Hello everyone.
This is our 3rd and last lecture for Chapter 9 – An Introduction to Hypothesis Testing
In this lecture video, we will discuss decision errors and power.
Because the hypothesis test relies on sample data, and because sample data are not completely
reliable, there is always the risk that misleading data will cause the hypothesis test to reach
a wrong conclusion.
Hypothesis testing is an inferential process.
It uses limited information to reach general conclusions.
Sample data are used to draw conclusions about a population.
There is always some probability of error in the results.
Two types of errors are possible: Type I errors and Type II errors.
Type I error is the probability of rejecting the null hypothesis when it is, in fact, true.
Type I errors occur when the sample data appear to show an effect when, in fact, there is
no effect or difference.
In this case, the researcher will reject the null hypothesis and falsely conclude that
there is a difference or effect.
The researcher rejects a null hypothesis that is actually true.
Type I errors are caused by unusual, or unrepresentative samples.
Just, by chance, the researcher selects an extreme sample with the result that the sample
falls in the rejection region even though there was no actual effect or difference.
The probability of making a Type I error is equal to alpha, α.
Type I errors are also known as "false positives."
Examples of Type I errors happen in the medical world when someone gets the results from their
biopsies and they are told they have cancer (but they really do not have cancer).
Or drug testing…someone fails their drug test when, in fact, they should have passed
it (because they are drug-free).
Someone is convicted of a crime they never committed.
Type II error is the probability of not rejecting the null when it is, in fact, false.
Type II errors occur when the sample does not appear to show an effect or difference
when, in fact, there is a true effect or difference.
In this case, the researcher will fail to reject the null hypothesis and falsely conclude
that there is no difference or effect.
The hypothesis test failed to detect a real effect or difference.
Type II errors are commonly the result of a very small effect.
Even though there really is a difference, it is not large enough to show up in a research
study.
There is an inverse relationship between Type I and Type II errors.
The probability of Type II errors increase as the probability of Type I errors decrease.
The probability of a Type II error (NOT Type I) equals beta, β.
Type II errors are also known as "false negatives."
Examples of Type II errors happen in the medical world too: someone goes to the hospital and
they are sent home, when they should have been admitted to the hospital (the test did
not find the "bigger" problem).
Or lie detector testing…someone passes the lie detector test when, in fact, they should
have failed it (because they are lying through their teeth).
Someone is acquitted for a crime they actually committed.
Here is the table of decision errors or what we fondly refer to as "The Confusion Matrix,"
because it tends to confuse students.
This table shows that there are four decisions we could make: 2 decisions are errors (Type
I error & Type II error) and 2 of them are correct decisions.
Power, 1 - beta, β or 1 - alpha, α (not alpha it's Type I error); 1 – alpha is
the correct decision.
What we will be focusing on next is Power, which is the probability of correctly rejecting
a false null hypothesis.
Power is the probability of detecting an effect that truly exists.
Power is equal to not making a Type II error (NOT Type I) or 1 - beta, β.
There are a number of factors that affect power, or the probability of correctly rejecting
the null hypothesis.
So let's take a look at what factors increase power:
Increasing sample size, n, decreases standard error, increases test statistic, which increases
likelihood of rejecting the null, which will increase power and vice versa (decreasing
sample size, decreases the likelihood of rejecting the null, which will decrease power)
Increasing alpha, α, increases the rejection area, increases likelihood of rejecting the
null, which will increase power and vice versa Increasing mean differences between M and
μ, increases our test statistic, increases likelihood of rejecting the null, which will
increase power and vice versa Increasing effect size, increases power and
vice versa Decreasing population standard deviation,
σ, decreases standard error, which increases our test statistic, increases likelihood of
rejecting the null, which will increase power and vice versa
Conducting a one-tailed or directional hypothesis test, increases the rejection area, which
increases likelihood of rejecting the null, which will increase power and vice versa (a
two-tailed test decreases our rejection area, decreases likelihood of rejecting the null,
which will decrease power)
This leads us into the factors that affect hypothesis testing, which are related to power:
Increasing sample size, n, decreases standard error, increases the test statistic, which
increases likelihood of rejecting the null (and vice versa)
Increasing mean differences between M and μ, increases test statistic, which increases
likelihood of rejecting the null (and vice versa)
Decreasing standard deviation, σ, decreases standard error, increases test statistic,
which increases likelihood of rejecting the null ( and vice versa)
One last thing we need to discuss is the assumptions for hypothesis testing.
In order to conduct what we call parametric hypothesis tests, we must meet three assumptions:
1.
Random sampling – we assume that data were obtained from a random sample
2.
Independence – we assum that each outcome or observation is independent, one outcome
or observation has no effect on another 3.
Normality – we assume that data in the population are normally distributed, especially for samples
of n < 30.
In larger samples of n > 30, this assumption is not as critical (remember due to the central
limit theorem).
This concludes our coverage for Chapter 9.
I will post one more video that will show you how to conduct hypothesis tests, both
directional and non-directional.
This video will also show you how to write appropriate APA conclusions.
Không có nhận xét nào:
Đăng nhận xét