Hipotesis Nula

Why We Don’t “Accept” the Null Hypothesis

by Keith M. Bower, M.S. and James A. Colton, M.S.

Reprinted with permission from the American Society for Quality

en performing statistical hypothesis tests such as a one-sample t-test or the AndersonDarling

test for

normality,

an investigator will either reject

or fail

to reject

the null

hypothesis,

based upon sampled

data. Frequently,

results in Six Sigma

projects contain

the

verbiage “accept the null hypothesis,” which implies

that the null hypothesis has been

proven

true. This article discusses why such a practice is incorrect, and why this issue is

re

than a matter

of

semantics.

Overview

of Hypothesis Testing

In

a statistical hypothesis test, two

hypotheses are evaluated: the null (H

alternative (H

1

). The null hypothesis is assumed true until proven otherwise. If the

weight of evidence leads us to believe that the null hypothesis is highly unlikely (based

upon probability theory), then we have a statistical basis upon which we may reject the

null hypothesis.

A common misconception is that statistical hypothesis tests are designed to select the

more likely of two hypotheses. Rather, a test will stay with the null hypothesis until

enough evidence (data) appears to support the alternative.

The amount of evidence required to “prove” the alternative may be stated in terms

of a confidence level (denoted X%). The confidence level is often specified before a test

is conducted as part of a sample size calculation. We view the confidence level as

equaling one minus the Type I error rate (α). A Type I error is committed when the null

hypothesis is incorrectly rejected. An α value of 0.05 is typically used, corresponding to

95% confidence levels.

The p-value is used to determine if enough evidence exists to reject the null

hypothesis in favor of the alternative. The p-value is the probability of incorrectly

rejecting the null hypothesis.

The two possible conclusions, after assessing the data, are to:

1. Reject the null hypothesis (p-value <= α) and conclude that the alternative

hypothesis is true at the pre-determined confidence level of X%, or at the

observed and more specific confidence level of 100*(1 – p-value)%.

2. Fail to reject the null hypothesis (p-value > α) and conclude that there is not

enough evidence to state that the alternative is true at the pre-determined

confidence level of X%. Note that it is possible to state the alternative to be true at

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