1. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

3. By the end of lecture today 10/30/15
Logic of hypothesis testing
Steps for hypothesis testing
Levels of significance (Levels of alpha)
what does p < 0.05 mean?
what does p < 0.01 mean?
Two-sample t-tests

4. Before next exam (November 20th)
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. Homework Assignment
No Homework due
Monday, November 2nd

6. Confidence Interval of 95% Has and alpha of 5% α = .05
Critical t
close to -2.58
Confidence Interval of 99%
Has and alpha of 1%
α = .01
99%
Critical t
close to -2.58
Area outside confidence interval is alpha
Confidence Interval of 95% Has and alpha of 5% α = .05
95%
Critical t
close to -1.96
Critical t
close to 1.96
Area in the tails is called alpha
Confidence Interval of 90%
Has and alpha of 10%
α = . 10
Critical t
close to -1.64
90%
Critical t
close to 1.64
Area associated with most extreme scores is called alpha

7. Review of the homework assignment

8. Melvin
Melvin
Mark
Difference not due sample size because both samples same size
Difference not due population variability because same population
Yes! Difference is due to sloppiness and random error in Melvin’s sample
Melvin

9. 6 – 5 = 4.0 .25 Two tailed test 1.96 (α = .05) 1 1 = = .25 16 4 √ 4.0
z- score : because we know the population standard deviation
Ho: µ = 5
Bags of potatoes from that plant are not different from other plants
Ha: µ ≠ 5
Bags of potatoes from that plant are different from other plants
Two tailed test
1.96
(α = .05) 1 1 =
= .25
6 – 5 16 4 √
= 4.0
.25
4.0
-1.96
1.96

10. Because the observed z (4.0 ) is bigger than critical z (1.96)
These three will always match
Yes
Yes
Probability of Type I error is always equal to alpha
Yes
.05
1.64 No
Because observed z (4.0) is still bigger than critical z (1.64)
2.58 No
Because observed z (4.0) is still bigger than critical z(2.58)
there is a difference
there is not
there is no difference
there is
1.96
2.58

11. 89 - 85 Two tailed test (α = .05) n – 1 =16 – 1 = 15
-2.13
2.13
t- score : because we don’t know the population standard deviation
Two tailed test
(α = .05)
n – 1 =16 – 1 = 15
Critical t(15) = 2.131
2.667 6 √ 16

12. Because the observed z (2.67) is bigger than critical z (2.13)
These three will always match
Yes
Yes
Probability of Type I error is always equal to alpha
Yes
.05
1.753 No
Because observed t (2.67) is still bigger than critical t (1.753)
2.947
Yes
Because observed t (2.67) is not bigger than critical t(2.947) No
These three will always match No No
consultant did improve morale
she did not
consultant did not improve morale
she did
2.131
2.947

13. Value of observed statistic
Finish with statistical summary z = 4.0; p < 0.05
Or if it *were not* significant:
z = 1.2 ; n.s.
Start summary with two means (based on DV) for two levels of the IV
Describe type of test (z-test versus t-test) with brief overview of results
n.s. = “not significant”
p<0.05 = “significant”
The average weight of bags of potatoes from this particular plant
is 6 pounds, while the average weight for population is 5 pounds.
A z-test was completed and this difference was found to be
statistically significant. We should fix the plant. (z = 4.0; p<0.05)
Value of observed statistic

14. Value of observed statistic
Finish with statistical summary t(15) = 2.67; p < 0.05
Or if it *were not* significant:
t(15) = 1.07; n.s.
Start summary with two means (based on DV) for two levels of the IV
Describe type of test (z-test versus t-test) with brief overview of results
n.s. = “not significant”
p<0.05 = “significant”
The average job-satisfaction score was 89 for the employees who went
On the retreat, while the average score for population is 85. A t-test
was completed and this difference was found to be statistically
significant. We should hire the consultant. (t(15) = 2.67; p<0.05)
Value of observed statistic df

15. Hypothesis testing Is this a single sample or two sample test?
Is it a z or a t test or an ANOVA?
Hypothesis testing
Is it a one-tail test or a two tail test?
Step 1: Identify the research problem
Did the sheriff keep her promise to change response times from the previous average of 30 minutes?
Step 2: Describe the null and alternative hypotheses
Ho: The response times are not changed
H1: The response times did change
As the new chief of police, I am going to change response times for traffic accidents. Before I started the average response time was 30 minutes 15

16. Hypothesis testing Two-tailed test n = 10 df = 9 alpha = 0.05
Gather the data:
We measured the time for police to respond to 10 accidents
Two-tailed test
One or two tailed test?
What is our sample size
What is size of our degrees of freedom?
What is our alpha
What is our critical t value?
n = 10 (df = 9)
Alpha = .05
Decision rule: critical t = 1.83
n = 10
df = 9
alpha = 0.05 16

17. Hypothesis testing Two-tailed test Alpha of 0.05
Gather the data:
We measured the time for police to respond to 10 accidents
One or two tailed test?
What is our sample size
What is size of our degrees of freedom?
What is our alpha
What is our critical t value?
Decision rule: critical t = 2.262
Two-tailed test
Alpha of 0.05
Critical t (9) = 2.262 17

18. Average time for response before 30 minutes
Step 3: Calculations:
Average time for response before 30 minutes
Average time for response after 24 minutes
Observed t =
Step 4: Make decision whether or not to reject null hypothesis
Observed t =
Critical t = 2.262
-2.71 is farther out on the curve than 2.262
so, we do not reject the null hypothesis
Step 5: Conclusion: There appears to be a significant difference
between the sheriff’s times and 30 minutes 18

19. Hypothesis testing:
Did the sheriff keep her promise to reduce response times to less than 30 minutes?
Start summary with two means (based on DV) for two levels of the IV
notice we are comparing a sample mean with a population mean:
single sample t-test
Finish with statistical summary t(9) = -5.71; p < 0.05
Describe type of test (t-test versus anova) with brief overview of results
Or if it had been different results that *were not* significant:
t(9) = -1.71; ns
The mean response time for following the sheriff’s new plan was
24 minutes, while the mean response time prior to the new plan
was 30 minutes. A t-test was completed and there appears to be
a significant difference in the response time following the
implementation of the new plan t(9) = -2.71; p < 0.05
Type of test with degrees of freedom
n.s. = “not significant”
p<0.05 = “significant”
n.s. = “not significant”
p<0.05 = “significant”
Value of observed statistic 19

20. 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)

21. A note on variability versus effect size Difference between means.
A note on variability
versus effect size
Difference between means
Difference between means
Variability of curve(s)
Variability of curve(s) (within group variability)

22. A note on variability versus effect size Difference between means.
A note on variability
versus effect size
Difference between means
Difference between means .
Variability of curve(s)
Variability of curve(s) (within group variability)

23. Effect size is considered relative to variability of distributions.
Effect size is considered relative to variability of distributions
1. Larger variance harder to find significant difference
Treatment
Effect x
Treatment
Effect
2. Smaller variance easier to find significant difference x

24. Effect size is considered relative to variability of distributions.
Effect size is considered relative to variability of distributions
Treatment
Effect x
Difference between means
Treatment
Effect x
Variability of curve(s) (within group variability)

25. Thank you!
See you next time!!