1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
March 13

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The
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Sheets

3. Before next exam (April 5th)
Schedule of readings
Before next exam (April 5th)
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. Labs continue this week
Lab sessions
Everyone will want to be enrolled
in one of the lab sessions
Labs continue this week

7. 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

8. 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
Review

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 = -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
Review

10. 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
Review

11. 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
Review

12. 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
Review

13. 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
Review

14. 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
Review

15. 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

16. 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
Review

17. Two tail tests One tail tests Review
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
Review

18. Whether or not feed had corn oil
No, feed had no corn oil
Yes, the feed had corn oil
Weight of eggs
There is no difference in the weight of eggs based on corn oil in food
There is a difference in the weight of eggs based on corn oil in food
This is a two-tailed test (no prediction was made)
true experiment
between
nominal
ratio
1.96

19. Yes
Yes
Yes
Yes
2.58 No No No No
The weights of eggs for chickens who received the corn oil was 63
grams, while the weights of the eggs for chickens who did not receive
the corn oil was 60 grams. A z-test found this to be a significant
difference z = 2.42; p < 0.05

20. Whether or not offered incentive
Was offered incentive
Was not offered incentive
Grade point average
There is no difference in GPA based on level of incentive
There is a difference in GPA based on level of incentive
This is a two-tailed test (no prediction was made)
true experiment
between
nominal
interval
1.96

21. Yes Yes Yes Yes 2.58 Yes Yes Yes Yes
The average GPA was 2.3 for students who were offered an incentive and was
2.1 for students who were not offered an incentive. A z-test was completed
and we found this to be a significant difference z = 3.64; p < 0.05

22. Whether or not video included sound
Video with no sound
Video with sound
Number of items correctly recalled
There is no difference in the number of items recalled
There is a difference in the number of items recalled
This is a two-tailed test (no prediction was made)
true experiment
between
nominal
ratio
1.96

23. No No No No
2.58 No No No No
The average number of items recalled was 3.7 for the students who
watched the ads with no sound, and was 3.3 for students who watched
video with sound. A z-test was completed and we found no significant
difference z = 1.17; n.s.

24. Location of air conditioner plant
Japan
United States
Turnover rate
There is no difference in the turnover rates between Japan and USA
There is no difference in the turnover rates between Japan and USA
This is a two-tailed test (no prediction was made)
quasi
between
nominal
ratio
1.96

25. Yes Yes Yes Yes 2.58 Yes Yes Yes Yes
The average turnover rate in the Japanese plants is 3.12 while the average
turnover rated in the American plants is A z-test showed a significant
difference, z = -4.46; p < 0.05

26. Thank you!
See you next time!!