Speak Statistics: 6 Memorable Steps to Wield Data Decisively

Why Would I Care to Speak Statistics?

MANOVA. P-test. Kruskal Wallis. Principal Component Analysis.

What does all this mean!?  Statistics is a language, and your inability to speak statistics may spell doom. Why? Because we can be easily deceived: by others and – especially – by ourselves.

This article is for all humans – including those in Academia – but especially directed to those in business and product leadership, namely executives (CxOs), Product Mangers (PM) and User Experience (UX) teams.

Enough indecisiveness! If you can speak English (or any human language), you can speak data.

Read on to never let data daunt you again. Read on to cut through deception.

Statistics is a language: wielding it properly cuts through deception and forms accurate decision.
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Statistics sounds scary. But, it’s actually quite simple. So simple – in fact – understanding it immediately alters how you perceive the world. As data science’s backbone, statistics is so foundational it can impact every presentation and – thus – promotion. 

Allow us to explain this career-building language in a few paragraphs – to condense years of undergraduate and graduate courses into a single page.

Understanding statistics alters how you perceive the world.
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What are Statistics?

What actually are statistics? It’s in the name. Statistics – from the Latin root status – simply describe the state of things. Like grammatical adjectives, statistics are modifiers. A furry cow. 13 cows. Around a dozen cows. All are modifiers, while the latter two counts are a descriptive statistic. All “cows” – a total of a scoped state – is what we call a parameter. More on this later.

Statistics is also a study. A field of mathematics – from the Greek máthēma, “that which is learned” – statistics is a set of learned instructions for how to describe things in our surrounding world. Simply put, statistics are numerical characteristics and also how to derive these characteristics.

Statistics – both as modifiers and as a study – simply describes the state of things.
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Math assumes we know everything about the world. Statistics is far more humble: acknowledging we are a mere part of this world – sampling the unreachable parametrics, or “all-encompassing” characteristics.

Simply put: our counts are limited, a mere sample of things far more constant. We can describe a drop of water, but we must acknowledge it isn’t the entire ocean.

This is paramount to speak statistics.

Math assumes we see everything; Statistics acknowledges we are a part of everything.
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Herein lies your pre-requisite: understanding constants. You are a variable living in a world of variables. Variable – from the Latin variare – describes anything changing. You change. I change. The sun, moon, and stars change.

How can we say this? Because we observe differences across time. Time is the mechanism and the setting for change, for variation. Anything outside time is constant. Strictly speaking, there is only one true constant outside time – one Being presiding over it: “I am that I am”.

Time is the mechanism for variation.
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Now that you know your place in time, you have everything you need to begin speaking statistics. As a PM or UX team member – this is integral to every decision you have to make.

Speak Statistics – Step 1: Ask Questions

Understanding time is essential, because it helps understand why we ask the questions we ask. Humans typically ask about the constants: the unchanging unseen forces affecting the world around us. Which products will increase our company’s revenue the most? Is this career change profitable? No one inside time knows the future. Someone outside time does.

Humans typically ask about the unchanging: the unseen.
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This is the first step: ask questions. People forget: questions are at the base of every statistical inquiry. Why bother counting, calculating, and presenting data if it isn’t answering any question or pain point? The mistake people make is to put limits on their questions. What do you want to answer, even if unanswerable?

How to Ask Questions

Start with brutal honesty. Why do people ask poor questions? Because they don’t understand what they want. Questions stem from desires. What do you want? What decision do you have to make? What outcome do you strive for? What outcome do you strive to prevent?

If we’re honest: questions stem from desires.
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But wait, aren’t we biasing our study? The only unbiased study is one where the experimenter admits their bias a priori – or before it is conducted. It is more irresponsible to pretend you are unbiased – you’re not.

Why? Because honesty is distinct from truth. Your study begins with honesty and seeks the truth. Confirmation bias is the opposite.

For example, you may want a successful product and admit your notions of getting there – and then discover the difference between your thoughts and the truth. Then, you grow.

If you are on a product team, this is simple: a product that is widely adopted, highly useful, different from others, and enriches your users, your company, and yourself is what you should want. Thus, admit it – and ask how to get there.

Discover the difference between your subjective honesty and the objective truth.
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Now, time to write your outcomes.

Speak Statistics – Step 2: Write Outcomes

Outcomes are projected answers to your questions. We don’t merely speak to the “yes” or “no” of a business-critical decision, but reverse engineering every statistic – every description – you need to accurately inform said decision.

Reverse engineer the statistics you need to answer your questions – check biases at the door.
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Take an example: which project should be funded to maximize revenue? The “y” variable hinging on the line, depending on your decision, is your revenue. The “x” variable you are comparing, independently in your manipulation, is the project.

Think like Gandalf: “All you have to decide is what to do with the time that is given to you.” What should I do with x to achieve y?

Failing to scope your variables is like coming back from the store without eggs to cook an omelet. It’ll cost you money and time you don’t have. Let’s take a deeper look.

Failing to scope your statistical variables will cost you time and money you don’t have.
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How to Write Outcomes

At some point you’ll share data with stakeholders to inform or explain a decision. Take a sticky note, and sketch a graph or a tabular answer to your question. The formatting is especially important.

What’s the best way to do this? Role play. Put on the hat of a skeptic: the CEO. Imagine you are being presented data to inform your decision.

Now put on the hat of the presenter and sketch out a few fictitious graphs and tables to inform the CEO’s decision.

Put on the hat of a skeptic.
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Often, this entails breaking your fundamental question into what a healthy audience should scrutinize. Start with this scrutiny. 

Continuing the example – which project to fund to maximize revenue – imagine your CEO or other stakeholders asking: (1) “What generated revenue in the past?”, (2) “What do our customers value most?”, (3) “What do they most use?”.

Each question may use its own slide or – as of now – sticky note. Imagine you wave a magic wand and could answer each with slides. Question 1 may have a pareto chart showing the effects previous projects had on revenue.

Question 2 may have a stacked area chart showing revenue broken down by customer segment, followed by a slide showing a value-per-dollar histogram. Question 3 may have a product-wide heatmap of total customer engagement per current product feature.

Excellent. You’ve broken down the seemingly unanswerable into the answerable. You now know you need to collect data from multiple sources: revenue, customers, feature requests, and product analytics. These are now your units of analysis: the very things your statistics are describing the state of.

Statistics describe the states of units of analysis: things we’re analyzing.
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Speak Statistics – Step 3: Capture Data

Ten. It’s the number of fingers you have. It’s also the source of our decimal – “ten-based” – counting system where “10” resets our numeric symbols. This isn’t a coincidence. We are wired to count. Counting is the prerequisite to calculating, which is the prerequisite to creating.

We are wired to count.
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Before you lift your pinky, you need to know how you plan to measure data. This is essential, because how you measure your unit of analysis determines what you are allowed to do with the data. Valuxr has an acronym to remember the five types. Put on a detective hat, and think “NOIR”.

Nominal. Ordinal. Interval. Ratio. Each “upgrade” what you can do with the data. This is a strange analogy, but think of it as butter that gets more “spreadable” the more it is softened.

Nominal means names – like colors – often of traits difficult to measure. Ordinal means order – like siblings by age – where named things also have a describable sequence. Interval means in-between – like time of day or temperature – where there is infinitesimal counting between counts (-1.9923…) but there isn’t a true zero. Ratio means having “in-betweenness” and including a true zero – like money – where something can be fully depleted.

To decide what data to capture: put on a detective hat and think, “NOIR”.
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Nominal and Ordinal data are called “non-continuous” or “categorical” while Interval and Ratio data are called “continuous” due to the in-betweenness the numbers allow.

NOIR. Great! So what? Why does this matter? Knowing what type of data you need informs how to capture it.

How to Capture Data

Say you need to record temperature. You can go outside and describe “hot” or “cold” – subjectively flawed nominal statistics. You could expand the categories to “cold”, “cool”, “warm”, or “hot” – ordinal statistics. 

You could take a thermometer and measure the temperature – interval statistics. Or, you could measure in Kelvin – a scale that includes an “absolute zero” – making the data ratio.

If you captured ratio data, you can calculate more data from it: multiplying or dividing it with or by other variables. Now let’s make this all mean something.

Extending our goal to inform which product to fund, say you discover you have most of the data you need – except for “value per dollar” ratings from customers. Time to set up a survey. In this survey, you are trying to measure how valuable they rate the feature they paid for. 

You can (1) give them categories – bad, neutral, good; (2) give them a scale of 1 to 10 without a number line; (3) give them a scale of 1 to 10 with a number line; or (4) give them a scale of 0 to 10 with a number line. Believe it or not options 1 and 2 are both categorical data. Option 3 is interval – the number line signifying in-betweenness – and option 4 is ratio.

How you set up a survey affects the quality of your data.
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Go with Option 4: “How much value has the product/service given you for the amount you paid? (0 = no value; 10 = maximum value).” You can do so much more with this data, and you can convert it back to categorical if you need to – a process called “binning”. Not bad for simply adding a “0” and line, right?

As you capture data, think about what you’ll need to compare. Customer name? Company? Role? It’s better to go back to your intended data outcomes before rather than after capturing data – especially when conducting a survey where people give you time.

Great! Now you have a data set. It’s time to describe it.

Speak Statistics – Step 4: Describe Data

There are two types of statistics: descriptive and inferential statistics. For descriptive statistics, you describe a single data set. For inferential statistics, you compare multiple data sets to make a data-supported guess. You cannot have good inferential statistics without good descriptive statistics.

Just like how good food comes from good ingredients, bad statistics comes from bad data. Descriptive statistics help you evaluate your single ingredient quality. Before principal component analyses and multivariate models, you must examine each variable. Before you move onto baking soufflés, you must first start with good butter, flour, and meat. Customers won’t appreciate you using moldy flour.

Descriptive statistics help you evaluate your ingredient quality.
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Think of a table or a spreadsheet. Every row on the spreadsheet is a unit of analysis. In the above survey example, this was each customer. Every column is a characteristic of this unit: a variable. Each column also represents a single data set – a single ingredient in the above metaphor.

Let’s describe your data.

How to Describe your Data

Continuing our attempt to decide which project to fund, we previously conducted a survey. Congratulations, you now have data! Forty-five customers responded. Not bad! They also gave you their roles, companies, company sizes, and explanations for their score – all nominal data.

First, you should take all the scores the customers gave you – your butter – and spread it on a piece of bread. This is called a univariate distribution. Take a piece of software – like Excel, Google sheets, SPSS, or R – or take out a sheet of grid paper.

Go to the list of 45 responses each customer gave for the “0 to 10” value-per-dollar rating. Count how many “0”s, “1”s, and so forth you received, and graph these counts on a histogram. 

These are called frequencies. The X axis should have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The Y axis should have bars representing how many of each you have. Congratulations, now you can evaluate the distribution.

Literally. What does it look like? Is it skewed to the right or left? Does it look like a bell? Is it ugly or strange? Did people hate the product or love it?

The reason you spread data on bread, or distribute it, is to see how consistent it is. If it’s pinched tightly around a center point – people in your sample of 45 had common opinions. If it’s all over the place, you have a lot of differing opinions. 

This immense amount of change is called variance. The larger the sample size, the smaller the variance. At some point, patterns from the underlying constants will surface. You just need to hone in on where they are.

How consistent is your butter?
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This variance can be calculated. Data can have a “central” point. What is it, in your variable’s data set? This central point is called an average, and it doesn’t necessarily mean you add everything and divide it by the count. That definition is exclusively for what is called the mean.

The averages – measures of central tendency – you can calculate depend on the data. Below is a guide.

• Nominal -> Mode (the most common data point)
• Ordinal -> Mode, Median (the sequentially middle data point)
• Interval -> Mode, Median, Mean (adding everything and dividing it by the sample size)
• Ratio -> Mode, Median, Mean

Now that you’ve defined “center points”, you can proceed to describe how much your distribution deviates from these averages. This is called “standard deviation”. Note that this is for your sample, don’t confuse this with “standard deviation of the mean”. 

You can either have your software calculate for you; or subtract each data point from your mean, square this difference, sum the squares, divide by the sample size, and square root the thing to get your number. The bigger it is, the more “all over the place” your responses are. Standard deviation is but one measure of variance – how different or variable all your data points are from each other.

Variance is a measure of how different or variable all your data points are from each other.
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Great, you’ve tested your butter stick and walked through three types of descriptive statistics: measures of frequency, central tendency, and variance. Now it’s time to cook!

Speak Statistics – Step 5: Infer from Data

Congratulations! You’re already at the advanced stages. You’ve flown through descriptive statistics. Now let’s use your data to finally answer questions. Welcome to inferential statistics: where you ask how much is happening due to chance vs due to some unseen factor, relationship, or – more difficult to prove – cause.

First, give yourself a pat on the back. You can’t get to inferential statistics without descriptive statistics. All those confusing names – MANOVA, P-test, Kruskal Wallis, Principal Component Analyses – are just convoluted labels for tests: for putting your data on trial.

Think of this like a court case. There are two opposing lawyers: one cynical lawyer believing everything happens due to chance, “Mr. Null”; and one mystical lawyer into alternative medicine believing there’s always some unseen force or relationship at play, “Mrs. Alternative”. 

This may sound ridiculous, but this is the basis of most statistical tests – no matter how confusing. Most tests operate from a Null vs Alternative Hypothesis. The remainder of inferential statistics has to do with using your data to estimate new data.

Think of hypothesis testing like a court case.
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While we can’t go through every statistical test, let’s dive into how this process works.

How to Infer from your Data

First Inferential Statistic: Is My Data Parametric?

Before you move onto using your butter stick, you may need to ask if the butter you collected is “normal” butter. Some of the inferential tests you can make depend on how “normal” your data is. For example, if your butter is blue margarine from Mars – it’s irresponsible to assume you can make inferences about all butter using your strange smelly sample.

You already did this using your own perceptions, but sometimes you need hard facts to evidence how normal your sample is. That is exactly what a test for normality is intended to provide. These tests attempt to answer: does your data fit the “norm” or the mold of what samples typically fit?

You can probably already poke holes in these tests. Who defines what normal is? How can we even calculate it? The answer to this is other randomly sampled data typically form a pattern. You’re testing your data against this pattern – a “goodness of fit”. These tests are just numbers to prove data does or doesn’t fit a certain mold. 

If the butter checks out to be butter, you can use it for recipes involving butter. If your data checks out to be normal, you can use it for what is called a parametric test. If your data isn’t normal, you can use it for a non-parametric test.

Parametric tests simply test if your data fits a “normal” mold of randomness.
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There are several tests for normality, which we recommend to let a piece of software like SPSS or R do for you. Our recommendation is to run the Shapiro-Wilk test, which is well accepted. If your data tests as normal, you can use a parametric test. If your data isn’t normal, you can use a non-parametric test.

Second Inferential Statistic: Using Parametric and Non-Parametric Tests for your Hypothesis

Let’s finally answer the question: which project should be funded? Let’s invite our data to tell us which test we can use.

Say your finance friends sent over last year’s completed projects and resultant revenue data. Not all previous projects map to a future project, but you can bin projects to project types – which may inform future project types.

You want to know which project type correlates with the highest increase in revenue. You want money, it’s your main dependent variable, so we’ll focus on a few single variable tests.

The question is simple: what thing (1) are you using to infer something about another thing (2)? Thing 1 and Thing 2’s data type define what fancy test to run. In our case, Thing 1 is project type – ordinal – and Thing 2 is revenue – ratio. If Thing 2 is ever nominal or ordinal – go with non-parametric tests. Let’s keep it simple and go with one variable.

Here are your options, if using nominal data to infer something:

• “Is there a difference between thing 1 and thing 2?”
  • 2 categories, comparing different things
    • Parametric = Independent T test
    • Non-parametric = Mann-Whitney U test
• “Is there a difference across thing 1, through two different conditions of itself?”
  • 2 categories, comparing a thing against itself
    • Parametric = Paired T test
    • Non-parametric = Wilcoxon Signed Rank test
• “Is there a difference between thing 1, thing 2, thing 3…?”
  • 2+ categories, comparing different things
    • Parametric = One-way Analysis of Variance (ANOVA)
    • Non-parametric = Kruskal Wallis test
• “Is there a difference across thing 1, thing 2, thing 3… through multiple different conditions of themselves?”
  • 2+ categories, comparing things against themselves
    • Parametric = Repeated Measures ANOVA
    • Non-parametric = Friedman test

Say we’re comparing 12 project types against each other. Our data is normal. Which test should we use?

If you chose a one-way ANOVA test – good job! You can probably look up how to run the tests, and let our computers or data science friends conduct them.

However, we do want to give you advice on interpreting test results. Most statistical tests set what is called a “p-value”. “P” stands for probability that any relationship between the two data sets you are testing is related to chance. Think of this “p-value” as the judge ruling between Mr. Null and Mrs. Alternative.

If the p-value is low, meaning there is low probability this is mere chance – Mrs. Alternative wins. This is called statistical significance – which comes with a warning label. One of the biggest fallacies is thinking statistical significance equates rigor. This is akin to saying a the sun does not exist because we can’t take a photo of it – either a limitation of the tool or its wielder.

Judges can make mistakes. Statistics are not facts. Statistics are attempts at finding consistency – finding truth.

To speak statistics you must understand statistics are error-prone samples of data using mathematical models to make more educated error-prone guesses. At the end of the day, these are still guesses – regardless of the P-value’s verdict. Don’t focus on proving a point, focus on strengthening how you gather information to get closer to the truth.

Statistical significance does not equate rigor nor truth – it just means there’s high probability the sampled differences are due to mere chance.
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Third Inferential Statistic: Estimating, Modeling, and Predicting

We won’t go into too many details, but we do want to stress that data is built. After conducting one variable or the univariate tests above; you can actually perform similar hypotheses tests with multiple variables.

Moreover, you can move beyond the court case and start using your data to estimate and predict more data. This can be incredibly powerful.

But it all comes with the most important final step of them all.

Let’s finally answer the question: which project should be funded?

Speak Statistics – Step 6: Acknowledge Gaps

A grain of sand will never capture the mountain it came from. Comparing grains of sand from different mountains will never fully compare each mountain. Even if you have computers simulate the remaining mountain, it will never be the facts – only inferential statistics.

A grain of sand will never capture the mountain it came from. Comparing rocks is not the same as comparing mountains.
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That doesn’t mean you can’t confidently learn from your experiments. Statistics and data science are only effective if you acknowledge these gaps. When you finally put together the slide show you sketched up in step 2, make these gaps front and center. Never change the truth: if there’s anything you learned from this article – it is that truth is unchangeable because it is outside the mechanism of change you reside in.

Confirmation bias, or marriage to theories named after egotistical professors is rampant in almost every discipline. It’s what makes every course about Statistics a chore to listen to, and what we tried to cut through in this article. 

Don’t follow crowds. No amount of man can change what is unreachable by man. Man is subjective. Variable. Truth is objective. Constant. Follow the truth.

Look beyond the variables of this time-driven world into the timeless. Look beyond the seen into the unseen. Only the broken will see and relate to the timeless.

“Humility is the mother of giants. One sees great things from the valley; only small things from the peak.” G.K. Chesterton

Congratulations. You now know how to wield data, and you also know how to recognize poorly wielded data. Go seek the unchanging amongst the changing. Go seek value.