1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

3. By the end of lecture today 10/28/16
Introduction to Hypothesis Testing
Using z scores
Type I versus Type II Errors

4. Homework Assignments Homework Assignment 17:
Hypothesis Testing Type I versus Type II Errors
Due Monday October 31st
Homework Assignment 18
Hypothesis testing using z scores and t scores
Comparing Two means
(Single sample and population mean)
Due Wednesday November 2nd

5. Before next exam (November 18th)
Please read chapters in OpenStax textbook
Please read Chapters 2, 3, and 4 in Plous
Chapter 2: Cognitive Dissonance
Chapter 3: Memory and Hindsight Bias
Chapter 4: Context Dependence

6. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
Next week
With Project 3

8. Confidence Interval of 95% Has and alpha of 5% α = .05
Critical z
-2.58
Critical z
2.58
Confidence Interval of 99%
Has and alpha of 1%
α = .01
99%
Area in the tails is called alpha
Critical z
-1.96
Critical z
1.96
Confidence Interval of 95% Has and alpha of 5% α = .05
95%
Critical Z separates rare from common scores
Critical z
-1.64
Critical z
1.64
Confidence Interval of 90%
Has and alpha of 10%
α = . 10
90%
It would be easiest to reject the null at which alpha level?
Review
why?

9. Deciding whether or not to reject the null hypothesis. 05 versus
Deciding whether or not to reject the null hypothesis .05 versus .01 alpha levels
What if our observed z = 2.0?
How would the critical z change?
α = 0.05
Significance level = .05
α = 0.01
Significance level = .01
-1.96 or
+1.96
p < 0.05
Yes, Significant difference
Reject the null
Remember,
reject the null if the observed z is bigger than the critical z
-2.58 or
+2.58
Not a Significant difference
Do not Reject the null
Review

10. One versus two tail test of significance 5% versus 1% alpha levels
What if our observed z = 2.45?
How would the critical z change?
One-tailed
Two-tailed
α = 0.05
Significance level = .05
α = 0.01
Significance level = .01
-1.64 or
+1.64
-1.96 or
+1.96
Remember,
reject the null if the observed z is bigger than the critical z
Reject the null
Reject the null
-2.33 or
+2.33
-2.58 or
+2.58
Reject the null
Do not Reject the null
Review

11. Review Rejecting the null hypothesis
The result is “statistically significant” if:
the observed statistic is larger than the critical statistic
observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) to be big!!
the p value is less than 0.05 (which is our alpha)
p < If we want to reject the null, we want our “p” to be small!!
we reject the null hypothesis
then we have support for our alternative hypothesis
Review

12. 90% Moving from descriptive stats into inferential stats….
For scores that fall into the middle range,
we do not reject the null
Moving from descriptive stats
into inferential stats….
Critical z
1.64
Critical z
-1.64
90%
Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there 5% 5%
Measurements that occur outside this middle ranges are suspicious, may be an error
or belong elsewhere
For scores that fall into the regions of rejection,
we reject the null
What percent of the distribution will fall in region of rejection
Critical
Values

13. Rejecting the null hypothesis
The result is “statistically significant” if:
the observed statistic is larger than the critical statistic
observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) to be big!!
the p value is less than 0.05 (which is our alpha)
p < If we want to reject the null, we want our “p” to be small!!
we reject the null hypothesis
then we have support for our alternative hypothesis
A note on decision making following procedure
versus being right relative to the “TRUTH”

14. Procedures versus outcome Best guess versus “truth”.
Decision making:
Procedures versus outcome
Best guess versus “truth”
What does it mean to be correct?
Why do we say:
“innocent until proven guilty”
“not guilty” rather than “innocent”
Is it possible we got a verdict wrong?

15. We make decisions at Security Check Points.
We make decisions at Security Check Points .

16. Does this airline passenger have a snow globe?.
Type I or Type II error? .
Does this airline passenger have a snow globe?
Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!!
As detectives, do we accuse her of brandishing a snow globe?

17. Does this airline passenger have a snow globe?.
Does this airline passenger have a snow globe?
Status of Null Hypothesis (actually, via magic truth-line)
Are we correct or have we made a Type I or Type II error?
True Ho
No snow globe
False Ho
Yes snow globe
You are wrong!
Type II error (miss)
Do not reject Ho “no snow globe move on”
You are right!
Correct decision
Decision made by experimenter
You are wrong!
Type I error (false alarm)
Reject Ho
“yes snow globe, stop!”
You are right!
Correct decision
Note: Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!!

18. Type I error (false alarm)
Type I or type II error? .
Decision made by experimenter
Reject Ho
Do not Reject Ho
True Ho
False Ho
You are right!
Correct decision
You are wrong!
Type I error (false alarm)
Type II error (miss)
Does this airline passenger
have a snow globe?
Two ways to be correct:
Say she does have snow globe when she does have snow globe
Say she doesn’t have any when she doesn’t have any
Two ways to be incorrect:
Say she does when she doesn’t (false alarm)
Say she does not have any when she does (miss)
Which is worse?
What would null hypothesis be?
This passenger does not have any snow globe
Type I error: Rejecting a true null hypothesis
Saying the she does have snow globe when in fact she does not (false alarm)
Type II error: Not rejecting a false null hypothesis
Saying she does not have snow globe when in fact she does (miss)

19. Type I error (false alarm)
Type I or type II error .
Decision made by experimenter
Reject Ho
Do not Reject Ho
True Ho
False Ho
You are right!
Correct decision
You are wrong!
Type I error (false alarm)
Type II error (miss)
Does advertising
affect sales?
Two ways to be correct:
Say it helps when it does
Say it does not help when it doesn’t help
Which is worse?
Two ways to be incorrect:
Say it helps when it doesn’t
Say it does not help when it does
What would null hypothesis be?
This new advertising has no effect on sales
Type I error: Rejecting a true null hypothesis
Saying the advertising would help sales, when it really wouldn’t help people (false alarm)
Type II error: Not rejecting a false null hypothesis
Saying the advertising would not help when in fact it would (miss)

20. What is worse a type I or type II error?.
Decision made by experimenter
Reject Ho
Do not Reject Ho
True Ho
False Ho
You are right!
Correct decision
You are wrong!
Type I error (false alarm)
Type II error (miss)
What if we were looking at a new HIV drug that had
no unpleasant side affects
Two ways to be correct:
Say it helps when it does
Say it does not help when it doesn’t help
Two ways to be incorrect:
Say it helps when it doesn’t
Say it does not help when it does
Which is worse?
What would null hypothesis be?
This new drug has no effect on HIV
Type I error: Rejecting a true null hypothesis
Saying the drug would help people, when it really wouldn’t help people (false alarm)
Type II error: Not rejecting a false null hypothesis
Saying the drug would not help when in fact it would (miss)

21. Which is worse? Type I or type II error.
Which is worse?
Type I or type II error
What if we were looking to see if there is a fire burning in an apartment building full of cute puppies
Two ways to be correct:
Say “fire” when it’s really there
Say “no fire” when there isn’t one
Two ways to be incorrect:
Say “fire” when there’s no fire (false alarm)
Say “no fire” when there is one (miss)
What would null hypothesis be?
No fire is occurring
Type I error: Rejecting a true null hypothesis (false alarm)
Type II error: Not rejecting a false null hypothesis (miss)

22. Which is worse? Type I or type II error.
Which is worse?
Type I or type II error
What if we were looking to see if an individual were guilty of a crime?
Two ways to be correct:
Say they are guilty when they are guilty
Say they are not guilty when they are innocent
Two ways to be incorrect:
Say they are guilty when they are not
Say they are not guilty when they are
What would null hypothesis be?
This person is innocent - there is no crime here
Type I error: Rejecting a true null hypothesis
Saying the person is guilty when they are not (false alarm)
Sending an innocent person to jail (& guilty person to stays free)
Type II error: Not rejecting a false null hypothesis
Saying the person in innocent when they are guilty (miss)
Allowing a guilty person to stay free

23. .
The null hypothesis is typically that something is not present, that there is no effect, that there is no difference between population and sample or between treatment and control.
Null Hypothesis
A measure of sickness
people taking drug people not taking drug
(There are two distributions here,
they are just on top of each other)
(overlapping)
people taking drug
people not taking drug
A measure of sickness
A measure of sickness
Null is FALSE
Null is TRUE
Drug does have effect
Something
going on
Nothing going on
No effect of drug
There is a difference between the groups
There is no difference between the groups

24. Remember: “procedure” vs “TRUTH”.
(There are two distributions here,
they are just on top of each other)
(overlapping)
A measure of sickness
people taking drug
people not taking drug
people taking drug people not taking drug
A measure of sickness
A measure of sickness
Null is FALSE
Null is TRUE
Score
should fall
in this
region
critical stat
critical stat
Score
should fall in
one of these
regions
critical stat
critical stat
Score
should fall in
one of these
regions
Null is FALSE
Null is TRUE
Drug does have effect
Something
going on
No effect of drug
Nothing going on

25. Type I error (false alarm).
Type I or type II error?
Decision made by experimenter
Reject Ho
Do not Reject Ho
True Ho
False Ho
You are right!
Correct decision
You are wrong!
Type I error (false alarm)
Type II error (miss)
Does this airline passenger
have a snow globe?
Two ways to be correct:
Say she does have snow globe when she does have snow globe
Say she doesn’t have any when she doesn’t have any
Two ways to be incorrect:
Say she does when she doesn’t (false alarm)
Say she does not have any when she does (miss)
What would null hypothesis be?
This passenger does not have any snow globe
Type I error: Rejecting a true null hypothesis
Saying the she does have snow globe when in fact she does not (false alarm)
Type II error: Not rejecting a false null hypothesis
Saying she does not have snow globe when in fact she does (miss)

26. Five steps to hypothesis testing
Step 1: Identify the research problem (hypothesis)
Describe the null and alternative hypotheses
Step 2: Decision rule
Alpha level? (α = .05 or .01)?
One or two tailed test?
Balance between Type I versus Type II error
Critical statistic (e.g. z or t or F or r) value?
Step 3: Calculations
Step 4: Make decision whether or not to reject null hypothesis
If observed z (or t) is bigger then critical z (or t) then
reject null
Step 5: Conclusion - tie findings back in to research problem

27. We lose one degree of freedom for every parameter we estimate
Degrees of Freedom
Degrees of Freedom (d.f.) is a parameter based on the sample size that is used to determine the value of the t statistic.
Degrees of freedom tell how many observations are used to calculate s, less the number of intermediate estimates used in the calculation.

28. A note on z scores, and t score: . .
A note on z scores, and t score:
Numerator is always distance between means
(how far away the distributions are or “effect size”)
Denominator is always measure of variability
(how wide or much overlap there is between distributions)
Difference between means
Difference between means
Variability of curve(s) (within group variability)
Variability of curve(s)

29. Thank you!
See you next time!!