Q. Explain Type I and Type
II errors, with suitable examples. 6
Type I Error
When the null hypothesis is true rejecting it
is an error and this kind of error is known as type I error in statistics. The
probability of making a type I error is denoted as ‘α’ (read as alpha).
A Type I error occurs when
we reject the null hypothesis even though it is actually true. In terms of the
research hypothesis, we make a Type I error when we conclude that the study
supports the research hypothesis when in reality the research hypothesis is
false.
Suppose we conduct a
study and set the significance level (α) at a relatively lenient value, such as
20% (0.20). This high alpha level means we are allowing a fairly large
probability of rejecting the null hypothesis (H₀) even when it is actually
true.
In practical terms, this
means we do not require very strong evidence (i.e., very extreme data) to
reject the null hypothesis. As a result, if we were to conduct many such
studies, we would expect to make a Type I error — that is, incorrectly
rejecting a true null hypothesis — in about 20% of those studies.
Thus, by setting α =
0.20, we are saying that we are willing to accept a 20% chance of falsely
concluding that the research hypothesis is supported when, in fact, it is not.
Even when we set the
significance level at the conventional levels of .05 or .01, there is still a
chance of making a Type I error—rejecting the null hypothesis when it is
actually true. This means that in 5% or 1% of studies (depending on the level
chosen), researchers may conclude that an effect exists when it does not.
Consider the example of
evaluating a new therapy for depression. Suppose this new therapy is actually
no more effective than the usual treatment. However, if researchers randomly
select one depressed patient for a study, they might, by chance, pick someone
who responds especially well to either treatment. In such a case, the outcome
might suggest a difference in effectiveness even though there truly isn't one.
If the data from this
single patient leads the psychologists to reject the null hypothesis, they
would incorrectly conclude that the new therapy is different from the standard
one. This would be a Type I error—an error that occurs not due to bias
or misconduct, but simply due to random variation in sampling.
Researchers cannot know
when they’ve made a Type I error in any specific case. However, they take
comfort in the fact that the statistical method limits the probability
of such an error to a low, predefined rate—such as 5% when using a .05
significance level.
The significance
level—which represents the probability of making a Type I error—is denoted by
the Greek letter α (alpha). The lower the alpha level, the smaller the chance
of committing a Type I error.
Type II Error
When null hypothesis is false, a decision to
accept it is known as type II error.
When we choose a very
strict significance level, such as 0.001, we greatly reduce the likelihood of
making a Type I error—that is, rejecting the null hypothesis when it is
actually true. However, this increases the risk of a different kind of mistake.
In such a case, even if the research
hypothesis is actually true, the results may not be extreme enough to cross the
high threshold required to reject the null hypothesis. Specifically, even if
the research hypothesis is correct, the evidence might not be strong enough to
meet the high threshold required to reject the null hypothesis. This situation
results in a Type II error—failing to recognize a true effect. In
practical terms, this means the study may appear to show no significant result,
even though the research hypothesis is actually valid.
Considering the above example of evaluating a
new therapy for depression. Suppose this new therapy is actually effective than
the usual treatment. The null hypothesis states that the therapy has no effect,
while the alternative hypothesis states that the therapy is effective. If the
researcher conducts a statistical test and fails to reject the null hypothesis
concluding that the new therapy is not effective, when in fact it does have an
effect, this would be a Type II error.
The probability of making
a Type II error is denoted by β (beta).