MATH1324 Assignment 3
Supermarket Price Wars
Individual Details
- Kevin Johnson (s3207343)
Whilst this assignment was completed as an individual/indepenant task, please note the sample data required was collected as a joint effort with Anthony Tsoukas. (s3671956)
Executive Statement
This assignment investigated which major supermarket, Coles or Woolworths (also referred to as Safeway or Wooley’s), aiming to determine which one is cheaper. My thoughts and personal (non empirical) observations of the two supermarkets over the years was that they were similarly priced however my perception was that Safeway was the cheaper supermarket.
Randomly sampled, matched products were selected from each supermarket and appropriate hypothesis testing was conducted to determine if there is a statistically significant difference between prices from the major supermarkets and if one is cheaper. Conducting a paired sample t-test on a matched sample of 61 products, my investigation found no statistically significant evidence to indicate there was a difference in the unit prices of either Coles or Safeway products. In conclusion, based on the tests conducted on the sample data, it was found that both supermarkets were priced similarly. This is not surprising considering large supermarkets would compete heavily based on price
Load Packages and Data
The following packages are required for this assignment.
# Required Packages
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodelibrary(granova)Data
After looking at numerous methods at selecting random samples of products for this investigation, 20 products were randomly selected from each of my wife Nellie’s last 3 shopping lists, totalling 61 products to be matched. This method provided a level of randomisation and also a realistic representation of products from a typical family/household’s shopping list, across a number of product categories. These products were then added to a list at each supermarket’s website shopping carts to ensure current prices and matched with a product of similar volume and brand at that of the rival supermarket. Supermarket ‘Home brands’ were selected where possible. If a similar product was not available to be matched either another product was selected from the list or the cheapest alternative brand was selected. To ensure that appropriate volumes were equally matched, the ‘unit price’ of each item was calculated in proportion to the volume of the product. The overall collection of data was a manual process. The product lists and unit price information were converted to a csv file and imported to R.
# Import the csv file to R
Supermarket_Data <- read.csv("/DATA/RMIT/ass3/ass3_data_version_3.csv")
Supermarket_Data## coles_homebrand_product_name
## 1 Jelly Beans 147g
## 2 Coles Smart Buy Lemon Bleach
## 3 Full Cream Milk 1L
## 4 Coles Toilet Cleaner Liquid Pot Pourri
## 5 Cole Squeezy BBQ Sauce
## 6 Coles Super Strength dishwashing Liquid Lemon 1L
## 7 Bubble Bath 1L
## 8 Coles Choc Chip Muesli Bars 8 pack
## 9 Orange Mango Juice 2L
## 10 Homebrand Canola Oil Spray
## 11 Wholemeal High Fibre Sliced Bread 700g
## 12 Dijon Mustard 200g
## 13 Full Cream Milk 2L
## 14 French Onion Dip 200g
## 15 Soft Black Licorice 250g
## 16 Marshmallows 204g
## 17 Hass Avocados
## 18 White Toast Bread 700g
## 19 Rubber Bands 100g
## 20 Coles Total Care Medium Toothbrush
## 21 Fair Trade Organic English Breakfast Tea Bags 50 pack
## 22 Chunky Frozen Potato Wedges 750g
## 23 Green Cucumber
## 24 Homebrand Brown Paper Sandwich
## 25 Coles Thickened Cream
## 26 Jam Lamingtons 6 pack 350g
## 27 Spring Water 350mL Bottles 6 pack
## 28 Australian Frozen Peas 1kg
## 29 Hawaiian Frozen Pizza 500g
## 30 Little Explorer Fragrance Free Thick Baby Wipes 80 pack
## 31 Full Cream Milk 3L
## 32 Mild American Mustard 250g
## 33 Baby Spinach Leaves Prepacked 120g
## 34 Refills Reinforced A4 100 pack
## 35 Coconut Whole
## 36 Kent Pumpkin Crescents 500g
## 37 Butter Pat 500g
## 38 Vanilla Yoghurt 1kg
## 39 Antiseptic Solution 250mL
## 40 Coles Oxy Booster Advanced Laundry Soaker
## 41 Comfy Bots Scented Nappy Bags 200 pack
## 42 Original Granulated Coffee 200g
## 43 Snakes 750g
## 44 Dishwashing Powder Concentrate 1kg
## 45 Revitalising Oxygen Burst Body Wash 1L
## 46 Greek Style Yoghurt 1kg
## 47 Coles Aluminium Foil Wrap 30M
## 48 Sliced Brown Mushrooms Prepacked 200g
## 49 Budgie & Canary Bird Seed 2kg
## 50 Free Range Jumbo Eggs 12 pack 800g
## 51 Pink Lady Apples Prepacked 1kg
## 52 2 Star Beef Mince 800g
## 53 Instant Skim Milk Powder 1kg
## 54 Australian Sliced Roast Beef 200g
## 55 Short Cut Australian Rindless Bacon 200g
## 56 Lean Pork Mince 500g
## 57 Australian Chicken Breast Sliced 200g
## 58 Fish Food Flakes Gold 100g
## 59 Coles Olive Oil Extra Virgin
## 60 Purple Eggplant
## 61 Cheese Slices 84 pack 1kg
## coles_quantity_in_item coles_measurement coles_price coles_unit_price
## 1 147 g 1.00 0.00680
## 2 2000 ml 1.20 0.00060
## 3 1000 ml 1.25 0.00125
## 4 500 ml 1.50 0.00300
## 5 500 ml 1.50 0.00300
## 6 1000 ml 1.60 0.00160
## 7 1000 ml 1.80 0.00180
## 8 248 g 1.90 0.00766
## 9 2000 ml 2.00 0.00100
## 10 400 g 2.00 0.00500
## 11 700 g 2.00 0.00286
## 12 200 g 2.00 0.01000
## 13 2000 ml 2.00 0.00100
## 14 200 g 2.00 0.01000
## 15 250 g 2.00 0.00800
## 16 204 g 2.00 0.00980
## 17 1 units 2.00 2.00000
## 18 700 g 2.00 0.00286
## 19 100 g 2.00 0.02000
## 20 1 units 2.20 2.20000
## 21 50 units 2.30 0.04600
## 22 750 g 2.50 0.00333
## 23 1000 g 2.50 0.00250
## 24 100 units 2.60 0.02600
## 25 600 ml 2.64 0.00440
## 26 350 g 2.75 0.00786
## 27 6 units 2.80 0.46667
## 28 1000 g 2.90 0.00290
## 29 500 g 3.00 0.00600
## 30 80 units 3.00 0.03750
## 31 3000 ml 3.00 0.00100
## 32 250 g 3.00 0.01200
## 33 120 g 3.00 0.02500
## 34 100 units 3.20 0.03200
## 35 1 units 3.50 3.50000
## 36 500 g 3.50 0.00700
## 37 500 g 3.60 0.00720
## 38 1000 g 3.60 0.00360
## 39 250 ml 3.65 0.01460
## 40 1000 g 3.70 0.00370
## 41 200 units 3.70 0.01850
## 42 200 g 4.00 0.02000
## 43 750 g 4.00 0.00533
## 44 1000 g 4.00 0.00400
## 45 1000 ml 4.00 0.00400
## 46 1000 g 4.20 0.00420
## 47 1 units 4.50 4.50000
## 48 200 g 4.90 0.02450
## 49 2000 g 5.00 0.00250
## 50 12 units 5.20 0.43333
## 51 1000 g 5.50 0.00550
## 52 800 g 5.50 0.00688
## 53 1000 g 5.70 0.00570
## 54 200 g 5.80 0.02900
## 55 200 g 6.30 0.03150
## 56 500 g 6.50 0.01300
## 57 200 g 6.90 0.03450
## 58 100 g 7.00 0.07000
## 59 1000 ml 7.00 0.00700
## 60 1000 g 7.90 0.00790
## 61 1000 g 9.00 0.00900
## safeway_homebrand_product_name
## 1 Homebrand Jelly Beans
## 2 Homebrand Bleach Lemon
## 3 Woolworths Full Cream Milk 1L
## 4 Homebrand Toilet Cleaner Liquid Pot Pourri
## 5 Woolworths Barbecue Sauce Squeeze
## 6 Woolworths Select Dishashing Liquid
## 7 Fun Time Kids Bubble Bath Space Bubbles 1L
## 8 Homebrand Choc Chip Museli Bar 8pk
## 9 Homebrand Orange and Mango Fruit Drink
## 10 Homebrand Canola Oil Spray
## 11 Woolworths Bread Wholemeal Sliced Loaf
## 12 Woolworths Select Mustard Dijon
## 13 Woolworths Full Cream Milk 2L
## 14 Willow Farm French Onion Dip
## 15 Woolworths Select Licorice Black Soft Twist
## 16 Homebrand Marshmellows
## 17 Hass Avocados
## 18 Wonder White Bread Vitamins & Mineral Toast
## 19 Rubber Bands 100g
## 20 Woolworths Select Toothbrush Medium
## 21 Madura English Breakfast Tea Bag
## 22 Woolworths Potato Wedges
## 23 Fresh Cucumber Lebanese
## 24 Homebrand Brown Paper Sandwich
## 25 Woolworths Thickened Cream
## 26 Select Lamingtons Jam Filled
## 27 Woolworths Select Mountain Spring Water 6pack 600ml
## 28 Woolworths Australian Frozen Peas
## 29 Woolworths Frozen Pizza Hawaiian
## 30 Little Ones Baby Wipes Thick and Unscented
## 31 Woolworths Full Cream Milk 3L
## 32 Masterfood Mild American Mustard Squeeze Bottle
## 33 Spinach Baby Organic
## 34 Refills Reinforced A4 100 pack
## 35 Coconut Fresh
## 36 Kent Pumpkin Crescents
## 37 Homebrand Salted Butter
## 38 Yoplait Vanilla Yoghurt
## 39 Homebrand Antiseptic Solution
## 40 Homebrand Laundry Soaker & Inwash Booster
## 41 Once Upon a Time Scented Nappy Bags
## 42 Homebrand Instant Coffee Granules Granulated Coffee
## 43 Woolworths Select Snakes
## 44 Woolworths Dishwashing Powder Concentrate
## 45 Radox Shower Gel Revitilising Body Wash
## 46 Pauls Athentikos Greek Yoghurt
## 47 Homebrand Aluminium Foil
## 48 Sliced Brown Mushrooms Prepacked 200g
## 49 Budgie & Canary Bird Seed 2kg
## 50 Farm Pride Free Range Eggs Jumbo
## 51 Pink Lady Apples
## 52 Homebrand Beef Mince
## 53 Woolworths Select Skim Milk Powder
## 54 Woolworths Roast Beef Sliced
## 55 Primo Short Cut Rindless Bacon
## 56 Beef Heart Smart Mince min 500g
## 57 Don Chicken Breast Thinly Sliced
## 58 Marine Master Gold Fish Flakes
## 59 Woolworths Select Extra Virgin Olive Oil
## 60 Eggplant Fresh
## 61 Woolworths Cheese Slices 84 pack 1kg
## safeway_quantity_in_item safeway_measurement safeway_price
## 1 450 g 2.50
## 2 2000 ml 1.19
## 3 1000 ml 1.25
## 4 500 ml 1.50
## 5 500 ml 1.50
## 6 900 ml 2.69
## 7 1000 ml 2.15
## 8 200 g 1.80
## 9 2000 ml 1.70
## 10 400 ml 1.85
## 11 680 g 1.90
## 12 200 g 2.00
## 13 2000 ml 2.00
## 14 200 g 2.00
## 15 300 g 2.40
## 16 250 g 2.45
## 17 1 units 2.90
## 18 700 g 3.30
## 19 100 g 4.00
## 20 1 Units 1.99
## 21 50 units 2.70
## 22 750 g 2.69
## 23 1000 g 3.90
## 24 100 units 2.60
## 25 600 ml 2.40
## 26 6 units 2.50
## 27 6 units 3.00
## 28 1000 g 2.90
## 29 500 g 2.95
## 30 80 units 3.00
## 31 3000 ml 3.00
## 32 250 g 3.50
## 33 100 g 4.00
## 34 100 units 3.00
## 35 1 units 2.90
## 36 500 g 4.00
## 37 500 g 3.60
## 38 1000 g 4.00
## 39 250 ml 3.65
## 40 1000 g 2.49
## 41 200 units 3.69
## 42 200 g 3.70
## 43 500 g 3.79
## 44 1000 g 4.00
## 45 1000 ml 9.40
## 46 1000 g 4.00
## 47 1 Units 2.79
## 48 200 g 5.00
## 49 220 g 3.30
## 50 12 units 6.49
## 51 1000 g 5.00
## 52 1000 g 8.00
## 53 1000 g 5.70
## 54 300 g 6.00
## 55 175 g 5.00
## 56 1000 g 8.00
## 57 250 g 4.80
## 58 90 g 6.99
## 59 1000 ml 9.99
## 60 1000 g 7.90
## 61 1000 g 9.00
## safeway_unit_price price_difference unit_price_difference
## 1 0.00556 1.50 -0.00125
## 2 0.00060 -0.01 -0.00001
## 3 0.00125 0.00 0.00000
## 4 0.00300 0.00 0.00000
## 5 0.00300 0.00 0.00000
## 6 0.00299 1.09 0.00139
## 7 0.00215 0.35 0.00035
## 8 0.00900 -0.10 0.00134
## 9 0.00085 -0.30 -0.00015
## 10 0.00463 -0.15 -0.00037
## 11 0.00279 -0.10 -0.00006
## 12 0.01000 0.00 0.00000
## 13 0.00100 0.00 0.00000
## 14 0.01000 0.00 0.00000
## 15 0.00800 0.40 0.00000
## 16 0.00980 0.45 0.00000
## 17 2.90000 0.90 0.90000
## 18 0.00471 1.30 0.00186
## 19 0.04000 2.00 0.02000
## 20 1.99000 -0.21 -0.21000
## 21 0.05400 0.40 0.00800
## 22 0.00359 0.19 0.00025
## 23 0.00390 1.40 0.00140
## 24 0.02600 0.00 0.00000
## 25 0.00400 -0.24 -0.00040
## 26 0.41667 -0.25 0.40881
## 27 0.50000 0.20 0.03333
## 28 0.00290 0.00 0.00000
## 29 0.00590 -0.05 -0.00010
## 30 0.03750 0.00 0.00000
## 31 0.00100 0.00 0.00000
## 32 0.01400 0.50 0.00200
## 33 0.04000 1.00 0.01500
## 34 0.03000 -0.20 -0.00200
## 35 2.90000 -0.60 -0.60000
## 36 0.00800 0.50 0.00100
## 37 0.00720 0.00 0.00000
## 38 0.00400 0.40 0.00040
## 39 0.01460 0.00 0.00000
## 40 0.00249 -1.21 -0.00121
## 41 0.01845 -0.01 -0.00005
## 42 0.01850 -0.30 -0.00150
## 43 0.00758 -0.21 0.00225
## 44 0.00400 0.00 0.00000
## 45 0.00940 5.40 0.00540
## 46 0.00400 -0.20 -0.00020
## 47 2.79000 -1.71 -1.71000
## 48 0.02500 0.10 0.00050
## 49 0.01500 -1.70 0.01250
## 50 0.54083 1.29 0.10750
## 51 0.00500 -0.50 -0.00050
## 52 0.00800 2.50 0.00113
## 53 0.00570 0.00 0.00000
## 54 0.02000 0.20 -0.00900
## 55 0.02857 -1.30 -0.00293
## 56 0.00800 1.50 -0.00500
## 57 0.01920 -2.10 -0.01530
## 58 0.07767 -0.01 0.00767
## 59 0.00999 2.99 0.00299
## 60 0.00790 0.00 0.00000
## 61 0.00900 0.00 0.00000Summary Statistics & Visualisation
The following code was used to determine summary information of the product prices from each supermarket.
Summary Statistics
#Coles Supermarket price Stats
supermarket_coles_n <- Supermarket_Data %>% nrow() #Count (n)
supermarket_coles_mean <- Supermarket_Data$coles_unit_price %>% mean() #Mean
supermarket_coles_min <- Supermarket_Data$coles_unit_price %>% min() #Min
supermarket_coles_max <- Supermarket_Data$coles_unit_price %>% max() #Max
supermarket_coles_range <- supermarket_coles_max - supermarket_coles_min
supermarket_coles_var <- Supermarket_Data$coles_unit_price %>% var() #Variance
supermarket_coles_sd <- Supermarket_Data$coles_unit_price %>% sd() #Standard Deviation
supermarket_coles_iqr <- Supermarket_Data$coles_unit_price %>% IQR() #Interquartile range
#Safeway Supermarket price Stats
supermarket_safeway_n <- Supermarket_Data %>% nrow() #Count (n)
supermarket_safeway_mean <- Supermarket_Data$safeway_unit_price %>% mean() #Mean
supermarket_safeway_min <- Supermarket_Data$safeway_unit_price %>% min() #Min
supermarket_safeway_max <- Supermarket_Data$safeway_unit_price %>% max() #Max
supermarket_safeway_range <- supermarket_safeway_max - supermarket_safeway_min
supermarket_safeway_var <- Supermarket_Data$safeway_unit_price %>% var() #Variance
supermarket_safeway_sd <- Supermarket_Data$safeway_unit_price %>% sd() #Standard Deviation
supermarket_safeway_iqr <- Supermarket_Data$safeway_unit_price %>% IQR() #Interquartile range
#Supermarket price differnce Stats
supermarket_difference_n <- Supermarket_Data %>% nrow() #Count (n)
supermarket_difference_mean <- Supermarket_Data$unit_price_difference %>% mean() #Mean
supermarket_difference_min <- Supermarket_Data$unit_price_difference %>% min() #Min
supermarket_difference_max <- Supermarket_Data$unit_price_difference %>% max() #Max
supermarket_difference_range <- supermarket_difference_max - supermarket_difference_min
supermarket_difference_var <- Supermarket_Data$unit_price_difference %>% var() #Variance
supermarket_difference_sd <- Supermarket_Data$unit_price_difference %>% sd() #Standard Deviation
supermarket_difference_iqr <- Supermarket_Data$unit_price_difference %>% IQR() #Interquartile range
paste(
sprintf ("Supermarket Unit Price Summary Statistics"),
sprintf("=========================================\n"),
sprintf(" \t\t Coles\t\t Safeway\t Difference"),
sprintf(" \t\t -----\t\t -------\t ----------\n"),
sprintf("Sample Size \t: %8.0f\t %8.0f\t %8.0f", supermarket_coles_n, supermarket_safeway_n, supermarket_difference_n),
sprintf("Mean \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_mean, supermarket_safeway_mean, supermarket_difference_mean ),
sprintf("Min \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_min, supermarket_safeway_min, supermarket_difference_min ),
sprintf("Max \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_max, supermarket_safeway_max, supermarket_difference_max ),
sprintf("Range \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_range, supermarket_safeway_range, supermarket_difference_range ),
sprintf("Variance \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_var, supermarket_safeway_var, supermarket_difference_var ),
sprintf("Standard Deviation \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_sd, supermarket_safeway_sd, supermarket_difference_sd ),
sprintf("Interquartile range \t: %8.4f\t %8.4f\t %8.4f", supermarket_coles_iqr, supermarket_safeway_iqr, supermarket_difference_iqr ),
sep = "\n"
)%>% cat()## Supermarket Unit Price Summary Statistics
## =========================================
##
## Coles Safeway Difference
## ----- ------- ----------
##
## Sample Size : 61 61 61
## Mean : 0.2253 0.2085 -0.0168
## Min : 0.0006 0.0006 -1.7100
## Max : 4.5000 2.9000 0.9000
## Range : 4.4994 2.8994 2.6100
## Variance : 0.6445 0.4442 0.0717
## Standard Deviation : 0.8028 0.6664 0.2678
## Interquartile range : 0.0209 0.0210 0.0015Examining the mean unit prices for Coles and Safeway, it appears Safeway mean prices are lower with figure of 0.2085 as opposed to 0.2253
Data Visulaisation
Box Plots
Review of the box plot of the product prices indicated the means, visually appear to be approximately the same.
boxplot(
main = "Product Price Distributions for Coles and Safeway",
Supermarket_Data$coles_price,
Supermarket_Data$safeway_price,
ylab = "Supermarket Prices",
xlab = "Supermarket"
)
axis(1, at = 1:2, labels = c("Coles", "Safeway"))
#### Testing for Assumption of Normality QQPlots were used to test the assumption of normality. Whilst the data generally appears not to be perfectly normally distributed, the Central Limit Theorem implies the sampling distribution of the mean will be approximately normally distributed when the sampling size is greater than 30. This holds in this case as the n=61.
qqPlot(
main = "Testing the Assumption of Normality for Differences",
Supermarket_Data$price_difference, dist="norm")
### Visualisation of Mean Differences
The granova plot provides us with an excellent visualisation of product unit price differences between the supermarkets. The solid black line and thick dashed red lines running diagonally from left to right are indicative of the differences. The thick black dots are indicative of the positive and negative differences between the product unit prices. My rudimentary understanding and observation from this plot is that visually, the unit price differences between the two supermarkets appear to be minimal. (Hoping to know much more about tis plot after I take the visualisation subject)
library(granova)
granova.ds(
data.frame(Supermarket_Data$coles_unit_price, Supermarket_Data$safeway_unit_price),
xlab = "Coles Supermarket",
ylab = "Safeway Supermarket"
)
## Summary Stats
## n 61.000
## mean(x) 0.225
## mean(y) 0.208
## mean(D=x-y) 0.017
## SD(D) 0.268
## ES(D) 0.063
## r(x,y) 0.950
## r(x+y,d) 0.516
## LL 95%CI -0.052
## UL 95%CI 0.085
## t(D-bar) 0.490
## df.t 60.000
## pval.t 0.626Hypothesis Test
In the case of this investigation, as products were selected at the first supermarket and matched at the second, the samples are said to be ‘related’ and the measurements are considered to be paired or dependant. Hence the paired-samples t-test (also known as the dependent samples t-test) was used to determine if there is a statistically significant difference between the mean unit prices of Coles and Safeway supermarket products. This test assumes the data are normally distributed, applying the Central Limit Theorem as n>30. Specifically, the assumption of normality lies in the distribution of the difference between the unit prices. This assignment investigated if there is significant price difference between the mean of the product unit prices between the two supermarkets. A two-tailed, paired t-test was used to test this hypothesis.
The Null and Alternate Hypothesis for this component of investigation are presented as follows:
Null Hypothesis: There is no difference between Coles and Safeway product unit prices, H0:μΔ=0
Alternative Hypothesis : There is a significant price difference in the prices between Coles and Woolworths, HA:μΔ≠0
t.test(Supermarket_Data$coles_unit_price, Supermarket_Data$safeway_unit_price,
paired = TRUE,
alternative = "two.sided")##
## Paired t-test
##
## data: Supermarket_Data$coles_unit_price and Supermarket_Data$safeway_unit_price
## t = 0.49009, df = 60, p-value = 0.6259
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.05177683 0.08538207
## sample estimates:
## mean of the differences
## 0.01680262Interpretation
A paired-samples t-test was used to test for a significant mean difference between unit prices at Coles and Woolworths Supermarket. The mean difference in the unit prices was found to be 0.0168 (SD = 0.2678). Visual inspection of the Q-Q plot of the unit price differences was indicative of the data being approximately normally distributed.
The paired-samples t-test failed to find a statistically significant mean difference in unit prices between Coles and Safeway supermarkets, t(df = 60) = 0.49009, p < 0.6259, 95% [-0.0518 0.0854]. The investigation failed reject the null hypothesis and did not find statistically significant evidence to support the alternative hypothesis. There was no significant evidence found to support the view that product unit prices were significantly different at each supermarket.
Discussion
When comparing unit prices between Coles and Safeway supermarkets, the investigation failed to find significant evidence to support there was a difference in product unit prices. In conclusion, from a statistically significant perspective it appears the products at both Coles and Safeway are similarly priced. Whilst I have a personal preference for Safeway and was of the opinion they were cheaper, findings from my investigation appear not to support my views.
One of the limitations of this investigation was the man/person power required to conduct the sampling. More human resources may have enabled a collection of a larger sample that may have been more representative of the population. One thing I would consider for future similar investigation would be endeavouring to acquire a larger sample size and sample across more product categories and increase the randomisation of the sample. I would also consider approaching the Supermarkets directly to provide the entire product pricing and in a tabular format. This would facilitate a significantly more accurate analysis. One of the strengths of the investigation was the speed and reduced manual calculations at which the computations and analysis was done.