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 10/26/16
Introduction to Hypothesis Testing
Type I versus Type II Errors

4. 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

5. No Homework Due
Friday 10/28/16

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

8. 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%

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. 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

11. .. 95% 95% X X Reject the null hypothesis
Relative to this distribution I am unusual maybe even an outlier X
95% X
Relative to this distribution I am utterly typical
Do not reject the
null hypothesis

12. 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

13. 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

14. 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?
why?

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. Setting our decision threshold
Area in the tails is alpha
99%
α = .01
95%
α = .05
90%
α = .10
Setting our decision threshold
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

22. How would the critical z change?
One versus two tail test of significance: Comparing different critical scores (but same alpha level – e.g. alpha = 5%)
One versus two tailed test of significance
z score = 1.64
95%
95% 5%
2.5%
2.5%
How would the critical z change?
Pros and cons…

23. One versus two tail test of significance 5% versus 1% alpha levels
How would the critical z change?
One-tailed
Two-tailed
α = 0.05
Significance level = .05
α = 0.01
Significance level = .01 1% 5%
2.5%
.5%
.5%
2.5%
-1.64 or
+1.64
-1.96 or
+1.96
-2.33 or
+2.33
-2.58 or
+2.58

24. One versus two tail test of significance 5% versus 1% alpha levels
What if our observed z = 2.0?
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
Do not Reject the null
Do not Reject the null

25. One versus two tail test of significance 5% versus 1% alpha levels
What if our observed z = 1.75?
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
Do not
Reject the null
Reject the null
-2.33 or
+2.33
-2.58 or
+2.58
Do not Reject the null
Do not Reject the null

26. 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

27. Thank you!
See you next time!!