1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

2. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
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Harvill 150
renumbered
table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk

3. Schedule of readings Before our fourth and final exam (December 4th)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

4. Over next couple of lectures 11/27/17
Logic of hypothesis testing with Correlations
Interpreting the Correlations and scatterplots
Simple and Multiple Regression
Using correlation for predictions
r versus r2
Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent) Coefficient of correlation is name for “r” Coefficient of determination is name for “r2” (remember it is always positive – no direction info) Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation)
Coefficient of regression will “b” for each variable (like slope)

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

6. Project 4 Please hand in your Project 4 now

7. Homework Assignment

8. A note on doodling

9. Scatterplot displays relationships between two continuous variables
Correlation: Measure of how two variables co-occur and
also can be used for prediction
Range between -1 and +1
The closer to zero the weaker the relationship
and the worse the prediction
Positive or negative

10. by height (centimeters)
Positive correlation: as values on one variable go up, so do values for the other variable
Negative correlation: as values on one variable go up, the values for the other variable go down
Positive
Correlation
Negative
Correlation
Perfect
Correlation
Height of Mothers
by height of Daughters
Brushing teeth
by number cavities
Height (inches)
by height (centimeters)
Height in
Centimeters
inches
Height of Mothers
Brushing Teeth
Height of
Daughters
Number Cavities

11. Height of Daughters (inches)
Height of Mothers (in)
This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches).
Variable name is listed clearly
Description includes:
Both variables
Strength (weak,moderate,strong)
Direction (positive, negative)
Estimated value (actual number)
Both axes have real numbers listed
Both axes and values are labeled
Variable name is listed clearly
Statistically significant p < 0.05
Reject the null hypothesis
Revisit this slide

12. Finding a statistically significant correlation
The result is “statistically significant” if:
the observed correlation is larger than the critical correlation we want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero)
the p value is less than 0.05 (which is our alpha)
we want our “p” to be small!!
we reject the null hypothesis
then we have support for our alternative hypothesis
Revisit this slide

13. Five steps to hypothesis testing
Step 1: Identify the research problem (hypothesis)
Describe the null and alternative hypotheses
For correlation null is that r = 0 (no relationship)
Step 2: Decision rule
Alpha level? (α = .05 or .01)?
Critical statistic (e.g. critical r) value from table?
Degrees of Freedom = (n – 2)
Step 3: Calculations
df = # pairs - 2
Step 4: Make decision whether or not to reject null hypothesis
If observed r is bigger than critical r then reject null
Step 5: Conclusion - tie findings back in to research problem

14. Five steps to hypothesis testing
Problem 1
Is there a relationship between the:
Price
Square Feet
We measured 150 homes recently sold

15. Five steps to hypothesis testing
Step 1: Identify the research problem (hypothesis)
Is there a relationship between the cost of a home
and the size of the home
Describe the null and alternative hypotheses
null is that there is no relationship (r = 0.0)
alternative is that there is a relationship (r ≠ 0.0)
Step 2: Decision rule – find critical r (from table)
Alpha level? (α = .05)
Degrees of Freedom = (n – 2)
150 pairs – 2 = 148 pairs
df = # pairs - 2

16. α = .05 Critical r value from table df = 148 pairs
Critical value r(148) = 0.195
df = # pairs - 2

17. Five steps to hypothesis testing
Step 3: Calculations

18. Five steps to hypothesis testing
Step 3: Calculations

19. Five steps to hypothesis testing
Step 3: Calculations
r =
Critical value r(148) = 0.195
Observed correlation
r(148) =
Step 4: Make decision whether or not to reject null hypothesis
If observed r is bigger than critical r then reject null
Yes we reject the null
0.727 > 0.195

20. These data suggest a strong positive correlation
Conclusion:
Yes we reject the null.
The observed r is bigger than critical r (0.727 > 0.195)
Yes, this is significantly different than zero – something going on
These data suggest a strong positive correlation
between home prices and home size. This correlation
was large enough to reach significance,
r(148) = 0.73; p < 0.05

21. Finding a statistically significant correlation
The result is “statistically significant” if:
the observed correlation is larger than the critical correlation we want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero)
the p value is less than 0.05 (which is our alpha)
we want our “p” to be small!!
we reject the null hypothesis
then we have support for our alternative hypothesis

22. Correlation matrices
Correlation matrix: Table showing correlations for all possible
pairs of variables
Education
Age IQ
Income
0.38*
1.0**
0.41*
0.65** IQ
Age
Education
Income
0.41*
-0.02
0.52*
1.0**
1.0**
0.27*
0.65**
1.0**
Remember,
Correlation = “r”
* p < 0.05
** p < 0.01
Revisit this slide

23. Correlation matrices
Correlation matrix: Table showing correlations for all possible
pairs of variables
Education
Age IQ
Income
0.41*
0.38*
0.65** IQ
Age
Education
Income
-0.02
0.52*
0.27*
* p < 0.05
** p < 0.01

24. Correlation matrices Variable names Make up any name that
means something to you
VARX = “Variable X”
VARY = “Variable Y”
VARZ = “Variable Z”
Correlation of X with X
Correlation of Y with Y
Correlation of Z with Z

25. Correlation matrices Variable names Make up any name that
Does this correlation reach statistical
significance?
Variable names
Make up any name that
means something to you
VARX = “Variable X”
VARY = “Variable Y”
VARZ = “Variable Z”
Correlation of X with Y
Correlation of X with Y
p value for correlation of
X with Y
p value for correlation of X with Y

26. Correlation matrices Variable names Make up any name that
Does this correlation reach statistical
significance?
Variable names
Make up any name that
means something to you
VARX = “Variable X”
VARY = “Variable Y”
VARZ = “Variable Z”
Correlation of X with Z
Correlation of X with Z
p value for correlation of
X with Z
p value for correlation of X with Z

27. Correlation matrices Variable names Make up any name that
Does this correlation reach statistical
significance?
Variable names
Make up any name that
means something to you
VARX = “Variable X”
VARY = “Variable Y”
VARZ = “Variable Z”
Correlation of Y with Z
Correlation of Y with Z
p value for correlation of
Y with Z
p value for correlation of
Y with Z

28. Correlation matrices
What do we care about?

29. Correlation matrices What do we care about?
We measured the following characteristics of 150 homes
recently sold
Price
Square Feet
Number of Bathrooms
Lot Size
Median Income of Buyers

30. Correlation matrices
What do we care about?

31. Correlation matrices
What do we care about?

32. Correlation matrices
What do we care about?

33. α = .05 Critical r value from table df = 148 pairs
Critical value r(148) = 0.195
df = # pairs - 2

34. Correlation matrices What do we care about?
Critical value from table r(148) = 0.195

35. 3
0.878

37. 3
0.878
Yes
Yes
The relationship between the hours worked
and weekly pay is a strong positive correlation.
This correlation is significant, r(3) = 0.92; p < 0.05

38. 3
-0.73 3
0.878 No No
The relationship between wait time and number of
operators working is negative and strong, but not
reliable enough to reach significance.
This correlation is not significant, r(3) = -0.73; n.s.

39. We are measuring 9 students

41. Critical r = 0.666
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
Do not reject null
r is not significant
Do not reject null
r is not significant
Reject Null
r is significant
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

42. 4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

43. 4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

44. 4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
GPA
GPA
GPA
High School GPA
SAT (Verbal)
SAT (Mathematical)
r(7) = 0.50
r(7) =
r(7) =
r(7) =
r(7) =
r(7) =

45. Thank you!
See you next time!!