Hypothesis Tests 101 Fort Zumwalt North Statistics– Mann
Second Semester 2013
The Basic Idea will culminate in students getting 45 questions or
In this issue:
more correct on a test with 60 questions. I will write the two competing hypotheses as: The average will be greater than or equal to 45
The Basic Idea
1
(null) The average will be less than 45 (alternative) In this case, my claim is the null hypothesis, but it need not be. I could have claimed this new teaching
Null and Alternative 1 Hypotheses
method would result in scores less than 45. In this At the beginning of the year, we used an analogy a few times between statistics and a court of law. This idea will come to complete fruition as we transition completely to inferential statistics - using statistics to make decisions.
case, the claim would be the alternative hypothesis.
Examples or
Once you have framed the situation in terms of these
Writing Null and
hypotheses, the matter becomes subject to the evidence of the situation. In this case, more than
Alternative Hypotheses
likely, we would look at a sample of student scores
What’s the
Hypothesis tests will begin with looking at two
and see how close the mean was to 45.
Evidence? P-values
competing ideas. These can come in three variations. I will elaborate later on that. But, here’s the jist of it.
From this point on, the statistical tests become using
and Levels of Significance
Let’s pretend that I am exploring the outcome of a
methods to see whether or not our average is sufficiently above 45 so as likely to not be due to
new teaching method. I believe that this new method
random chance.
2
2
Special points of interest: HT’s are about weighing statistical evidence against against a burden of proof Null and alternative hypotheses are opposites
Null and Alternative Hypo theses This basic concept seems to
The null hypothesis always
If the null contains an =, the
create more confusion in students
contains an equality sign when
alternative contains ≠. If the null
than anything else, and is the foundation for everything to
written mathematically (≤,≥, or =). The alternative hypothesis is a
contains ≥, the alternative is <. If the null is ≤, the alternative is >.
follow. Make certain you fully
statement of inequality (<,>, or
comprehend the ideas that follow.
≠).
For any hypothesis test, there is a
The null and alternative
null and alternative hypothesis.
hypotheses are always opposites.
Part of the challenge is converting verbal information to the mathematical representations.
We assume the null hypothesis is true if or until we obtain sufficient evidence to the contrary.
Basics on Hypothesis Writing Be able to write mathematical translations of verbal hypotheses. Here are some examples to give you the idea. Claim that a car gets at least 30 mpg. Null Hypothesis: µ≥30 (claim) Alternative Hyothesis: µ<30 Claim that new cars average less than $25,000 in cost. Null: µ≥25000 Alternative: µ<25000 (Claim) Claim that the average GPA of sophomores at Mizzou is 2.75 Null: µ=2.75 (Claim) Alternative: µ≠2.75 Always label which of your hypotheses is the claim.
Always keep in mind the big picture of what we are trying to accomplish with HT’s!
W h a t ’s t h e E v i d e n c e ? .In the “Basic Idea” section, I described a
This probability is called a p-value. You can
hypothesis test where the null hypothesis
think of it as the probability of obtaining a
was that the average would be at least 45. So, what would I decide if I looked at the
sample statistic as extreme (large or small) as the one obtained if the hypothesized
average and it was 45.5? Is this little
value is true. Let’s imaging that the
difference due simply to random chance? If
probability of a 45.5 or higher for the sample
you were a juror, would you decide that
size and sample SD we have is just 0.02.
beyond a reasonable doubt, my new method
This means that there is just a 2% chance
resulted in scores of at least 45?
that by random chance we would have
To do this, we can figure out what the probability would be of getting a 45.5. At this point, it’s not necessary to go into the
gotten a mean as high of 45.5 if the true mean was less than 45. In a hypothesis test, we compare p to the
details, but suffice it to say it simply involves
maximum risk we are willing to accept of
calculating the z-score and finding the
being wrong (level of significance called
probability of a score of that or higher. (We
α). Let’s say our α=0.05. In this case our
would need to also use the sample SD which
0.02 for p would lead us to conclude that
we would have from our sample)
our method worked. At α=.01, we would come to the opposite conclusion.
