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Drunks and Lampposts

It’s Time to Become Conversant in Statistics

Imagine if the key to your extraordinary success could be found in data sitting right in front of you. All you need to unlock that success is to know the right questions to ask of the data and to understand the responses they give.

Developing a digital mindset means using data to advance your goals and develop an intuitive sense of underlying patterns in data that can work for you. Having data isn’t an issue. There’s an abundance of it that would be hard for previous generations to fathom. Interpreting the data and drawing conclusions from them are what you need to do. You want to use data as evidence that drives sound decisions and strategies.

Often, this requires statistics. Even if you are not conducting statistical analyses, you need to know how that’s done so you can provide directives to the team that will help you uncover the right information you need in your work. In this chapter, we will provide the minimum threshold of computational material you need to understand about statistics to develop your digital mindset.

Historically, statistics has gotten a bad reputation as something people use to twist data into saying what they need it to say. There’s a famous saying, often attributed to the Scottish novelist and folklorist Andrew Lang that’s a good reminder of the perils of statistical reasoning. It goes, “Statistics are used much like a drunk uses a lamppost, for support, not illumination.”¹ Of course, that’s the very antithesis of having a digital mindset. While it’s true that numbers can be twisted or misinterpreted, resulting in erroneous conclusions, or manipulated to bolster weak arguments, that’s all the more reason for you to have a basic understanding of it—to spot the distortions and mistakes. You don’t need to become an expert statistician, but once you have collected data, statistical analyses can be a powerful tool to make sense of what is otherwise a confusing morass. If you are one of the many people who believe that the study of statistics is overly confusing, boring, or intimidating, we are here to tell you not to worry. Statistics is just this: math used to analyze numerical or quantitative data. Understanding what types of statistics are available for what purposes will enable you to glimpse the reality of what interests you. You may even find it fun.

Whether you choose to learn how to run statistical analyses or not, there is one key prerequisite to developing a digital mindset with statistics: you must think like a data detective. Good detectives ask the right questions to get the answers they need. Good detectives observe what they see and pay attention to details. Sometimes you might need to come up with a reasoned conclusion from a hypothesis, which will require you to ask for certain types of data collection. Other times, you will need to take observational data and work backward to a plausible hypothesis.

To get to 30 percent with statistics, let’s start by understanding two types: descriptive statistics and inferential statistics.

Descriptive Statistics: What Are the Underlying Patterns in the Data?

Suppose you started a streaming platform: How would you learn how your customers use your service? You might begin by collecting data about your customers’ usage preferences, including when they logged in and for how long. This information would give you a measure of your service’s performance. Spotify, a Swedish audio streaming and media service, measures performance in this way. But it’s the use of statistics that enables the company to detect answers to questions about how their customers use their service. For example, is usage going up or down each month and by how much? How does it differ from last year? Spotify used statistics to learn that in 2017, their users played an average of 630 audio streams per month (up from 438 in 2015).² In 2019, average revenue per user (ARPU) was $5.32 USD (down from $5.51 in 2018).³ To discover this information, Spotify needed to run some descriptive statistics.

Descriptive statistics summarize the features of a data set. They describe the data.

Once you are able to see the patterns of the raw data, descriptive statistics can represent that data in useful ways. You may have experienced descriptive statistics in assessing an organization’s past performance, since that is an area where they are commonly used. Key performance indicators (KPIs) across all aspects of a business, from sales to human resources, are descriptive statistics in action.

Amazon uses descriptive statistics to determine the demographic characteristics of its customer base and then measures those findings against averages of the overall population in order to determine the average customer age and the average customer income. They can build a profile of the typical user and keep building it to see how it evolves and how it compares to other groups. In a November 2019 report, the data showed that Amazon customers tended to be younger and have a lower income than the average US consumer.⁴

Spotify and Amazon were able to understand their customers’ characteristics and needs by analyzing descriptions of their past behaviors as collected in the data. Such statistics could then inform all sorts of business decisions and initiatives.

The trick with descriptive statistics is to know which ones matter. There are plenty to create and analyze, and plenty will look like they might mean something you need to know, but not all do. To figure out what was statistically important, companies like Spotify use summary statistics that focus on two main features of a data set: central tendency and dispersion. Let’s look at each in turn.

Central tendency

These statistics describe where the values of a data set tend to land. The most common measure of central tendency is the mean, or the average of a data set (each value of the data added together, then divided by the number of values). Other measures are median (the value that falls at the midpoint of all your data), and the mode (the most common value in the range of data). In the examples above, both Spotify and Amazon analyzed for central tendency statistics. For example, Amazon looks at average or mean number of purchases in a time period. Spotify looks at the most common genre streamed (the mode).

Dispersion

These statistics analyze how the data are spread out. Measurements of dispersion can be as simple as the range of the data (the difference between the highest value and the lowest value). Other more complex measurements are variance (an estimate of the distance of each value from the mean) and standard deviation (a measure of how spread out the data are from the mean).

For example, suppose you wanted to know how engaged your employees were at work. The 2018 Gallup poll defines employee engagement by asking employees the extent to which employees are involved in, enthusiastic about, and committed to their workplace.⁵ They found that the annual percentage of engaged US workers in the past two decades has ranged from a low of 26 percent to a high of 34 percent in 2018—a measure of dispersion—and averaged out at 30 percent, a measure of central tendency. Ultimately, they used these statistics to show that the higher percentages in employee engagement are associated with higher business performance for the organization.

In developing your digital mindset around statistics, remember that descriptive statistics are a method of finding the underlying patterns in data. Depending on what you want to know, the same data can be used to answer many different questions. Spotify could also run the numbers to describe which song was downloaded the most frequently, for example, or compare which song was most frequently downloaded depending on the season. Amazon could analyze the same data to describe the range of incomes of their customers or compare that range with geographical data to describe which locales tended to have the most customers. The possibilities are nearly endless.

Inferential Statistics: What Conclusions Can We Draw from the Data?

While descriptive statistics summarize the underlying patterns of data that have already been collected, inferential statistics examine the data from a relatively small subset of the total population—called a sample set—that might reflect the nature of the broader population. For example, the Gallup poll about employee engagement only asks a tiny fraction of all US workers how they feel, but then draws inferences from those responses that apply to the entire population.

In order for a sample to reliably represent a bigger population, the people that comprise the data set must be selected randomly—that is, pulled from the overall population without any preconceived criteria. For example, you could ask a sample of 500 people that you see in the mall if they like shopping at the Apple store. If 250 people say “Yes,” and 250 people say, “No,” you can infer that 50 percent of the population in all malls like shopping at the Apple store.

Think of inferential statistics as the method that allows you to draw statistical conclusions and make predictions without collecting data from everyone you are trying to understand. The auto insurance company Geico wanted to determine the level of risk for a potential customer. One of the first questions that the company website’s risk calculator asks is marital status.⁶ A married driver is considered a lower risk and given lower premiums. How did Geico reach this conclusion? Their policy is based on inferential statistics—the available data show that married people on average get into fewer accidents than unmarried people. Geico used the sample set to infer that this average reflects the population as a whole.⁷

What if your company wants to determine the likelihood that consumers will buy from you? Inferential statistics are often used for this purpose. Consider the work of startup Embr Labs, which produces an innovative wrist-wearable device that regulates an individual’s body temperature.⁸ The estimated demand for the product was initially based on statistics from a UC Berkeley study that analyzed the relationship between people’s personal comfort and room temperature. Relying on the statistical evidence from the study’s sample data, Embr inferred that demand for a product regulating body temperature would be high for a population of consumers much broader than those actually studied at UC Berkeley.⁹

We make inferences all the time. If rain is predicted, we infer we will need an umbrella when we go out. Learning to use numerical insights to inform a digital mindset means fine-tuning this natural way we think. Technically speaking, there are two main approaches used to draw inferences from a sample: confidence intervals and hypothesis testing.

Confidence Intervals: How Reliable Is My Inference?

It’s easy to say that because 30 percent of people say they’re engaged at work in a survey that means 30 percent of all workers are engaged at work, but how sure are you that what a few people said in a survey applies to everyone?

That’s what confidence intervals are used for: to assess the reliability of our inferential statistics. They are used in market research, risk assessment, or budget forecasting. Election forecasts derived from polled sample sets of the voting public are an inference we see regularly in politics that have confidence intervals attached to them.

Another way to think about it is that a confidence interval describes the plausibility of the range of values of summary statistic like an average in the overall population. If you were completely certain that our inference would play out in a broader population you would have a 100 percent confidence interval. Conversely, if you think your inference is wrong, you’d have a 0 percent confidence interval. A 50 percent interval is effectively a guess.

In practice you don’t see confidence intervals like this. The most commonly used confidence interval is a “95 percent confidence interval” because this number represents a comfortable balance between precision and reliability. A 99 percent confidence interval may appear to be more reliable, but it would necessarily have a much wider range of possible values and therefore be less useful.

For example, we could say with 99 percent confidence that the average age of MBA students is between eight and eighty, but that wide a variance in ages wouldn’t be saying much, would it? Alternatively, we could calculate a 90 percent confidence interval indicating that the average age of MBA students is between twenty-seven and thirty, but there is a greater possibility that this range is inaccurate because it’s too narrow; some students may in fact be twenty-five or thirty-two or thirty-five years old. The range of a confidence interval depends on the variance in the data set. Higher variance in the data—as in our theoretical MBA population of students aged eight to eighty—limits our ability to draw inferences about the greater population, and results in a wider range of values for the confidence interval. Variance in the data that is too low also limits our ability to draw meaningful inferences.

Consider the example of a McKinsey study on the business value of diversification—companies entering into new industries. From a sample of over forty-five hundred companies, the study found that diversification in emerging markets led to a higher average value for companies than did diversification in developed markets. Note, however, the confidence intervals for each of these averages. The -0.2 percent decrease in average value for diversification in developed markets has a relatively tight 95 percent confidence interval, while the 3.6 percent average value increase for diversification in emerging markets has a much wider 95 percent confidence interval. In other words, the study is more confident that the statistics showing a small decrease of value (0.2 percent) in developed markets are true for all companies across the world, and less confident inferring that the larger increase of value (3.6 percent) in developing markets is actually true for all companies across the world.¹⁰

Becoming comfortable with the statistical insights a digital mindset affords is more about having the vocabulary to understand the different relationships between numbers than memorizing percentages or specific numbers. Having the vocabulary to describe these basic concepts means you will be able to discern, for example, if you have cause to doubt statistical conclusions that have been drawn from a sample size because it has too wide or too narrow a confidence interval.

Hypothesis Testing: How Do I Compare Statistical Evidence?

A digital mindset informed by numerical insights can also ask questions by comparing two or more pieces of statistical evidence. Are people more likely to purchase your product in the winter or the summer? Do teams that contain an equal number of men and women do better than teams that contain an unequal gender distribution? To answer questions like these using statistics requires that you use a methodical process called hypothesis testing. The basic format for hypothesis testing compares two summary statistics (or parameters) in a set or multiple sets of data. The test starts with what’s called a null hypothesis, most often a conservative position that assumes the status quo. It then proposes an alternative hypothesis. If there is enough statistical evidence to support the alternative hypothesis, the null hypothesis is rejected in favor of the alternative. However, if there is not enough statistical evidence, the null hypothesis remains.

Let’s create a hypothesis test for the actual average age of Harvard MBA students based on the data from a sample of thirty students. Let’s say the average age of the sample is twenty-six, and you come across an article online stating that the average age of MBA students at top business schools is twenty-eight. Does this mean that the average age of all Harvard MBAs is actually different from the overall average of MBAs at top programs? Not necessarily—remember, the sample set represents only a portion of the Harvard MBAs; the overall student body may actually have an average age that is different than twenty-six.

Indeed, as the statistic found online seems to imply, the average of the overall MBA student population could very well actually be twenty-eight. That average comes from a much bigger sample set (students at multiple MBA programs rather than just the thirty Harvard MBA students), so let’s take twenty-eight as the baseline assumption and test it. A hypothesis test can assess the likelihood that the average age of the thirty MBA students is twenty-eight or in fact different, as your sample set indicates.

First, formulate a null hypothesis: “The average age of Harvard MBA students is twenty-eight.” Then, propose the alternative hypothesis: “The average age of Harvard MBA students is NOT twenty-eight.” Now calculate the probability of seeing the average age in your sample set—twenty-six—under the assumption that the hypothesis test is true. In other words, you are asking how likely it is that you would see an average age of twenty-six in your sample set of thirty Harvard MBAs if the average age of all Harvard MBAs is actually twenty-eight. If you find that probability is very low, you can reject the null hypothesis in favor of the alternative hypothesis. However, if, for example, you calculate a 2 percent chance of seeing an average age of twenty-six in your sample set of thirty students if the actual average of the overall student population is twenty-eight, that’s some pretty convincing statistical evidence in favor of your alternative hypothesis. You may conclude that, statistically, the average age of a Harvard MBA is likely to be twenty-eight, in keeping with the larger sample size. Again, hypothesis testing is a very specific method of statistical analysis. Understanding how such a method can provide numerical insights is part of developing your digital mindset.

A classic use of hypothesis testing is A/B testing, a methodology used in marketing and product development for digital products such as apps and websites that we will discuss more in chapter 6.¹¹ A/B testing compares user response to two variations (A and B) of a specific product in order to determine which version is more effective. In a standard A/B test, the null hypothesis would be that versions A and B have the same usage rate. The alternative hypothesis would be that version B (an experimental variation of the product) attracts more users than version A (the current version of the product). The test would then calculate the probability of observing the usage rate of version B under the premise that the null hypothesis is true. Let’s take a look at two examples of how A/B testing has led to highly successful marketing campaigns and products.

Electronic Arts (EA) is one of the largest video game companies in the world. Their SimCity games allow players to build cities from scratch. For SimCity 5, released in 2013, EA used A/B testing to create an effective online marketing campaign. Version A of the game’s web page offered anyone who bought SimCity 5 20 percent off a future EA game purchase. Version B of the page did not offer the discount on future purchases but did give users the ability to preorder SimCity 5. Surprisingly, the version without the discount incentive performed 40 percent better than the preorder version. The A/B testing showed EA that SimCity customers, contrary to the alternative hypothesis, were not as interested in other game options as some might expect; most customers were there specifically for the SimCity franchise.¹² The null hypothesis remains. In this case, the testers were digitally minded when they compared customer responses to the A/B offers. The marketers were also digitally minded when they relied on the results of A/B testing to guide their selling strategy.

In another example, HubSpot, a software development company specializing in marketing, sales, and customer service software products, used A/B testing to determine the best design for a search bar at the top of its web page. The test was composed of three versions of search bars (A, B, and C). In Version A, the search bar included the text “Search by Topic” and provided results from across the entire HubSpot site. Version B had the same text but provided results only from within the blog instead of the entire site. Version C changed the text of the search bar to “Search the Blog” and provided results for only the blog. The results of the test showed that usage rate was highest in Version C.¹³

In the SimCity and HubSpot examples, the data, once collected and analyzed, offered evidence for the best possible choice. EA could conclude that there was no benefit in offering customers a discount on future games when selling the new SimCity. HubSpot could conclude that search bar text “Search the Blog” would lead to higher usage than the other two versions. If you were reviewing these conclusions, you would also want to ask how high or low the numerical difference between the data results has to be before rejecting or accepting the null or alternative hypothesis. In that case, you would want to know about the p-value, which refers to the probability of observing the statistics in a sample data set if you assume that the given null hypothesis is true. A smaller p-value means there is stronger evidence in favor of the alternative hypothesis, while a significance level is the designated threshold that marks the maximum limit that a p-value can be before you say it is too high to reject the null hypothesis in favor of the alternative. A common significance level is 0.05: if the p-value is below 0.05, then you reject the null hypothesis in favor of the alternative. If the p-value is above 0.05, then you reject the alternative and retain the null.

Possibility of Being Wrong

We love how Larry Gonick and Woolcott Smith describe the possibility of being wrong when making statistical inferences. You can never say you are “100 percent confident” about a data sample representing the properties of an overall population precisely because you want to acknowledge the fact that you could be wrong. Gonick and Smith use the analogy of smoke detectors to describe the two types of errors that you can anticipate in hypothesis testing and significant tests. They call the first a type I error, an alarm without fire (or a false positive). The second, referred to as type II error, is fire without an alarm (a false negative). “Every cook knows how to avoid a type I error: just remove the batteries. Unfortunately, this increases the incidence of type II errors! Similarly reducing the chance of a type II error, for example by making the alarm hypersensitive, can increase the number of false alarms.¹⁴

Type I error: An alarm without fire

Type I error is an outright rejection of the null hypothesis when it is actually true. Consider the ramifications of this error in the example of EA’s SimCity video game sales page. What if the null hypothesis that favored the presale offer page (version A) was actually true after all? Then EA would lose potential sales revenue by choosing version B, which seemed more effective based on available (and apparently misleading) data. If we want to reduce the likelihood of committing a type I error, we can lower the significance level (for example, to 0.01), making it even more difficult to reject the null hypothesis. However, this cautionary approach increases the likelihood of a type II error.

Type II error: Fire without an alarm

Type II error is failing to reject the null hypothesis when the alternative is true. For example, let’s imagine that HubSpot’s A/B test for the search bar on its blog page led to the mistaken conclusion that their original design and functionality for the search bar remained the most effective. This mistake would prevent HubSpot from adopting the new version of the search bar, which in fact had a higher usage rate. To reduce the likelihood of this error, we can raise the significance level (for example, to 0.10) to make it easier to reject the null hypothesis. However, this more flexible approach increases the likelihood of committing a type I error and moving forward with data that are actually meaningless or misleading. See table 4-1 for a breakdown of these errors (H₀ is “null hypothesis” and H_A is “alternative hypothesis”).

This possibility of error, either in reasoning or numerical calculation, and the fact that we must make decisions with the knowledge of their possibility is perhaps what gives credence to the quote about “lies, damned lies, and statistics.” A digital mindset means accepting the fact that numbers don’t lie but the humans interpreting the numbers may make mistakes. The real error might be in expecting 100 percent accuracy from statistical analysis. Your decision-making will be guided by understanding that the likelihood of each type of error is affected by the relative value of the significance level. Raise it and you increase the chances of a type I error. Push it down and chances of a type II error increase.

Predicting Outcomes with Regressions

A statistically informed digital mindset requires a general understanding of predictive modeling, which could be described as using statistical models to predict outcomes. A common model used to make predictions is the linear regression model.¹⁵

You don’t need to run regressions, but you need to understand how they function and when they are important to use. For now, you just need to remember that a regression analyzes the relationship between two or more variables or factors. It is an essential tool for predictive analytics to forecast potential outcomes, opportunities, and risks. Regression is also used to increase operational efficiencies, from product development to hiring practices.

For example, McKinsey wanted to examine if an organization’s demographic diversity, defined as “a greater share of women and a more mixed ethnic/racial composition in the leadership of large companies,” had an impact on financial performance.¹⁶ The study’s model used financial data and leadership demographics from hundreds of organizations and thousands of executives. By placing each organization’s financials on the Y axis and its leadership demographics on the X axis, the study sought to determine if higher X values (how diverse the company was) were matched by higher Y values (how well the company was doing).¹⁷ Based on the model, the study found a positive association between a more diverse leadership and financial performance: more diverse leadership teams were in organizations with better financial results. On a chart the dots plotted would literally trend up and to the right. Diversity and performance rose together.

Linear regression is a powerful tool in predicting future sales and demand for a product. For example, if a sales manager can map product demand on customers’ annual salary, the manager could then predict the demand of the product based on a specific salary of an individual consumer. A customer with a salary below a certain value would presumably be less likely to buy a particular product. Additionally, too high a product price might lower customer demand.

Another manager could use linear regression if interested in the actual price of kids’ shirts as a function of a given year to predict values for future years. These concepts of supply and demand and their relationship to price points are fairly intuitive and have been in existence since before computers came on the scene. With a digital mindset, however, you can access computational power and large data sets to run linear regression models to make predictions that have more accuracy and granularity.

Regression is also a key tool for improving business processes across all aspects of an organization, from operations to human resources. For example, a product developer might use a regression model to determine a possible relationship between the number of software developers on the team and the effectiveness of the product. Questions to ask include: Is there an optimal number of people on such a team? How many software developers are too many? How many are too few? To find the answers requires plotting the number of team members on one axis and a measure of product effectiveness on the other axis and then looking for relationships between the two. The model would help determine how to organize the team to maximize its performance. Or a hiring manager might use a regression model to explore a possible relationship between job candidates’ background and qualifications for a role. The model would help refine the manager’s search for the right pool of candidates to interview for the job.

Bear in mind, also, that you want to be intelligent about the variables you plot on the X and Y axes. If you were to, for example, use a regression model to conclude your best employees all had names that began with the letter S, you would not have optimized meaningful data for future job candidates. Even if that were true, it’s random and doesn’t inform you about the future. Again, it’s a matter of what questions you ask and what you want to know. As is so often the case when using a digital mindset, what’s important is to understand the stories the numbers can tell you rather than computing the numbers themselves.

P-value in regression

In the McKinsey diversity study cited above, 366 companies were in the sample set. The analysis shows the statistical significance of the relationship between diversity and financial performance for companies observed in the data. For the executive teams in the data of 366 companies, the EBIT (“Earnings before interest and taxes,” a measure of financial performance) margin is predicted to increase by 1.6 percent for every 10 percent increase in the gender diversity metric. The p-value of 0.01 tells us that there is only a 1 percent probability of seeing that coefficient or measure of strength of the relationship between financial performance and gender diversity on the executive board if in actuality there was no relationship between them. In other words, ninety-nine times out of a hundred when you get this result it means diversity correlates to increased performance. The same model was applied to boardroom diversity (as opposed to executive teams) and again found an even stronger connection: EBIT margin should increase by a factor of 3.5 for every 10 percent increase in the gender diversity metric in the boardroom.

However, the corresponding p-value in this case was 0.11, meaning that there is an 11 percent chance of seeing this result even when there was no correlation.

Remember that the lower the p-value, the greater the reliability of the statistical conclusion. In other words, while the predicted increase in financial performance for gender diversity in the boardroom is much higher than it is for gender diversity on executive teams, this prediction is much less reliable.

Correlation vs. causation

In discussing their findings, the authors of the McKinsey diversity study draw a crucial distinction: “The relationship between diversity and performance highlighted in the research is a correlation, not a causal link.”¹⁸ Put more simply, the study’s regression model can only show that financial performance increases as the level of diversity in leadership increases by a certain factor, on average; it does not show that diversity in leadership actually causes financial performance to increase. There are many other elements involved (what statisticians would call “confounding variables”) that must be considered. Perhaps, for example, more diverse companies tend to be in more developed markets where the EBIT for executives would naturally tend higher. Whenever building a regression model to explore the relationship between two variables, businesses must be wary of mistaking causation for correlation. Fortunately, a relationship does not always have to be causal to be insightful; in most cases, a strong correlation is more than sufficient evidence for drawing valuable insights in business and pursuing a course of action.

Integrate Statistics into Your Digital Mindset

So, that wasn’t so bad, right? Just by reading and reviewing this chapter, you have already begun to inform your digital mindset with a basic understanding of statistical concepts and the vocabulary for statistical analysis. You encounter statistics regularly in annual reports, decision-making documents, and in newspaper articles. People often use statistics as evidence to bolster their arguments or to make suggested strategies credible. Developing a digital mindset that can integrate statistics means becoming conversant enough in the language of statistics so as to understand the conclusions drawn from data sets and to form conclusions of your own. As a detective who can ask questions using statistical data, you are likely to put together clues that take some of the mystery out of, for example, product marketing and sales predictions. Statistics can also be used to pose and answer questions about the relationship between data sets—for example, diversity hiring and organizational performance. Sound critical reasoning plays a role when distinguishing between the stories that numbers tell, as in not mistaking cause for correlation or in remembering to scrutinize for p-value. You need statistical analysis to make proper and useful sense of all the data that surround us. Finally, it’s important to remember that while numbers don’t lie, people make mistakes, especially in the numbers we input or in the way we interpret results. As you continue to develop your digital mindset you will become attuned to the many and various ways that statistical analysis can help drive your success.

GETTING TO 30 PERCENT

Statistical Reasoning

Statistics are tools for analyzing underlying patterns in data. Developing a digital mindset means operating like a curious detective who asks the right questions and recognizes the stories that statistics can tell. Understanding a few basic concepts and terms will go a long way.

Descriptive statistics identify patterns in data:

· Central tendency statistics describe where the values of a data set tend to land (mean, median, mode).

· Dispersion statistics analyze how the data are spread out (range, variance, standard deviation).

Inferential statistics allow you to draw conclusions about a population from a sample set of available data.

Confidence intervals are a range of values that estimate the accuracy of a statistic about a population from the available data.

Hypothesis testing is the process of comparing two assumptions in order to assess the likelihood that a data sample actually reflects the overall population:

· The null hypothesis is the assumption of the status quo (there is no actual difference in the sample set and the overall population).

· The alternative hypothesis refutes the null hypothesis (there in fact is a difference in the sample set and the overall population).

The measurement for assessing these two hypotheses is the p-value:

· A smaller p-value means there is stronger evidence in favor of the alternative hypothesis.

· Significance level is an acceptable threshold for a p-value, past which point we can say that the null hypothesis is more likely than the alternative. A common significance level is 0.05.

Predictive statistics use statistical models to anticipate outcomes.

Regression models analyze the relationship between two or more variables by plotting them on an X and a Y axis.

Distinguish between correlation and causation, but remember that in business, a strong correlation is more than sufficient evidence for drawing valuable insights and pursuing a course of action.

You don’t need to become an expert, but keep in mind that statistical analyses are a necessary and powerful tool to interpret data that can otherwise be confusing or useless. Statistical reasoning is more intuitive than you might think at first glance.