1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome

2. A note on doodling

4. Presentation Skills

5. Presentation Skills

6. Presentation Skills

7. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Project 2
Presentations

8. By the end of lecture today 3/6/17
Introduction to hypothesis testing
Interpreting
Alpha levels
p values

9. Before next exam (April 7th)
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

10. Homework
On class website:
Please print and complete homework worksheet #17

11. No class on Friday Have a safe and happy spring break .
Please note we DO have class on Wednesday 3/8

12. Some Mean Some Variability
Construct a 95 percent confidence
interval around the mean ?
95% ?
raw score = mean ± (z score)(s.d.)
Some Mean Some Variability
We used this one when finding raw scores
associated with an area under the curve.
We had all population info. Not really a
“confidence interval” because we know the mean of the population,
so there is nothing to estimate or be “confident about”.
Hint always draw a picture!
We used this one when finding raw scores associated with an
area under the curve. We used this to provide an interval within
which we believe the mean falls. We have some level of confidence about our guess. We know the population standard deviation.
raw score = mean ± (z score)(s.e.m.)

13. 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 outside confidence interval is alpha
Critical z
-1.96
Critical z
1.96
Confidence Interval of 95% Has and alpha of 5% α = .05
95%
Area in the tails is called alpha
Critical z
-1.64
Critical z
1.64
Confidence Interval of 90%
Has and alpha of 10%
α = . 10
90%
Area associated with most extreme scores is called alpha

14. 99% 95% 90% Moving from descriptive stats into inferential stats….
Area outside confidence interval is alpha
Area outside confidence interval is alpha
Moving from descriptive stats
into inferential stats….
99%
Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there
95%
Measurements that occur outside this middle ranges are suspicious, may be an error
or belong elsewhere
90%

15. How do we know if something is going on
How do we know if something is going on? How rare/weird is rare/weird enough?
Every day examples about when is weird, weird enough to
think something is going on?
Handing in blue versus white test forms
Psychic friend – guesses 999 out of 1000 coin tosses right
Cancer clusters – how many cases before investigation
Weight gain treatment – one group gained an average of pound more than other group…what if 10?

16. Why do we care about the z scores that define the middle 95% of the curve? Inferential Statistics
Hypothesis testing with z scores allows us to make inferences
about whether the sample mean is consistent with the known
population mean.
Is the mean of my observed sample consistent with the
known population mean or did it come from some other
distribution?

17. Why do we care about the z scores that define the middle 95% of the curve?
If the z score falls outside the middle
95% of the curve, it must be from
some other distribution
Main assumption: We assume that
weird, or unusual or rare things
don’t happen
If a score falls out into the 5% range we conclude that it “must be”
actually a common score but from some other distribution
That’s why we care about the z scores that define the middle
95% of the curve

18. I’m not an outlier I just haven’t found my distribution yet.
Main assumption: We assume that weird, or unusual or rare things don’t happen
I’m not an outlier I just haven’t found my distribution yet
If a score falls out into the tails (low probability) we
conclude that it “must be” a common score from some
other distribution

19. 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

20. Rejecting the null hypothesis.
null
notnull
big z score x x
If the observed z falls beyond the critical z in the distribution (curve):
then it is so rare, we conclude it must be from some other distribution
then we reject the null hypothesis
then we have support for our alternative hypothesis
Alternative Hypothesis
If the observed z falls within the critical z in the distribution (curve):
then we know it is a common score and is likely to be part of this distribution,
we conclude it must be from this distribution
then we do not reject the null hypothesis
then we do not have support for our alternative .
null x x
small z score

21. Rejecting the null hypothesis
If the observed z falls beyond the critical z in the distribution (curve):
then it is so rare, we conclude it must be from some other distribution
then we reject the null hypothesis
then we have support for our alternative hypothesis
If the observed z falls within the critical z in the distribution (curve):
then we know it is a common score and is likely to be part of this distribution,
we conclude it must be from this distribution
then we do not reject the null hypothesis
then we do not have support for our alternative hypothesis

22. How do we know how rare is rare enough?
Area in the tails is alpha
99%
α = .01
95%
α = .05
90%
α = .10
How do we know how rare is rare enough?
Level of significance is called alpha (α)
The degree of rarity required for an observed outcome
to be “weird enough” to reject the null hypothesis
Which alpha level would be associated with most “weird” or rare scores?
Critical z: A z score that separates common from rare outcomes
and hence dictates whether the null hypothesis should
be retained (same logic will hold for “critical t”)
If the observed z falls beyond the critical z in the distribution
(curve) then it is so rare, we conclude it must be from some
other distribution

23. Rejecting the null hypothesis
The result is “statistically significant” if:
the observed statistic is larger than the critical statistic (which can be a ‘z” or “t” or “r” or “F” or x2)
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

24. 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%

25. 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

26. 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 = 1.5?
How would the critical z change?
α = 0.05
Significance level = .05
α = 0.01
Significance level = .01
-1.96 or
+1.96
Do Not
Reject the null
Not a Significant difference
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

27. 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 = -3.9?
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
p < 0.01
Yes, Significant difference
Reject the null

28. 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 = -2.52?
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

29. 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

30. Thank you!
See you next time!!