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What Does Statistically Significant Mean?

by Jeff Sauro | October 21, 2014

Statistically significant.

It’s a phrase that’s packed with both meaning, and syllables. It’s hard to say and harder to understand.

Yet it’s one of the most common phrases heard when dealing with quantitative methods.

While the phrase statistically significant represents the result of a rational exercise with numbers, it has a way of evoking as much emotion. Bewilderment, resentment, confusion and even arrogance (for those in the know).

I’ve unpacked the most important concepts to help you the next time you hear the phrase.

Not Due to Chance

In principle, a statistically significant result (usually a difference) is a result that’s not attributed to chance.

More technically, it means that if the Null Hypothesis is true (which means there really is no difference), there’s a low probability of getting a result that large or larger.

Statisticians get really picky about the definition of statistical significance, and use confusing jargon to build a complicated definition. While it’s important to be clear on what statistical significance means technically, it’s just as important to be clear on what it means practically.

Consider these two important factors.

What it Means in Practice

Let’s look at a common scenario of A/B testing with, say, 435 users. During a week, they are randomly served either website landing page A or website landing page B.

Do we have evidence that future users will click on landing page A more often than on landing page B? Can we reliably attribute the 5-percentage-point difference in click-through rates to the effectiveness of one landing page over the other, or is this random noise?

How Do We Get Statistical Significance?

The test we use to detect statistical difference depends on our metric type and on whether we’re comparing the same users (within subjects) or different users (between subjects) on the designs. To compare two conversion rates in an A/B test, as we’re doing here, we use a test of two proportions on different users (between subjects). These can be computed using the online calculator or downloadable Excel calculator .

Below is a screenshot of the results using the A/B test calculator

To determine whether the observed difference is statistically significant, we look at two outputs of our statistical test:

What it Doesn’t Mean

Statistical significance does not mean practical significance.

The word “significance” in everyday usage connotes consequence and noteworthiness.

Just because you get a low p-value and conclude a difference is statistically significant, doesn’t mean the difference will automatically be important. It’s an unfortunate consequence of the words Sir Ronald Fisher used when describing the method of statistical testing.

To declare practical significance, we need to determine whether the size of the difference is meaningful. In our conversion example, one landing page is generating more than twice as many conversions as the other. This is a relatively large difference for A/B testing, so in most cases, this statistical difference has practical significance as well. The lower boundary of the confidence interval around the difference also leads us to expect at LEAST a 1% improvement. Whether that’s enough to have a practical (or a meaningful) impact on sales or website experience depends on the context.

Sample Size

As we might expect, the likelihood of obtaining statistically significant results increases as our sample size increases. For example, in analyzing the conversion rates of a high-traffic ecommerce website, two-thirds of users saw the current ad that was being tested and the other third saw the new ad.

The difference in conversion rates is statistically significant (p = 0.039) but, at 0.0006%, tiny, and likely of no practical significance. However, since the new ad now exists, and since a modest increase is better than none, we might as well use it (oh and just in case you thought a lot of people clicked on ads, let this remind you of how they don’t!)

Conversely, small sample sizes (say fewer than 50 users) make it harder to find statistical significance; but when we do find statistical significance with small sample sizes, the differences are large and more likely to drive action.

Some standardized methods express differences, called effect sizes , which help us interpret the size of the difference. Here, too, the context determines whether the difference warrants action.

Conclusion and Summary

Here’s a recap of statistical significance:

Now say statistically significant three times fast.

: The blue bar shows 5% difference. The black line shows the boundaries of the 95% confidence interval around the difference. Because the lower boundary is above 0%, we can also be 95% confident the difference is AT LEAST 0–another indication of statistical significance.

Gerry Huggins at Chaumette
Saturday, June 11, 2016 - 1:00pm to 4:00pm
Chaumette Vineyard Winery
Live Music at Riverwood Winery
Saturday, June 11, 2016 - 1:00pm to 4:00pm
Riverwood Winery

Uncork from your long week outside with a glass of wine and live music with Brad Allen.

Clayton Music Wine Festival
Saturday, June 11, 2016 - 5:00pm to 10:00pm

Taste wines while enjoying great musical performances at the Music Wine Festival in Clayton, MO!

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Tall Poppies Live at Blumenhof Winery
Saturday, June 11, 2016 - 5:00pm to 8:00pm
Blumenhof Winery

Tall Poppies (Rock Band) will perform at Blumenhof Winery in Dutzow, MO on Saturday, June 11 from 5-8pm.

Sippin’, Smokin’ Singin’ Saturday Night
Saturday, June 11, 2016 - 6:00pm to 9:00pm
Jowler Creek Winery

Gather your friends and come watch the sunset from our wine garden as we stay open late this Saturday night with live music (if it’s rainy, we’ll have the band inside our barrel room)! Listen to Damien Gunn + The Bang Bangs play country rock-n-roll while enjoying cigars made locally by Weston Tobacco around our beautiful fire pit. We’ll be selling wine and beer by the glass and bottle, and we’ll also have picnic pails pre-packed with foods available for purchase to enjoy alongside your favorite wine. Cost to attend is FREE. No reservations are required to join the fun...just come on out! No outside food or beverages (alcoholic or non-alcoholic) allowed.

Tipple Hill Winery Vineyard- Music
Saturday, June 11, 2016 - 7:00pm to 9:30pm
Tipple Hill Winery Vineyard

Music by Bill Hoffman, playing your favorite hits.

Dinner at The Estates
Saturday, June 11, 2016 - 7:00pm to 9:30pm
Mount Pleasant Estates

Course 1 - Caesar Salad paired with Villagio Crisp romaine lettuce, garlic croutons, Parmesan crackers, house-made dressing

Passing by the shipyards, Cole was called out by an Fila Mens Dalliance 2 Sneakers White / White / Metallic Silver ygF6cGZFdF
. He exclaimed that the Dust Men have taken Zeke hostage, and will kill him slowly. As Moya protested, telling Cole to leave Zeke to his fate, Cole made it clear he doesn't abandon friends. Zeke was rescued, and Cole reprimanded him because of ignoring the troubles and dangers of wandering off alone. Zeke interpreted it as Cole saying that Zeke's just a liability. Cole told him that it wasn't a game anymore, and Zeke left, mad at Cole. [2]

Cole and Alden's first encounter with one another.

After Trish was finished preparing her patients for transport, Cole returned to the Neon to help escort her bus. Eventually, they closed into the Bayview Hospital , but as they neared, an elderly man appeared at the hospital front, with one of his servants firing a rocket-propelled grenade at him. As Cole was pushed off of the bus, the old man, identified by Moya as Alden Tate , supposed leader of the First Sons, lifted the bus using telekinesis and threw it on the hospital roof. Cole immediately rushed to the hospital roof in order to save Trish and her patients, which he did. After this, Cole rested at the hospital. [2]

After resting at the Bayview hospital, Cole was tasked to help the 's 43rd Precinct in arresting Alden Tate. The police have declared an all out war with the Dust Men and wishes Cole to assist them. After settling the armored bus attacks by the transients, Cole went to the supposed rendezvous point with the police, but found only the body of a police officer. Using his powers, Cole was able to track down an echo sent off by the officer's residual energy, able to see a recent effigy of Alden. Cole then tracks the echo, which lead him to the infamous shanty town nicknamed " Pikolinos Mens Mackenzie M0C8028C1 Black feZfKWa7ps
". [2]

Cole made his way through the makeshift town, fending off the incoming transients as he made his way through. After navigating to the very top-most part of the town while following Alden's echo, Cole managed to make his way to the open terrace leading into the Serfas Mens Radium Cycling Shoe White bNs622
. As Cole was about to make his way there, the only path leading to it was barricaded by fire, and was guarded by a Golem Conduit . Despite the supposed disadvantage, Cole managed to overcome the conduit, though by the time he did, the police have already arrested Alden, and were moving him to Eagle Point Penitentiary for the FBI to extract him. Cole immediately left the area to go meet up at the facility.

Cole, looking at Zeke after his blunder.

Cole was greeted by Zeke, who was helping out the cops with their business. Cole was tasked with guarding the fence as Alden was being transferred to a different cell. After a successful defense, the facility was attacked by a large group of transients. As Cole and the cops fended them off, the generator holding Alden's power back ran out of power, due to some transients' meddling with it on the roof. Cole dealt with them and immediately returned to the open field and help the cops defend the facility. [2]

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