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 20

2. Even if you have not yet registered your clicker you can still participate
The
Green
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

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

8. These would be helpful to know by heart – please memorize
Standard deviation and Variance
For Sample and Population
Pop Quiz
Question 1
These would be helpful to know by heart – please memorize
these formula

9. Pop Quiz
Question 1
Standard deviation and Variance
For Sample and Population
Question 2:
Please draw two curves and include critical values for one-tailed test versus a two-tailed test
Question 3:
When we move from a two-tailed test to a one-tailed test the critical z score gets _____ (bigger or smaller?)

10. Pop Quiz
Question 4:
If we use a one-tailed test and the prediction is correct, then it is ____ (easier, harder or impossible) to reject the null
Question 5:
If we use a one-tailed test and the prediction is incorrect, then it is ____ (easier, harder or impossible) to reject the null
Question 6:
When do we use a t-test and when do we use a z-test?
        (Be sure to write out the formulae)

11. Standard deviation and Variance For Sample and Population
Pop Quiz
Question 1
Standard deviation and Variance
For Sample and Population
Question 2:
Please draw two curves and include critical values for one-tailed test versus a two-tailed test
Question 3:
When we move from a two-tailed test to a one-tailed test the critical z score gets _____ (bigger or smaller?)
1.64
Critical value gets smaller

12. When do we use a t-test and when do we use a z-test?
Pop Quiz
easier to reject
Question 4:
If we use a one-tailed test and the prediction is correct, then it is ____ (easier, harder or impossible) to reject the null
Question 5:
If we use a one-tailed test and the prediction is incorrect, then it is ____ (easier, harder or impossible) to reject the null
Question 6:
When do we use a t-test and when do we use a z-test?
        (Be sure to write out the formulae)
impossible to reject
Use the t-test when you don’t know the standard deviation of the population, and therefore have to estimate it using the standard deviation of the sample
Population versus sample standard deviation
Population versus sample standard deviation

13. 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)

14. 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

15. 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)

16. 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)

17. 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)

18. Hypothesis testing: A review.
Difference between means
Hypothesis testing: A review
Variability of curve(s)
If the observed stat is more extreme than the critical stat in the distribution (curve):
then it is so rare, (taking into account the variability) we conclude it must be from some other distribution
decision considers effect size and variability
then we reject the null hypothesis – we have a significant result
then we have support for our alternative hypothesis
p < (p < α)
If the observed stat is NOT more extreme than the critical stat in the distribution (curve):
then we know it is a common score (either because the effect size is too small or because the variability is to big) and is likely to be part of this null distribution,
we conclude it must be from this distribution
decision considers effect size and variability – could be overly variable
then we do not reject the null hypothesis
then we do not have support for our alternative hypothesis
p not less than (p not less than α) p is n.s.
Difference between means
critical statistic
critical statistic
Variability of curve(s)
(within group variability)
Variability of curve(s)
Review

19. Let’s try one
The central limit theorem states that, for any distribution, as n gets larger, the variability of the sampling distribution of the sample mean _______.
a. becomes larger
b. becomes smaller
c. is closer to a normal distribution
d. is closer to the standard deviation

20. Let’s try one
Mark and Melvin work inside Intel's semiconductor fabrication plants.
In these “clean rooms” the workers wear "bunny suits". Mark and Melvin are each assigned a different team to measure the workers. Both teams measure the same sample of 100 workers and determine the very specific dimensions of their “bunny suits”. Mark spends a week training his team of data collectors, providing identical tape measures and creating a strict protocol for measuring the workers. Melvin however, simply sends out his team to measure the workers, with little instruction, and consequently Melvin’s workers make many more mistakes in recording the data, and the data are more variable. How would you explain the difference in variability between the two groups? The difference in variability between these two group is due to:
a. the difference in sample size, because as sample size increases variability decreases
b. differences in the population, because if the population is more variable, the sample will be more variable
c. differences in the amount of random error in the two samples, because as random error increases so will variability
d. all of the above are reasons why Melvin’s data are more variable than Mark’s

21. Let’s try one
Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?
a. the means are the same, so the t-test would yield the same results.
b. the means are the same, but the variability would increase so
it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so
it would be easier to reject the null hypothesis.
correct

22. Let’s try one
Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?
a. the variance would get bigger and the confidence interval would get wider
b. the variance would get bigger and the confidence interval would get narrower
c. the variance would get smaller and the confidence interval would get wider
d. the variance would get smaller and the confidence interval would get narrower

23. Let’s try one: Just for fun
Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?
a. the means are the same, so the t-test would yield the same results.
b. the means are the same, but the variability would increase so
it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so
it would be easier to reject the null hypothesis.
correct

24. 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
(two-tailed α = .05) 1 1
6 – 5 =
= .25
= 4.0 4 √ 16
.25
-1.96
1.96
z = 4.0

25. Because observed z of 4 is still bigger than critical z of 1.64
Because the observed z (4.0 ) is bigger than critical z (1.96)
These three will always match
Yes
Probability of Type I error is always equal to alpha
Yes
Yes
0.05
1.64 No
Because observed z of 4 is still bigger than critical z of 1.64
2.58 No
Because observed z of 4 is still bigger than critical z of 2.58
there is a difference
there is not
there is no difference
there is
Lecture ended here
1.96
2.58

26. Two tailed test (α = .05) n – 1  16 – 1 = 15 Critical t(15) = 2.131
-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

28. Two tailed test (α = .05) n – 1  16 – 1 = 15 Critical t(15) = 2.131
-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

29. These three will always match Yes Yes
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

31. Yes
Yes
Yes
.05
1.753 No
Because observed t(15) = 2.67 is still bigger than critical t(15) of 1.753
2.947

33. These three will always match
Yes
Yes
Yes
.05
1.753 No
Because observed t(15) = 2.67 is still bigger than critical t(15) of 1.753
2.947
Yes
Because observed t(15) = is not bigger than critical t(15) of 2.947 No
These three will always match No No
consultant did improve morale when in fact she did not improve morale
consultant did not improve morale when in fact she did improve morale
2.131
2.947

34. The average weight of bags of potatoes from this particular plant
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

35. The average job-satisfaction score was 89 for the employees who went
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

36. Thank you!
See you next time!!