Bootstrapping Statistics in Canada

Bootstrapping is a technique used in statistics, which has gained popularity in recent years thanks to its flexibility and ability to provide accurate estimates of variability in a wide range of applications.

The term bootstrapping can also refer to a business strategy that involves starting and growing a company with personal savings or revenue generated by the business itself rather than taking out business loans or receiving funding from investors.

In this article, we start with what bootstrapping is and how it works. We will then cover the benefits and limitations of bootstrapping as well as look at examples of bootstrapping in Canada and companies that started as bootstrapping enterprises.

Bootstrapping Statistics for Canadians

• Bootstrapping is a statistical resampling technique that is used in a variety of settings in Canada.
• Bootstrapping can be more accurate than more traditional methods, especially when dealing with smaller sample sizes.
• Bootstrapping can be used to test hypotheses, assess accuracy, and estimate confidence intervals.
• Bootstrapping in Canada is used in, for example, environmental sciences, finance, and to create economic forecasts.
• Some Canadian bootstrapping companies such as Wattpad, Shopify, and Hootsuite.
• Starting a bootstrapping company can make it more challenging and mean slower growth as it is solely funded by the founder or founders.

What is Bootstrapping?

Bootstrapping, a statistical resampling technique involves the process of creating multiple subsets of datasets. These are randomly sampled with replacements from the original dataset. The subsets are called bootstrap samples and are used to estimate the distribution of a specific statistic of interest.

The idea behind bootstrapping is to use data from a sample to simulate what would happen if the study or survey had access to the entire population. We can estimate the uncertainty and variability of a statistic by creating a range of bootstrap samples and then calculating the statistics of interest for every sample.

It is a powerful technique because no assumptions about the underlying distribution of the data are required. Bootstrapping can be used to perform hypothesis testing, estimate confidence intervals, and assess the accuracy of a range of predictive models.

Bootstrapping is especially useful when the available sample size is small or the population distribution is non-normal or unknown. The technique is commonly used in data mining and machine learning to estimate model performance and validate a model’s results.

How Does Bootstrapping Work?

There are basic steps to the bootstrapping technique which are as follows:

• Choosing a sample size: This is the number of data points included in each bootstrap sample. Typically, this will be the same as the original dataset.
• Creating bootstrap samples: For each sample, users need to select random data points from the original set of data with replacements. This means that while some data points will be selected more than once, others may not be selected at all.
• Calculating the statistic: The statistic of interest could be median, mean, variance, or any other measure that the users want to estimate.
• Estimating the distribution of the statistic: When the statistic of interest has been calculated for each bootstrap sample, the estimates can be used to approximate the distribution of the statistic. As an example, the bootstrap sample means could be used to plot a histogram to estimate the distribution of the population means.
• Calculating confidence intervals: The estimated distribution of the statistic can then be used to calculate confidence intervals for the estimate. For example, a 95% confidence interval for the population mean could be calculated by finding the range of values that include 95% of the sample means for the bootstrap.

How is Boostrapping Used in Canada?

Bootstrapping is used for a variety of purposes in Canada just as it is in many other countries, too. Ways that bootstrapping is used in Canada include:

Economic Forecasting

In economic forecasting, bootstrapping is used to estimate the uncertainty of economic indicators such as inflation, GDP, and employment. Bootstrapping allows economists to simulate a range of scenarios and assess the potential impact of policy decisions.

Market Research

In market research, bootstrapping is used to estimate the uncertainty of market research data. Research can create multiple bootstrap samples of a survey and use them to estimate confidence intervals as well as to determine the statistical significance of differences between various groups.

Finance

Bootstrapping is used in the financial sector to estimate the value of financial derivatives such as swaps and options. By using the market data to create multiple bootstrap samples, financial analysts can assess the risk of different investment strategies and estimate the probability distribution of future prices.

Environmental Science

In the field of environmental science, bootstrapping is used to estimate the uncertainty of environmental models. Based on multiple bootstrap samples of environmental data, researchers can assess the potential impact of a range of environmental scenarios and estimate confidence intervals.

Why is Bootrsapping Used in Canada?

There are various reasons why bootstrapping is used in Canada. These include:

Improved Accuracy

Using bootstrapping can improve the accuracy of statistical estimates, especially when the sample size is small or the distribution of the population is non-normal or unknown. Creating multiple bootstrap samples and estimating the variability using bootstrapping can provide researchers with more precise estimates and reduce the risk of incorrect conclusions.

Validity of Inference

Bootstrapping is useful in assessing the validity of statistical inference, especially when more traditional methods would not be reliable or applicable. By using bootstrap samples to stimulate the distribution of the statistic of interest, the technique can provide more robust estimates of p-values, confidence intervals, and other statistical measures.

Flexibility

Because bootstrapping is such a flexible technique, it can be applied to a wide range of statistical analyses which include hypothesis testing, machine learning, and regression analysis.

Non-Parametric

Bootstrapping is a non-parametric technique, meaning it does not require any assumptions of the underlying distribution of the data. This quality makes it a helpful technique if the collected data does not follow a normal distribution or if there is uncertainty about the underlying distribution.

Examples of Bootstrapping in Canada

Bootstrapping in Canada has been used in the estimation of poverty rates. The government uses a measure known as the Low-Income Measure (LIM) to estimate the proportion of the Canadian population living in poverty. The LIM, however, is based on a fixed threshold that does not take into account, for example, the different living costs in different regions. Bootstrapping has been used to create new measures that take the variables into account and therefore provide more accurate estimates.

Another example of bootstrapping in Canada is the estimation of the impact of government policies on the economy. For example, in 2020 the Canadian government introduced a wage subsidy programme during the COVID-19 pandemic. They used bootstrapping to estimate what effect this policy would have on GDP and employment levels, which provided policymakers with information on the subsidy program’s effectiveness.

Another application of bootstrapping is to evaluate business performance metrics including customer lifetime value (CLV) and return on investment (ROI). By using bootstrapping to estimate the variability of these metrics, companies can gain a better understanding of the uncertainties and potential risks associated with their investments.

What Are Bootstrapping Companies?

The term bootstrapping can also be used to describe companies that are self-funded. This means they were started and grown using the personal savings of the founder, revenue generated from sales, and reinvested profits instead of relying on external funding through loans or from investors.

Bootstrapping businesses tend to prioritise profitability rather than rapid growth and often rely on the lean business mode to keep their expenses low. This may include operating from home and using open-source software as well as outsourcing certain tasks to freelancers instead of employing permanent members of staff to perform those tasks.

Bootstrapping is a viable, and popular, option for entrepreneurs who want to avoid taking on debt and maintain control of their business rather than giving up equity to investors. However, it can be a challenging business model as the founder or founders bear the full financial risk and this may limit their resources to invest in growing the business.

Some examples of bootstrapping companies include Mailchimp, Meta, Basecamp, and GitHub.All of these companies started small and grew gradually which meant they were able to become profitable without relying on external funding.

Bootstrapping Companies in Canada

Over the years, there have been many Canadian bootstrapping companies that have found success. Below are some Caniand bootstrapping companies.

Hootsuite

The social media management platform Hootsuite was founded in Vancouver, BC in 2008. It allows businesses and individuals to manage their social media accounts, track analytics, schedule posts, and engage with their audience. It supports popular social media platforms including Facebook, Instagram, YouTube, and Twitter. The platform has over 18 million users worldwide. The company has a valuation of over $750 million.

FreshBooks

Freshbooks is a cloud-based accounting software. It is designed for self-employed professionals and small business owners to manage their finances, expenses, and invoicing. Users can create and send invoices, manage their expenses, track time spent on tasks, and generate financial reports. The company, which was founded in Toronto, Ontario in 2003, has since grown into a widely used tool for freelancers and small business owners. FreshBooks has been valued at over $1 billion.

Shopify

Shopify, founded in Ottawa, Ontario in 2004, is an e-commerce platform with over one million merchants worldwide. The platform allows businesses and individuals to create their own online stores and sell their products and services online. It includes features such as payment and shipping options, tracking orders, inventory management, and customer management. Shopify serves over one million businesses worldwide and is valued at over $100 billion.

Wattpad

Founded in Toronto, Ontario in 2006, Wattpad has grown into a global multi-platform entertainment company. It is one of the most successful bootstrapping companies in Canada with more than 90 million users worldwide. Wattpad allows users to publish their stories online and users can follow their favourite writers and interact with other readers and writers through messages, comments, and voting. In 2021, Wattpad was acquired by a South Korean internet company Naver in a deal worth in excess of USD 600 million.

Vidyard

Vidyard was founded in Kitchener, Ontario in 2010 and is a video platform with over 1,200 customers worldwide. It provides businesses with the tools to create and share videos for various purposes including sales, marketing, and customer support. It also allows users to share their videos on social media, websites, and email campaigns.

Summary

Bootstrapping is a term that is used to describe a statistical resampling technique as well as a type of business that is self-funded. Bootstrapping as a statistical tool is used for a wide range of purposes in Canada including economic forecasting, environmental science, market research, and finance.

While starting a business using bootstrapping, which means not taking out any loans or money from investors, can be challenging, several Canadian companies that started that way have grown into successful companies that operate worldwide.