1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome
3/14/18

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3. Kristina Lecturer’s desk Attila Sezen Hannah Michelle Projection Booth
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Kristina
Lecturer’s desk
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Hannah
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5. Before next exam (April 6th)
Schedule of readings
Before next exam (April 6th)
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. Extended deadline

7. Labs continue this week
Lab sessions
Everyone will want to be enrolled
in one of the lab sessions
Labs continue this week
Presentations

9. 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%
Critical z separates rare from common scores
Critical z
-1.96
Critical z
1.96
Confidence Interval of 95% Has and alpha of 5% α = .05
95%
Area associated with most extreme scores is called alpha
Critical z
-1.64
Critical z
1.64
Confidence Interval of 90%
Has and alpha of 10%
α = . 10
90%
Area in the tails is called alpha

10. 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

11. Reject the null hypothesis Support for alternative.
Reject the null hypothesis
95% ..
Relative to this distribution I am unusual maybe even an outlier X
95% X
Relative to this distribution I am utterly typical
Support for alternative
hypothesis

12. 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?
Which situation
(alpha and tail) would make it easiest to reject the null?
α = 0.05
Significance level = .05
α = 0.01
Significance level = .01
why?
-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

13. 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?
Which situation
(alpha and tail) would make it easiest to reject the null?
One-tailed
Two-tailed
α = 0.05
Significance level = .05
α = 0.01
Significance level = .01
why?
-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

14. One versus two tail test of significance: Comparing different critical scores (but same alpha level – e.g. alpha = 5%)
1.64
95% 5%
95%
z score = -1.64
reject
null
2.5%
2.5%
95%
How would the critical z change?
Critical scores get smaller with one tailed test 5%
One tail test requires:
1. a unidirectional prediction (predict which group will have larger mean) and
2. that the results actually be in the predicted direction (predicted mean is larger)
So, in a one-tailed test the “region of rejection” refers to results in the predicted direction
If results are NOT in predicted direction, it is impossible to reject the null

15. Two tail tests One tail tests
In a one-tailed test do we use a negative or positive z score?
Doesn’t matter whether the z is positive or negative
If prediction was right, reject the null if observed score is larger than the critical score
Two tail tests
But, if prediction was wrong, it is impossible to reject the null anyway
One tail tests
Which type of test REQUIRES that you make a prediction about which group mean will be larger?
When we go from the regular two-tailed test to a one tail test, what happens to the critical z?
Only the one-tail test does
So, if prediction was right, it is easier to reject the null
The critical score get smaller
But, if prediction was wrong, it is impossible to reject the null
So, if prediction was right, it is easier to reject the null
But, if prediction was wrong, it is impossible to reject the null

16. 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)?
Critical z value?
Step 3: Calculations from collected data – “observed z”
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

17. 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”

18. 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?

19. 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

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

21. 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?

22. 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???!!

23. 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)

24. 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)

25. 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)

26. 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)

27. Another example Type I or type II Error Complete these 8 questions:.
Another example Type I or type II Error Complete these 8 questions:
This person is innocent - there is no crime here
1. The null hypothesis would be ____________________________________
“Reject the null” and be right
Two ways to be correct are:
2. Say ________________ when in fact __________
3. Say ________________ when in fact __________
they are
person is guilty
person is not guilty
they are not
“Do not reject the null” and be right
“Reject the null and be wrong”
Two ways to be in correct are:
4. Say ________________ when in fact __________
5. Say ________________ when in fact __________
they are not
person is guilty
person is not guilty
they are
“Do not reject the null” and be wrong”
6. Which of these statements would be the Type I Error?
Saying the person is guilty when they are not (false alarm)
8. Which is worse?
7. Which of these statements would be the Type II Error?
Saying the person in innocent when they are guilty (miss)

28. 1. The null hypothesis would be __________________
Writing Assignment: Your own example Type I or type II Error Complete these 8 questions:
1. The null hypothesis would be __________________
“Reject the null” and be right
Two ways to be correct are:
2. Say ____ when in fact ____
3. Say ____ when in fact ____
“Do not reject the null” and be right
Two ways to be wrong are:
4. Say ____ when in fact ____
5. Say ____ when in fact ____
“Reject the null and be wrong”
“Do not reject the null” and be wrong”
6. Which of these statements would be the Type I Error?
8. Which is worse?
7. Which of these statements would be the Type II Error?

29. Kristina Lecturer’s desk Attila Sezen Hannah Michelle Projection Booth
Screen
Screen
Kristina
Lecturer’s desk
Row A 15 14
Row A 13 3 2 1
Row A
Attila
Row B 23 20
Row B 19 5 4
3 2 1
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Row C 25 21
Row C 20 6 5 1
Row C
Row D 29 23
Row D 22 8 7 1
Row D
Row E 31 23
Row E 23 9 8 1
Row E
Michelle
Row F 35 26
Row F 25 11 10 1
Row F
Row G 35 26
Row G 25 11 10 1
Row G
Row H 37 28 27 13
Row H 12 1
Row H 41 29 28 14 1
Row J
Row J 13 41 29
Row K 28 14 13 1
Row K
Row L 33 25
Row L 24 10 9 1
Row L
Row M 21 20 19
Row M 18 4 3 2 1
Row M
Row N 15 1
Row P 15 1
Sezen
Hannah
table 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk
Harvill 150
renumbered

30. Thank you!
See you next time!!