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Welcome to MM570
Psychological Statistics
Unit 5 Seminar
Dr. Bob Lockwood
The Normal Distribution
• Normal curve and approximate percentage of
scores between the mean and 1, 2, and 3
standard deviations from the mean
* Other texts may refer to the Empirical Rule or
68% - 95% - 97.5%
Sample and Population
• Population
• Sample
• Methods of sampling
• Random selection
• Haphazard selection
Probability
• Range of probabilities
• Proportion: from 0 to 1
• Percentages: from 0% to 100%
• Probabilities as symbols
• P
• p < .05
• Probability and the normal distribution
• Normal distribution as a probability distribution
What is Hypothesis Testing?
• Any hypothesis is a “guess” about some condition,
Behavior Therapy is more effective than
Psychotherapy or the average time that Kaplan
students in MM570 spend studying is 12 hours per
week.
• How do we know if our guess is correct? We “test” it
using data.
• Will our data prove the guess is correct or
incorrect? No, it could be wrong.
• We use statistics to determine the likelihood that
our data either supports or does not support the
guess.
The Concept of Hypothesis Testing
• You and I are going to play a game flipping my
coin. If it lands heads I will give you a dollar. If it
lands tails you give me a dollar.
• Now let’s assume you agree to play my game. You
are making an assumption (guess) about my coin,
that it is fair!
• The assumption that it is fair is what we will test.
It is called the Null Hypothesis.
• We could state this as the probability of the coin
landing heads is .50 and landing tails is .50
The Null and Alternative Hypotheses
• We restate our “guess” so we can test it.
• There are many ways our guess can be wrong but
only one way it can be correct
• We write the Null Hypothesis as a statement
• Ho: p(heads) = .50
• The Alternative would be that the coin is not fair
• Ha: p(heads) ≠ .50
• Notice that these two statements include all
possible outcomes of our “test.”
Collecting Data
• We need to collect data to determine which
hypothesis, is the coin fair or not, to accept
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•
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I
I
I
I
I
flip
flip
flip
flip
flip
the
the
the
the
the
coin
coin
coin
coin
coin
and
and
and
and
and
it
it
it
it
it
is
is
is
is
is
heads, I give you $1
heads, I give you $1
tails, you give me $1
heads, I give you $1
tails, you give me $1
• At this point do the data seem to indicate that the
coin is fair? Yes I think we would agree it does.
Making a Decision with Data
• We continue the game
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•
•
•
•
I
I
I
I
I
flip
flip
flip
flip
flip
and
and
and
and
and
it
it
it
it
it
is
is
is
is
is
heads, I give you a $1
tails, you give me a $1
tails, you give me a $1
tails, you give me a $1
tails, you give me a $1
• Does the coin still seem to be fair? It is not as clear
as it was but maybe it is fair.
• We flip 10 more times and you lose all of them
• Now at this point you reject the claim that the coin
is fair and call me a cheat. But, could you be wrong
and the coin really is fair? The answer is YES!!
What Have We Done?
Started with an assumption
Created a null and alternative hypothesis
Collected data related to our question
Based on the data we either rejected or accepted
the null hypothesis (this is the one we test and if
we reject it, we are accepting the alternative)
• Made a decision about the original “guess” with
appropriate consideration of the fact that you could
be wrong!
•
•
•
•
An Example of the Test of Hypothesis
• Suppose a researcher thinks that not eating red meat
will significantly lower cholesterol. This assumes that
eating red meat will not lower cholesterol
• This leads us to an experiment comparing two groups,
those not eating red meat and those who do eat red
meat.
• Now, suppose I take a sample of 30 men (over age 45
from the USA) and separate them in to two groups,
each with 15 men. Then, for 6 months, group 2 does
not eat any red meat. After 6 months, I collect
everyone’s cholesterol.
• Group 1 (red meat OK)
• Group 2 (CANNOT eat red meat)
The Null and Alternative Hypothesis:
Ho and Ha
• Remember, our research idea is that not eating
meat will significantly reduce cholesterol. But,
we need to create our Ho and Ha.
• Remember that the Ho and Ha are ALWAYS
opposite!
• In our study we would have:
• Ho: mean cholesterol of Group
= mean cholesterol of Group 2
• Ha: mean cholesterol of Group
≠ mean cholesterol of Group 2
1 (meat OK)
(no meat)
1 (meat OK)
(no meat)
One-Tailed and Two-Tailed Tests
• Notice that Ho uses an “=“ sign. The null
hypothesis ALWAYS contains an “=“ sign.
• In our study the alternative or research hypothesis
Ha contains a “≠” sign. This means that our
hypothesis test is two-tailed!
• An alternative or research hypothesis can have
“>”, “<“, or “≠” sign. If the alternative hypothesis
has “>” or “<“ it is called one-tailed.
Here is what our “data in SPSS”
might look like after the 6 months
are over and I have collected
everyone’s cholesterol values.
*Notice that some people are in
Group 1 (meat OK) and some are
in Group 2 (no meat)
What we want to do is to compare
the mean cholesterol levels for
each group.
Using SPSS to get the mean for
each group
So, after 6 months, we have:
Group 1 (meat OK) mean = 255.40
Group 2 (no meat) mean = 143.47
Returning to our research question
about cholesterol
Group 1(meat OK) has mean cholesterol = 255.40
Group 2(No Meat) has mean cholesterol = 143.47
Now we can clearly see that 255.40 is not equal to 143.47!
But they are based on only a sample of 30 men over 45.
There are over millions of men over the age 45! Samples are
always much smaller than the population from which they
are drawn.
Is the difference we see in our small sample something that
happened by chance (the Null is actually true) or is the
difference real (the Alternative is actually true)?
This is what our “test” can help us determine.
What “tests” can we run to see if we
should reject or accept the null?
•
In this case, we have two samples and we are comparing the means
of these two samples.
•
We do not really have any other information – like a population
variance – so it is best to use the “t-test” to compare two sample
means.
•
•
Group 1(meat OK) has mean cholesterol = 255.40
Group 2(No Meat) has mean cholesterol = 143.47
•
If they are significantly different, we will reject the null that the
means are equal. If they are not significantly different, we will
NOT reject the null and by extension accept the alternative
that they are not equal.
We can use SPSS to run our t-test
(Yay!)
Here, our t = 8.148
Also, our Sig (2 –tailed) = .000
What do these values mean?
Using Alpha and our t test
We use “alpha” = .05 to determine the rejection region for
our t-test result.
We “reject the null” if our t test value is in our rejection
region (sometimes called the critical region)
Our “rejection region” for
the t-test is a curve that is
very similar to the normal
bell curve.
When alpha = .05 and a
2-tailed test we have .05/2
or 2.5% in each tail that
is our rejection region
Determining the rejection values or
critical values?
We have two
choices 
The first is to
use a table like
this:
Using SPSS Instead of the Table
• SPSS will tell us the p-value (Sig) which is the
probability that the difference is not just a chance
occurrence.
• The reported significance is tells us whether to
reject the null or not. SPSS calculates the p-value
using these table values.
• If the p-value given by SPSS is less than (<) .05
(our alpha), then we REJECT THE NULL!
• If the Sig > .05 we DO NOT reject the null, the
results are likely (more than 5 times in 100) if
there really is no difference.
Interpreting the SPSS Output
Because the sig or p-value = .000 is well less than our alpha of
.05 we can reject the null and conclude that there is sufficient
evidence to support our research hypothesis that not eating red
meat does lower cholesterol.
Have we “proven” that not eating red meat lowers cholesterol?
No we have not. The probability is very small but it is never 0,
and therefore whatever we decide there is some small proability
that we could be wrong!
SPSS and the Critical Values
Notice that our t test result is 8.148, equal variances assumed.
If you use the table and not SPSS with alpha = .05 and df = 28,
you will find that for a two-tailed test, the critical values or
rejection values are : 2.048 and -2.048
We see that 8.148 > 2.048 and so it IS in the rejection region.
It is same conclusion we got using the Sig or p-value of .000.
Visually, here is what SPSS is doing:
Conclusions from the Test of
Hypothesis
• Our t-test showed us that we can reject the Null hypothesis
and can accept our research hypothesis.
• Therefore, we can say that the evidence supports the
statement that not eating meat does lower cholesterol
levels.
Notice that we did two things here. First we made a
decision, based on the output from SPSS, about the Null
Hypothesis. Second, we made a statement about our
research question in the language of the question based
on our decision. The end is NOT just accepting or
rejecting the Null!!!!
QUESTIONS??