat_c$time=="JUN2015"] d_nt < p2p1 t.test(p2,p1,paired=TRUE)
## ## Paired ttest ## ## data: p2 and p1 ## t = 1.8179, df = 35, pvalue = 0.07765 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## 0.0003367942 0.0061057804 ## sample estimates: ## mean of the differences ## 0.002884493
You should be able to recognize the mean difference, the pvalue, and the confidence interval in the excerpt of Table S3 provided in Figure 3.4.
Let’s also replicate the last section of Table S3, which shows the difference between the price changes in taxed and untaxed products, that is, we want to know whether
d_t
ANDd_nt
have different means. We will apply the two sample hypothesis tests, but this time for unpaired data, as the products differ across samples.t.test(d_t,d_nt)
## ## Welch two sample ttest ## ## data: d_t and d_nt ## t = 3.2227, df = 55.955, pvalue = 0.002119 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## 0.003873834 0.016601603 ## sample estimates: ## mean of x mean of y ## 0.013122212 0.002884493
Again you should be able to identify the corresponding entries in Table S3 shown in Figure 3.4. The main entry in the table is 1.02, indicating that the means of the two groups differ by 1.02 cents. This is confirmed in our calculations, as $0.01312 − $0.00288 is about $0.0102 or 1.02 cents. The pvalue of 0.002 is also the same as the one in Table S3.
Part 3.2 The control group: beforeandafter comparisons with prices in other areas
When looking for any price patterns, it is possible that the observed changes were not due to the tax, but instead were due to other events that happened in Berkeley and the neighbouring areas. If prices changed in a similar way in nearby areas, then what we observed in Berkeley may not be a result of the tax. To investigate whether this was the case, the researchers collected price data from stores in the surrounding areas and compared them with prices in Berkeley.
Download the following files:
 The Berkeley PointofSale Stata file on the Global Food Research Program’s website, containing the price data they collected, including information on the date (year and month), location (Berkeley or NonBerkeley), beverage group (soda, fruit drinks, milk substitutes, milk and water), average price, and the consumer price index (CPI) for that month. Stata is another popular statistical software package, and the data is provided as a
.dta
file.  ‘S5 Table’ comparing the neighbourhood characteristics of the Berkeley and nonBerkeley stores.
 Based on ‘S5 Table’, do you think the researchers chose suitable comparison stores? Why or why not?
We will now plot a line chart similar to Figure 3 in the journal paper, to compare prices of similar goods in different locations and see how they have changed over time. To do this, we will need to summarize the data so that there is one value (the mean price) for each location and type of good in each month.
 Assess the effects of a tax on prices:
 Create a table similar to the one provided in Figure 3.5 to show the average price in each month for taxed and nontaxed beverages, according to location. Use ‘year and month’ as the row variables, and ‘tax’ and ‘location’ as the column variables. (Hint: You may find R walkthrough 3.4 helpful.)
 Plot the four columns of your table on the same line chart, with average price on the vertical axis and time (months) on the horizontal axis. Describe any differences you see between the prices of nontaxed goods in Berkeley and those outside Berkeley, both before the tax (January 2013 to December 2014) and after the tax (March 2015 onwards). Do the same for prices of taxed goods.
 Based on your chart, is it reasonable to conclude that the sugar tax had an effect on prices?
Nontaxed  Taxed  

Year/Month  Berkeley  NonBerkeley  Berkeley  NonBerkeley 
January 2013  
February 2013  
March 2013  
…  
December 2013  
January 2014  
…  
February 2016 
The average price of taxed and nontaxed beverages, according to location and month.
R walkthrough 3.7 Importing data from a Stata file and plotting a line chart
Import data and create a table of average monthly prices
To import data from a
.dta
file we need thereadstata13
package.library(readstata13) PoSd < read.dta13("public_use_weighted_prices2.dta")
Before proceeding, use the command
str(PoSd)
to look at the structure of this dataset (output not shown here). You will see that for each month and location (Berkeley or NonBerkeley), there are a number of prices for a variety of beverage categories, and we know whether the category is taxed or not. For any particular timelocationtax status combination we want the average price of all products.To make the summary table, we will use the
tidyverse
package again:table_test < PoSd %>% group_by(year,month,location,tax) %>% summarize(avg.price = mean(price)) %>% spread(location,avg.price) %>% print()
## # A tibble: 78 x 5 ## # Groups: year, month [39] ## year month tax Berkeley `NonBerkeley` ## <dbl> <dbl> <chr> <dbl> <dbl> ## 1 2013 1 Nontaxed 5.72 5.35 ## 2 2013 1 Taxed 8.69 7.99 ## 3 2013 2 Nontaxed 5.81 5.36 ## 4 2013 2 Taxed 8.65 8.18 ## 5 2013 3 Nontaxed 5.86 5.42 ## 6 2013 3 Taxed 8.82 8.19 ## 7 2013 4 Nontaxed 5.86 5.64 ## 8 2013 4 Taxed 9.02 8.25 ## 9 2013 5 Nontaxed 5.79 5.18 ## 10 2013 5 Taxed 8.68 7.76 ## # ... with 68 more rows
You can see that the data is not quite in the right shape yet, because we need to separate the
Taxed
from theNontaxed
data.tax_table < subset(table_test,tax == "Taxed") ntax_table < subset(table_test,tax == "Nontaxed")
Plot a line chart
Now we can create a line chart. Before we do this, we will convert the
Berkeley
andNonBerkeley
columns of both datasets to time series data using thets
function, which will make plotting a little easier. We then start by plottingtax_table$Berkeley
and subsequently add lines for the three other variables.# Note for below: Use inverted commas ('') to refer to the 'NonBerkeley' variable, since R interprets the hyphen as a minus sign. tax_table$Berkeley < ts(tax_table$Berkeley, start=c(2013,1), end=c(2016,3), frequency=12) tax_table$'NonBerkeley' < ts(tax_table$'NonBerkeley', start=c(2013,1), end=c(2016,3), frequency=12) ntax_table$Berkeley < ts(ntax_table$Berkeley, start=c(2013,1), end=c(2016,3), frequency=12) ntax_table$'NonBerkeley' < ts(ntax_table$'NonBerkeley', start=c(2013,1), end=c(2016,3), frequency=12) plot(tax_table$Berkeley, col = "deepskyblue4", lwd=2, ylab = "Average price", xlab = "Time", ylim=c(4, 12) ) title("Average price of taxed and nontaxed beverages \n in Berkeley and nonBerkeley areas") # \n creates a line break. lines(tax_table$'NonBerkeley',col="deeppink",lwd=2) lines(ntax_table$Berkeley,col="darkgreen",lwd=2) lines(ntax_table$'NonBerkeley',col="darkorange",lwd=2) abline(v = 2015.1, col = "grey") # Add vertical lines abline(v = 2015.3, col = "grey") text(2014.6,4,"Pretax") # Add labels text(2015.8,4,"Posttax") legend(2013.1, 12, legend=c("Taxed (Berkeley)", "Taxed (nonBerkeley)", "Nontaxed (Berkeley)", "Nontaxed (nonBerkeley)"),col=c("deepskyblue4", "deeppink", "darkgreen", "darkorange"), lwd=2,lty=1, cex=0.8)
It is important to know whether the observed differences between Berkeley and nonBerkeley prices are statistically significant or not. According to the journal paper, when comparing the mean Berkeley and nonBerkeley price of sugary beverages after the tax, the pvalue is less than 0.01, but it is greater than 0.05 for nonsugary beverages after the tax.
 Based on a cutoff (significance level) of 5%, what can we conclude about the difference in means and the effect of the sugar tax on the price of sugary beverages? (Hint: You may find the discussion in Part 2.3 helpful.)
The aim of the sugar tax was to decrease consumption of sugary beverages. Figure 3.7 shows the mean number of calories consumed and the mean volume consumed before and after the tax. The researchers tested whether the difference in means before and after the tax were statistically significant or not, and reported the pvalues in the last column.
Usual intake  Pretax (Nov–Dec 2014), n = 623 
Posttax (Nov–Dec 2015), n = 613 
Pretax–posttax difference  

Mean  95% CI  Mean  95% CI  
Caloric intake (kilocalories/per capita/day)  
Taxed beverages  45.1  29.4, 60.7  38.7  23.0, 54.4  −6.4, p = 0.56 
Nontaxed beverages  115.7  87.6, 142.5  116.3, 178.9  31.9*, p = 0.04  
Volume of intake (grams/capita/day)  
Taxed beverages  121.0  78.7, 163.3  97.0  56.5, 137.4  −24.0, p = 0.24 
Nontaxed beverages  1,839.4  1,692.7, 1,986.1  1,896.5  1,742.3, 2,050.8  57.1, p = 0.22 
Models account for age, gender, race/ethnicity, income level, and educational attainment. n is the sample size at each round of the survey after excluding participants with missing values on selfreported race/ethnicity, age, education, income, or monthly intake of sugarsweetened beverages. * Statistically significant difference in mean per capita intake between pretax and posttax values, p < 0.05. 
Changes in prices, sales, consumer spending, and beverage consumption one year after a tax on sugarsweetened beverages in Berkeley, California, US: A beforeandafter study.
Lynn D. Silver, Shu Wen Ng, Suzanne RyanIbarra, Lindsey Smith Taillie, Marta Induni, Donna R. Miles Jennifer M. Poti, and Barry M. Popkin. 2017. Table 1 in ‘Changes in prices, sales, consumer spending, and beverage consumption one year after a tax on sugarsweetened beverages in Berkeley, California, US: A beforeandafter study’. PLoS Med 14 (4): e1002283.
 Based on Figure 3.7, was there a statistically significant change in consumption behaviour in Berkeley after the tax (at a 5% significance level)? Suggest some reasons why or why not.
 Read the ‘Limitations’ in the ‘Discussions’ section of the paper and discuss the strengths and limitations of this study. How could future studies on the sugar tax in Berkeley address these problems? (Some issues you may want to discuss are: the number of stores observed, number of people surveyed, and the reliability of the price data collected.)
 Suppose that you have the authority to conduct your own sugar tax natural experiment in two neighbouring towns, Town A and Town B. Outline how you would conduct the experiment to ensure that any changes in outcomes (prices, consumption of sugary beverages) are due to the tax and not due to other factors. (Hint: think about what factors you need to hold constant.)

Lynn D. Silver, Shu Wen Ng, Suzanne RyanIbarra, Lindsey Smith Taillie, Marta Induni, Donna R. Miles, Jennifer M. Poti, and Barry M. Popkin. 2017. S3 Table in ‘Changes in prices, sales, consumer spending, and beverage consumption one year after a tax on sugarsweetened beverages in Berkeley, California, US: A beforeandafter study’. PLoS Med 14 (4): e1002283. ↩