what does fail to reject the null mean

Failing to reject the goose egg hypothesis is an odd fashion to land that the results of your hypothesis examination are not statistically significant. Why the peculiar phrasing? "Fail to reject" sounds like 1 of those double negatives that writing classes taught you to avoid. What does it mean exactly? There'southward an fantabulous reason for the odd diction!

In this mail service, learn what information technology means when you lot fail to reject the null hypothesis and why that's the correct diction. While accepting the cypher hypothesis sounds more straightforward, it is not statistically correct!

Before proceeding, let's epitomize some necessary information. In all statistical hypothesis tests, you lot have the following two hypotheses:

• The null hypothesis states that there is no effect or relationship between the variables.
• The alternative hypothesis states the effect or relationship exists.

Nosotros presume that the nada hypothesis is right until we have enough evidence to suggest otherwise.

After you perform a hypothesis exam, there are only two possible outcomes.

• When your p-value is less than or equal to your significance level, yous reject the null hypothesis. The data favors the alternative hypothesis. Congratulations! Your results are statistically pregnant.
• When your p-value is greater than your significance level, yous neglect to turn down the zippo hypothesis. Your results are not significant. You'll larn more nearly interpreting this event later in this post.

Related posts: Hypothesis Testing Overview and The Null Hypothesis

Why Don't Statisticians Have the Null Hypothesis?

To understand why we don't accept the zilch, consider the fact that you can't prove a negative. A lack of testify but means that you haven't proven that something exists. It does not show that something doesn't be. It might exist, only your study missed it. That'due south a huge departure and it is the reason for the convoluted wording. Let's expect at several analogies.

Species Presumed to be Extinct

Australian Tree Lobsters were causeless to exist extinct. In that location was no evidence that whatsoever were however living considering no one had seen them for decades. Yet in 1960, scientists observed them. The same affair happened to the Gracilidris Ant and the Nelson Shrew among many others. Dedicated scientists were looking for these species but hadn't been in the right time and place to observe them. The aforementioned idea applies to ghosts!

Lack of proof doesn't correspond proof that something doesn't be!

Criminal Trials

In a trial, we start with the assumption that the defendant is innocent until proven guilty. The prosecutor must piece of work hard to exceed an evidentiary standard to obtain a guilty verdict. If the prosecutor does not meet that burden, information technology doesn't bear witness the accused is innocent. Instead, there was insufficient evidence to conclude he is guilty.

Perhaps the prosecutor conducted a shoddy investigation and missed clues? Or, the defendant successfully covered his tracks? Consequently, the verdict in these cases is "not guilty." That judgment doesn't say the accused is proven innocent, merely that in that location wasn't enough evidence to move the jury from the default assumption of innocence.

Hypothesis Tests

When you're performing hypothesis tests in statistical studies, you typically desire to discover an effect or human relationship between variables. The default position in a hypothesis test is that the zilch hypothesis is correct. Like a court example, the sample testify must exceed the evidentiary standard, which is the significance level, to conclude that an effect exists.

The hypothesis exam assesses the evidence in your sample. If your exam fails to notice an consequence, information technology's not proof that the result doesn't exist. It but means your sample independent an insufficient amount of testify to conclude that it exists. Similar the species that were presumed extinct, or the prosecutor who missed clues, the effect might exist in the overall population just not in your particular sample. Consequently, the test results fail to refuse the null hypothesis, which is analogous to a "not guilty" verdict in a trial. There just wasn't plenty evidence to motility the hypothesis examination from the default position that the null is true.

The disquisitional betoken beyond these analogies is that a lack of evidence does non prove something does non exist—just that you didn't discover information technology in your specific investigation. Hence, you never have the nil hypothesis.

Related mail service: The Significance Level as an Evidentiary Standard

What Does Neglect to Turn down the Null Hypothesis Mean?

Accepting the null hypothesis would indicate that you've proven an effect doesn't exist. As you've seen, that'southward not the case at all. You can't prove a negative! Instead, the strength of your evidence falls brusk of being able to reject the zippo. Consequently, we fail to reject it.

Failing to reject the null indicates that our sample did non provide sufficient bear witness to conclude that the effect exists. Still, at the same time, that lack of testify doesn't prove that the effect does not exist. Capturing all that information leads to the convoluted wording!

What are the possible implications of failing to reject the null hypothesis? Let's work through them.

First, it is possible that the issue truly doesn't be in the population, which is why your hypothesis test didn't find it in the sample. Makes sense, right? While that is 1 possibility, it doesn't finish there.

Some other possibility is that the event exists in the population, but the exam didn't notice it for a variety of reasons. These reasons include the following:

• The sample size was too pocket-sized to detect the effect.
• The variability in the information was too loftier. The effect exists, but the racket in your data swamped the betoken (effect).
• By chance, you lot collected a fluky sample. When dealing with random samples, hazard always plays a role in the results. The luck of the describe might have caused your sample non to reflect an effect that exists in the population.

Notice how studies that collect a small corporeality of information or low-quality data are likely to miss an effect that exists? These studies had inadequate statistical power to detect the effect. Nosotros certainly don't desire to take results from low-quality studies as proof that something doesn't be!

Notwithstanding, declining to detect an issue does not necessarily mean a study is low-quality. Random chance in the sampling process can work against fifty-fifty the best research projects!

If you're learning virtually hypothesis testing and like the approach I employ in my blog, check out my eBook!

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Source: https://statisticsbyjim.com/hypothesis-testing/failing-reject-null-hypothesis/

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